TSTP Solution File: LCL501+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL501+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 04:56:32 EDT 2022
% Result : Timeout 291.84s 187.57s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL501+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 21:18:52 EDT 2022
% 0.12/0.33 % 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.
% 291.84/187.57 % SZS status Theorem
% 291.84/187.57 % SZS output start Proof
% 291.84/187.57 tff(is_a_theorem_type, type, (
% 291.84/187.57 is_a_theorem: $i > $o)).
% 291.84/187.57 tff(implies_type, type, (
% 291.84/187.57 implies: ( $i * $i ) > $i)).
% 291.84/187.57 tff(or_type, type, (
% 291.84/187.57 or: ( $i * $i ) > $i)).
% 291.84/187.57 tff(not_type, type, (
% 291.84/187.57 not: $i > $i)).
% 291.84/187.57 tff(tptp_fun_P_2_type, type, (
% 291.84/187.57 tptp_fun_P_2: $i)).
% 291.84/187.57 tff(tptp_fun_R_0_type, type, (
% 291.84/187.57 tptp_fun_R_0: $i)).
% 291.84/187.57 tff(tptp_fun_Q_1_type, type, (
% 291.84/187.57 tptp_fun_Q_1: $i)).
% 291.84/187.57 tff(and_type, type, (
% 291.84/187.57 and: ( $i * $i ) > $i)).
% 291.84/187.57 tff(equiv_type, type, (
% 291.84/187.57 equiv: ( $i * $i ) > $i)).
% 291.84/187.57 tff(op_implies_or_type, type, (
% 291.84/187.57 op_implies_or: $o)).
% 291.84/187.57 tff(op_implies_and_type, type, (
% 291.84/187.57 op_implies_and: $o)).
% 291.84/187.57 tff(op_or_type, type, (
% 291.84/187.57 op_or: $o)).
% 291.84/187.57 tff(op_and_type, type, (
% 291.84/187.57 op_and: $o)).
% 291.84/187.57 tff(op_equiv_type, type, (
% 291.84/187.57 op_equiv: $o)).
% 291.84/187.57 tff(r3_type, type, (
% 291.84/187.57 r3: $o)).
% 291.84/187.57 tff(r4_type, type, (
% 291.84/187.57 r4: $o)).
% 291.84/187.57 tff(modus_ponens_type, type, (
% 291.84/187.57 modus_ponens: $o)).
% 291.84/187.57 tff(substitution_of_equivalents_type, type, (
% 291.84/187.57 substitution_of_equivalents: $o)).
% 291.84/187.57 tff(kn3_type, type, (
% 291.84/187.57 kn3: $o)).
% 291.84/187.57 tff(r5_type, type, (
% 291.84/187.57 r5: $o)).
% 291.85/187.57 tff(1,plain,
% 291.85/187.57 (^[X: $i, Y: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 291.85/187.57 inference(bind,[status(th)],[])).
% 291.85/187.57 tff(2,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 291.85/187.57 inference(quant_intro,[status(thm)],[1])).
% 291.85/187.57 tff(3,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(4,plain,
% 291.85/187.57 (($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(5,plain,
% 291.85/187.57 ((~$true) <=> $false),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(6,axiom,(op_implies_or), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_implies_or')).
% 291.85/187.57 tff(7,plain,
% 291.85/187.57 (op_implies_or <=> $true),
% 291.85/187.57 inference(iff_true,[status(thm)],[6])).
% 291.85/187.57 tff(8,plain,
% 291.85/187.57 ((~op_implies_or) <=> (~$true)),
% 291.85/187.57 inference(monotonicity,[status(thm)],[7])).
% 291.85/187.57 tff(9,plain,
% 291.85/187.57 ((~op_implies_or) <=> $false),
% 291.85/187.57 inference(transitivity,[status(thm)],[8, 5])).
% 291.85/187.57 tff(10,plain,
% 291.85/187.57 (((~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)))),
% 291.85/187.57 inference(monotonicity,[status(thm)],[9])).
% 291.85/187.57 tff(11,plain,
% 291.85/187.57 (((~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))),
% 291.85/187.57 inference(transitivity,[status(thm)],[10, 4])).
% 291.85/187.57 tff(12,plain,
% 291.85/187.57 (((~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)))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(13,plain,
% 291.85/187.57 ((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)))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 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')).
% 291.85/187.57 tff(15,plain,
% 291.85/187.57 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[14, 13])).
% 291.85/187.57 tff(16,plain,
% 291.85/187.57 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[15, 12])).
% 291.85/187.57 tff(17,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[16, 11])).
% 291.85/187.57 tff(18,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[17, 3])).
% 291.85/187.57 tff(19,plain,(
% 291.85/187.57 ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 291.85/187.57 inference(skolemize,[status(sab)],[18])).
% 291.85/187.57 tff(20,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[19, 2])).
% 291.85/187.57 tff(21,plain,
% 291.85/187.57 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(implies(P!2, Q!1))), not(not(not(and(R!0, P!2))))) = or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.57 inference(quant_inst,[status(thm)],[])).
% 291.85/187.57 tff(22,plain,
% 291.85/187.57 (implies(not(not(implies(P!2, Q!1))), not(not(not(and(R!0, P!2))))) = or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))),
% 291.85/187.57 inference(unit_resolution,[status(thm)],[21, 20])).
% 291.85/187.57 tff(23,plain,
% 291.85/187.57 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 291.85/187.57 inference(bind,[status(th)],[])).
% 291.85/187.57 tff(24,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 291.85/187.57 inference(quant_intro,[status(thm)],[23])).
% 291.85/187.57 tff(25,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(26,plain,
% 291.85/187.57 (($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))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(27,axiom,(op_implies_and), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rosser_op_implies_and')).
% 291.85/187.57 tff(28,plain,
% 291.85/187.57 (op_implies_and <=> $true),
% 291.85/187.57 inference(iff_true,[status(thm)],[27])).
% 291.85/187.57 tff(29,plain,
% 291.85/187.57 ((~op_implies_and) <=> (~$true)),
% 291.85/187.57 inference(monotonicity,[status(thm)],[28])).
% 291.85/187.57 tff(30,plain,
% 291.85/187.57 ((~op_implies_and) <=> $false),
% 291.85/187.57 inference(transitivity,[status(thm)],[29, 5])).
% 291.85/187.57 tff(31,plain,
% 291.85/187.57 (((~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)))))),
% 291.85/187.57 inference(monotonicity,[status(thm)],[30])).
% 291.85/187.57 tff(32,plain,
% 291.85/187.57 (((~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))))),
% 291.85/187.57 inference(transitivity,[status(thm)],[31, 26])).
% 291.85/187.57 tff(33,plain,
% 291.85/187.57 (((~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)))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(34,plain,
% 291.85/187.57 ((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)))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(35,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')).
% 291.85/187.57 tff(36,plain,
% 291.85/187.57 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[35, 34])).
% 291.85/187.57 tff(37,plain,
% 291.85/187.57 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[36, 33])).
% 291.85/187.57 tff(38,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[37, 32])).
% 291.85/187.57 tff(39,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[38, 25])).
% 291.85/187.57 tff(40,plain,(
% 291.85/187.57 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 291.85/187.57 inference(skolemize,[status(sab)],[39])).
% 291.85/187.57 tff(41,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[40, 24])).
% 291.85/187.57 tff(42,plain,
% 291.85/187.57 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(implies(P!2, Q!1))), not(not(not(and(R!0, P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(not(not(and(R!0, P!2))))))))),
% 291.85/187.57 inference(quant_inst,[status(thm)],[])).
% 291.85/187.57 tff(43,plain,
% 291.85/187.57 (implies(not(not(implies(P!2, Q!1))), not(not(not(and(R!0, P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(not(not(and(R!0, P!2)))))))),
% 291.85/187.57 inference(unit_resolution,[status(thm)],[42, 41])).
% 291.85/187.57 tff(44,plain,
% 291.85/187.57 (not(and(not(not(implies(P!2, Q!1))), not(not(not(not(and(R!0, P!2))))))) = implies(not(not(implies(P!2, Q!1))), not(not(not(and(R!0, P!2)))))),
% 291.85/187.57 inference(symmetry,[status(thm)],[43])).
% 291.85/187.57 tff(45,plain,
% 291.85/187.57 (^[X: $i, Y: $i] : refl((or(X, Y) = not(and(not(X), not(Y)))) <=> (or(X, Y) = not(and(not(X), not(Y)))))),
% 291.85/187.57 inference(bind,[status(th)],[])).
% 291.85/187.57 tff(46,plain,
% 291.85/187.57 (![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))))),
% 291.85/187.57 inference(quant_intro,[status(thm)],[45])).
% 291.85/187.57 tff(47,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(48,plain,
% 291.85/187.57 (($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))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(49,axiom,(op_or), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rosser_op_or')).
% 291.85/187.57 tff(50,plain,
% 291.85/187.57 (op_or <=> $true),
% 291.85/187.57 inference(iff_true,[status(thm)],[49])).
% 291.85/187.57 tff(51,plain,
% 291.85/187.57 ((~op_or) <=> (~$true)),
% 291.85/187.57 inference(monotonicity,[status(thm)],[50])).
% 291.85/187.57 tff(52,plain,
% 291.85/187.57 ((~op_or) <=> $false),
% 291.85/187.57 inference(transitivity,[status(thm)],[51, 5])).
% 291.85/187.57 tff(53,plain,
% 291.85/187.57 (((~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)))))),
% 291.85/187.57 inference(monotonicity,[status(thm)],[52])).
% 291.85/187.57 tff(54,plain,
% 291.85/187.57 (((~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))))),
% 291.85/187.57 inference(transitivity,[status(thm)],[53, 48])).
% 291.85/187.57 tff(55,plain,
% 291.85/187.57 (((~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)))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(56,plain,
% 291.85/187.57 ((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)))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(57,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')).
% 291.85/187.57 tff(58,plain,
% 291.85/187.57 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[57, 56])).
% 291.85/187.57 tff(59,plain,
% 291.85/187.57 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[58, 55])).
% 291.85/187.57 tff(60,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[59, 54])).
% 291.85/187.57 tff(61,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[60, 47])).
% 291.85/187.57 tff(62,plain,(
% 291.85/187.57 ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 291.85/187.57 inference(skolemize,[status(sab)],[61])).
% 291.85/187.57 tff(63,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 291.85/187.57 inference(modus_ponens,[status(thm)],[62, 46])).
% 291.85/187.57 tff(64,plain,
% 291.85/187.57 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(not(not(and(R!0, P!2))))))))),
% 291.85/187.57 inference(quant_inst,[status(thm)],[])).
% 291.85/187.57 tff(65,plain,
% 291.85/187.57 (or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(not(not(and(R!0, P!2)))))))),
% 291.85/187.57 inference(unit_resolution,[status(thm)],[64, 63])).
% 291.85/187.57 tff(66,plain,
% 291.85/187.57 (or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2))))) = or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))),
% 291.85/187.57 inference(transitivity,[status(thm)],[65, 44, 22])).
% 291.85/187.57 tff(67,plain,
% 291.85/187.57 (or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))) = or(not(not(and(Q!1, R!0))), or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.57 inference(monotonicity,[status(thm)],[66])).
% 291.85/187.57 tff(68,plain,
% 291.85/187.57 (or(not(not(and(Q!1, R!0))), or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))) = or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2))))))),
% 291.85/187.57 inference(symmetry,[status(thm)],[67])).
% 291.85/187.57 tff(69,plain,
% 291.85/187.57 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(P!2, Q!1) = or(not(P!2), Q!1))),
% 291.85/187.57 inference(quant_inst,[status(thm)],[])).
% 291.85/187.57 tff(70,plain,
% 291.85/187.57 (implies(P!2, Q!1) = or(not(P!2), Q!1)),
% 291.85/187.57 inference(unit_resolution,[status(thm)],[69, 20])).
% 291.85/187.57 tff(71,plain,
% 291.85/187.57 (or(not(P!2), Q!1) = implies(P!2, Q!1)),
% 291.85/187.57 inference(symmetry,[status(thm)],[70])).
% 291.85/187.57 tff(72,plain,
% 291.85/187.57 (not(or(not(P!2), Q!1)) = not(implies(P!2, Q!1))),
% 291.85/187.57 inference(monotonicity,[status(thm)],[71])).
% 291.85/187.57 tff(73,plain,
% 291.85/187.57 (or(not(or(not(P!2), Q!1)), not(not(not(and(R!0, P!2))))) = or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))),
% 291.85/187.57 inference(monotonicity,[status(thm)],[72])).
% 291.85/187.57 tff(74,plain,
% 291.85/187.57 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(P!2), Q!1), not(not(not(and(R!0, P!2))))) = or(not(or(not(P!2), Q!1)), not(not(not(and(R!0, P!2))))))),
% 291.85/187.57 inference(quant_inst,[status(thm)],[])).
% 291.85/187.57 tff(75,plain,
% 291.85/187.57 (implies(or(not(P!2), Q!1), not(not(not(and(R!0, P!2))))) = or(not(or(not(P!2), Q!1)), not(not(not(and(R!0, P!2)))))),
% 291.85/187.57 inference(unit_resolution,[status(thm)],[74, 20])).
% 291.85/187.57 tff(76,plain,
% 291.85/187.57 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(P!2), Q!1), not(not(not(and(R!0, P!2))))) = not(and(or(not(P!2), Q!1), not(not(not(not(and(R!0, P!2))))))))),
% 291.85/187.57 inference(quant_inst,[status(thm)],[])).
% 291.85/187.57 tff(77,plain,
% 291.85/187.57 (implies(or(not(P!2), Q!1), not(not(not(and(R!0, P!2))))) = not(and(or(not(P!2), Q!1), not(not(not(not(and(R!0, P!2)))))))),
% 291.85/187.57 inference(unit_resolution,[status(thm)],[76, 41])).
% 291.85/187.57 tff(78,plain,
% 291.85/187.57 (not(and(or(not(P!2), Q!1), not(not(not(not(and(R!0, P!2))))))) = implies(or(not(P!2), Q!1), not(not(not(and(R!0, P!2)))))),
% 291.85/187.57 inference(symmetry,[status(thm)],[77])).
% 291.85/187.57 tff(79,plain,
% 291.85/187.57 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(P!2, Q!1) = not(and(P!2, not(Q!1))))),
% 291.85/187.57 inference(quant_inst,[status(thm)],[])).
% 291.85/187.57 tff(80,plain,
% 291.85/187.57 (implies(P!2, Q!1) = not(and(P!2, not(Q!1)))),
% 291.85/187.57 inference(unit_resolution,[status(thm)],[79, 41])).
% 291.85/187.57 tff(81,plain,
% 291.85/187.57 (not(and(P!2, not(Q!1))) = implies(P!2, Q!1)),
% 291.85/187.57 inference(symmetry,[status(thm)],[80])).
% 291.85/187.57 tff(82,plain,
% 291.85/187.57 (^[X: $i, Y: $i] : refl((and(X, Y) = not(or(not(X), not(Y)))) <=> (and(X, Y) = not(or(not(X), not(Y)))))),
% 291.85/187.57 inference(bind,[status(th)],[])).
% 291.85/187.57 tff(83,plain,
% 291.85/187.57 (![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))))),
% 291.85/187.57 inference(quant_intro,[status(thm)],[82])).
% 291.85/187.57 tff(84,plain,
% 291.85/187.57 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(85,plain,
% 291.85/187.57 (($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))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(86,axiom,(op_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_and')).
% 291.85/187.57 tff(87,plain,
% 291.85/187.57 (op_and <=> $true),
% 291.85/187.57 inference(iff_true,[status(thm)],[86])).
% 291.85/187.57 tff(88,plain,
% 291.85/187.57 ((~op_and) <=> (~$true)),
% 291.85/187.57 inference(monotonicity,[status(thm)],[87])).
% 291.85/187.57 tff(89,plain,
% 291.85/187.57 ((~op_and) <=> $false),
% 291.85/187.57 inference(transitivity,[status(thm)],[88, 5])).
% 291.85/187.57 tff(90,plain,
% 291.85/187.57 (((~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)))))),
% 291.85/187.57 inference(monotonicity,[status(thm)],[89])).
% 291.85/187.57 tff(91,plain,
% 291.85/187.57 (((~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))))),
% 291.85/187.57 inference(transitivity,[status(thm)],[90, 85])).
% 291.85/187.57 tff(92,plain,
% 291.85/187.57 (((~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)))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(93,plain,
% 291.85/187.57 ((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)))))),
% 291.85/187.57 inference(rewrite,[status(thm)],[])).
% 291.85/187.57 tff(94,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')).
% 291.85/187.57 tff(95,plain,
% 291.85/187.57 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 291.85/187.58 inference(modus_ponens,[status(thm)],[94, 93])).
% 291.85/187.58 tff(96,plain,
% 291.85/187.58 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 291.85/187.58 inference(modus_ponens,[status(thm)],[95, 92])).
% 291.85/187.58 tff(97,plain,
% 291.85/187.58 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 291.85/187.58 inference(modus_ponens,[status(thm)],[96, 91])).
% 291.85/187.58 tff(98,plain,
% 291.85/187.58 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 291.85/187.58 inference(modus_ponens,[status(thm)],[97, 84])).
% 291.85/187.58 tff(99,plain,(
% 291.85/187.58 ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 291.85/187.58 inference(skolemize,[status(sab)],[98])).
% 291.85/187.58 tff(100,plain,
% 291.85/187.58 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 291.85/187.58 inference(modus_ponens,[status(thm)],[99, 83])).
% 291.85/187.58 tff(101,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(P!2, not(Q!1)) = not(or(not(P!2), not(not(Q!1)))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(102,plain,
% 291.85/187.58 (and(P!2, not(Q!1)) = not(or(not(P!2), not(not(Q!1))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[101, 100])).
% 291.85/187.58 tff(103,plain,
% 291.85/187.58 (not(or(not(P!2), not(not(Q!1)))) = and(P!2, not(Q!1))),
% 291.85/187.58 inference(symmetry,[status(thm)],[102])).
% 291.85/187.58 tff(104,plain,
% 291.85/187.58 (not(not(or(not(P!2), not(not(Q!1))))) = not(and(P!2, not(Q!1)))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[103])).
% 291.85/187.58 tff(105,plain,
% 291.85/187.58 (not(not(or(not(P!2), not(not(Q!1))))) = or(not(P!2), Q!1)),
% 291.85/187.58 inference(transitivity,[status(thm)],[104, 81, 70])).
% 291.85/187.58 tff(106,plain,
% 291.85/187.58 (and(not(not(or(not(P!2), not(not(Q!1))))), not(not(not(not(and(R!0, P!2)))))) = and(or(not(P!2), Q!1), not(not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[105])).
% 291.85/187.58 tff(107,plain,
% 291.85/187.58 (not(and(not(not(or(not(P!2), not(not(Q!1))))), not(not(not(not(and(R!0, P!2))))))) = not(and(or(not(P!2), Q!1), not(not(not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[106])).
% 291.85/187.58 tff(108,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2))))) = not(and(not(not(or(not(P!2), not(not(Q!1))))), not(not(not(not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(109,plain,
% 291.85/187.58 (or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2))))) = not(and(not(not(or(not(P!2), not(not(Q!1))))), not(not(not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[108, 63])).
% 291.85/187.58 tff(110,plain,
% 291.85/187.58 (or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2))))) = or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))),
% 291.85/187.58 inference(transitivity,[status(thm)],[109, 107, 78, 75, 73, 65, 44, 22])).
% 291.85/187.58 tff(111,plain,
% 291.85/187.58 (or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))) = or(not(not(and(Q!1, R!0))), or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[110])).
% 291.85/187.58 tff(112,plain,
% 291.85/187.58 (or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))) = or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(transitivity,[status(thm)],[111, 68])).
% 291.85/187.58 tff(113,plain,
% 291.85/187.58 (equiv(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = equiv(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[112])).
% 291.85/187.58 tff(114,plain,
% 291.85/187.58 (equiv(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = equiv(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[113])).
% 291.85/187.58 tff(115,plain,
% 291.85/187.58 (^[X: $i, Y: $i] : refl((equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 291.85/187.58 inference(bind,[status(th)],[])).
% 291.85/187.58 tff(116,plain,
% 291.85/187.58 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 291.85/187.58 inference(quant_intro,[status(thm)],[115])).
% 291.85/187.58 tff(117,plain,
% 291.85/187.58 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 291.85/187.58 inference(rewrite,[status(thm)],[])).
% 291.85/187.58 tff(118,plain,
% 291.85/187.58 (($false | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 291.85/187.58 inference(rewrite,[status(thm)],[])).
% 291.85/187.58 tff(119,axiom,(op_equiv), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_equiv')).
% 291.85/187.58 tff(120,plain,
% 291.85/187.58 (op_equiv <=> $true),
% 291.85/187.58 inference(iff_true,[status(thm)],[119])).
% 291.85/187.58 tff(121,plain,
% 291.85/187.58 ((~op_equiv) <=> (~$true)),
% 291.85/187.58 inference(monotonicity,[status(thm)],[120])).
% 291.85/187.58 tff(122,plain,
% 291.85/187.58 ((~op_equiv) <=> $false),
% 291.85/187.58 inference(transitivity,[status(thm)],[121, 5])).
% 291.85/187.58 tff(123,plain,
% 291.85/187.58 (((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ($false | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[122])).
% 291.85/187.58 tff(124,plain,
% 291.85/187.58 (((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 291.85/187.58 inference(transitivity,[status(thm)],[123, 118])).
% 291.85/187.58 tff(125,plain,
% 291.85/187.58 (((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 291.85/187.58 inference(rewrite,[status(thm)],[])).
% 291.85/187.58 tff(126,plain,
% 291.85/187.58 ((op_equiv => ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 291.85/187.58 inference(rewrite,[status(thm)],[])).
% 291.85/187.58 tff(127,axiom,(op_equiv => ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_equiv')).
% 291.85/187.58 tff(128,plain,
% 291.85/187.58 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 291.85/187.58 inference(modus_ponens,[status(thm)],[127, 126])).
% 291.85/187.58 tff(129,plain,
% 291.85/187.58 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 291.85/187.58 inference(modus_ponens,[status(thm)],[128, 125])).
% 291.85/187.58 tff(130,plain,
% 291.85/187.58 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 291.85/187.58 inference(modus_ponens,[status(thm)],[129, 124])).
% 291.85/187.58 tff(131,plain,
% 291.85/187.58 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 291.85/187.58 inference(modus_ponens,[status(thm)],[130, 117])).
% 291.85/187.58 tff(132,plain,(
% 291.85/187.58 ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 291.85/187.58 inference(skolemize,[status(sab)],[131])).
% 291.85/187.58 tff(133,plain,
% 291.85/187.58 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 291.85/187.58 inference(modus_ponens,[status(thm)],[132, 116])).
% 291.85/187.58 tff(134,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = and(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(135,plain,
% 291.85/187.58 (equiv(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = and(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[134, 133])).
% 291.85/187.58 tff(136,plain,
% 291.85/187.58 (and(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))))) = equiv(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[135])).
% 291.85/187.58 tff(137,plain,
% 291.85/187.58 (not(implies(P!2, Q!1)) = not(or(not(P!2), Q!1))),
% 291.85/187.58 inference(symmetry,[status(thm)],[72])).
% 291.85/187.58 tff(138,plain,
% 291.85/187.58 (or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = or(not(or(not(P!2), Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[137])).
% 291.85/187.58 tff(139,plain,
% 291.85/187.58 (or(not(or(not(P!2), Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[138])).
% 291.85/187.58 tff(140,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(P!2), Q!1), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = or(not(or(not(P!2), Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(141,plain,
% 291.85/187.58 (implies(or(not(P!2), Q!1), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = or(not(or(not(P!2), Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[140, 20])).
% 291.85/187.58 tff(142,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(P!2), Q!1), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = not(and(or(not(P!2), Q!1), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(143,plain,
% 291.85/187.58 (implies(or(not(P!2), Q!1), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = not(and(or(not(P!2), Q!1), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[142, 41])).
% 291.85/187.58 tff(144,plain,
% 291.85/187.58 (not(and(or(not(P!2), Q!1), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))) = implies(or(not(P!2), Q!1), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[143])).
% 291.85/187.58 tff(145,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(P!2), Q!1), and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))) = not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(146,plain,
% 291.85/187.58 (and(or(not(P!2), Q!1), and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))) = not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[145, 100])).
% 291.85/187.58 tff(147,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))) = not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(148,plain,
% 291.85/187.58 (and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))) = not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[147, 100])).
% 291.85/187.58 tff(149,plain,
% 291.85/187.58 (not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[148])).
% 291.85/187.58 tff(150,plain,
% 291.85/187.58 (and(or(not(P!2), Q!1), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))) = and(or(not(P!2), Q!1), and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[149])).
% 291.85/187.58 tff(151,plain,
% 291.85/187.58 (and(or(not(P!2), Q!1), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))) = not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(transitivity,[status(thm)],[150, 146])).
% 291.85/187.58 tff(152,plain,
% 291.85/187.58 (not(and(or(not(P!2), Q!1), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))) = not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[151])).
% 291.85/187.58 tff(153,plain,
% 291.85/187.58 (not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))) = not(and(or(not(P!2), Q!1), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[152])).
% 291.85/187.58 tff(154,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(P!2), Q!1) = not(and(not(not(P!2)), not(Q!1))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(155,plain,
% 291.85/187.58 (or(not(P!2), Q!1) = not(and(not(not(P!2)), not(Q!1)))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[154, 63])).
% 291.85/187.58 tff(156,plain,
% 291.85/187.58 (not(and(not(not(P!2)), not(Q!1))) = or(not(P!2), Q!1)),
% 291.85/187.58 inference(symmetry,[status(thm)],[155])).
% 291.85/187.58 tff(157,plain,
% 291.85/187.58 (and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))) = and(or(not(P!2), Q!1), and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[156, 149])).
% 291.85/187.58 tff(158,plain,
% 291.85/187.58 (and(or(not(P!2), Q!1), and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))) = and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[157])).
% 291.85/187.58 tff(159,plain,
% 291.85/187.58 (not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))) = and(or(not(P!2), Q!1), and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[146])).
% 291.85/187.58 tff(160,plain,
% 291.85/187.58 (not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))) = and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(transitivity,[status(thm)],[159, 158])).
% 291.85/187.58 tff(161,plain,
% 291.85/187.58 (not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))) = not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[160])).
% 291.85/187.58 tff(162,plain,
% 291.85/187.58 (not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))) = not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[161])).
% 291.85/187.58 tff(163,plain,
% 291.85/187.58 (not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))) = or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(transitivity,[status(thm)],[162, 153, 144, 141, 139])).
% 291.85/187.58 tff(164,plain,
% 291.85/187.58 (implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2))))))) = implies(or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[163])).
% 291.85/187.58 tff(165,plain,
% 291.85/187.58 (implies(or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2))))))) = implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[164])).
% 291.85/187.58 tff(166,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(implies(P!2, Q!1)), not(and(R!0, P!2))) = not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(167,plain,
% 291.85/187.58 (or(not(implies(P!2, Q!1)), not(and(R!0, P!2))) = not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[166, 63])).
% 291.85/187.58 tff(168,plain,
% 291.85/187.58 (not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))) = or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))),
% 291.85/187.58 inference(symmetry,[status(thm)],[167])).
% 291.85/187.58 tff(169,plain,
% 291.85/187.58 (or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))) = or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[168])).
% 291.85/187.58 tff(170,plain,
% 291.85/187.58 (not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))) = not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[169])).
% 291.85/187.58 tff(171,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(Q!1, R!0)), and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))) = not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(172,plain,
% 291.85/187.58 (and(not(and(Q!1, R!0)), and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))) = not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[171, 100])).
% 291.85/187.58 tff(173,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))) = not(or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(174,plain,
% 291.85/187.58 (and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))) = not(or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[173, 100])).
% 291.85/187.58 tff(175,plain,
% 291.85/187.58 (not(or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))) = and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[174])).
% 291.85/187.58 tff(176,plain,
% 291.85/187.58 (and(not(and(Q!1, R!0)), not(or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2))))))) = and(not(and(Q!1, R!0)), and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[175])).
% 291.85/187.58 tff(177,plain,
% 291.85/187.58 (and(not(and(Q!1, R!0)), not(or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2))))))) = not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.85/187.58 inference(transitivity,[status(thm)],[176, 172, 170])).
% 291.85/187.58 tff(178,plain,
% 291.85/187.58 (not(and(not(and(Q!1, R!0)), not(or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))))) = not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[177])).
% 291.85/187.58 tff(179,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(Q!1, R!0)), or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))) = not(and(not(and(Q!1, R!0)), not(or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(180,plain,
% 291.85/187.58 (implies(not(and(Q!1, R!0)), or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))) = not(and(not(and(Q!1, R!0)), not(or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[179, 41])).
% 291.85/187.58 tff(181,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(Q!1, R!0)), or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))) = or(not(not(and(Q!1, R!0))), or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(182,plain,
% 291.85/187.58 (implies(not(and(Q!1, R!0)), or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))) = or(not(not(and(Q!1, R!0))), or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[181, 20])).
% 291.85/187.58 tff(183,plain,
% 291.85/187.58 (or(not(not(and(Q!1, R!0))), or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2)))))) = implies(not(and(Q!1, R!0)), or(not(not(not(implies(P!2, Q!1)))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[182])).
% 291.85/187.58 tff(184,plain,
% 291.85/187.58 (or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))) = not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.85/187.58 inference(transitivity,[status(thm)],[67, 183, 180, 178])).
% 291.85/187.58 tff(185,plain,
% 291.85/187.58 (or(not(or(not(P!2), Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = implies(or(not(P!2), Q!1), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[141])).
% 291.85/187.58 tff(186,plain,
% 291.85/187.58 (or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(transitivity,[status(thm)],[138, 185, 143, 152, 161])).
% 291.85/187.58 tff(187,plain,
% 291.85/187.58 (implies(or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2))))))) = implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(monotonicity,[status(thm)],[186, 184])).
% 291.85/187.58 tff(188,plain,
% 291.85/187.58 (implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = implies(or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(symmetry,[status(thm)],[187])).
% 291.85/187.58 tff(189,plain,
% 291.85/187.58 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.85/187.58 inference(quant_inst,[status(thm)],[])).
% 291.85/187.58 tff(190,plain,
% 291.85/187.58 (implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.85/187.58 inference(unit_resolution,[status(thm)],[189, 20])).
% 291.85/187.58 tff(191,plain,
% 291.85/187.58 (or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.85/187.59 inference(symmetry,[status(thm)],[190])).
% 291.85/187.59 tff(192,plain,
% 291.85/187.59 (not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))) = not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[170])).
% 291.85/187.59 tff(193,plain,
% 291.85/187.59 (or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))))) = or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[192])).
% 291.85/187.59 tff(194,plain,
% 291.85/187.59 (or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))))) = implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.59 inference(transitivity,[status(thm)],[193, 191, 188, 165])).
% 291.85/187.59 tff(195,plain,
% 291.85/187.59 (implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[163])).
% 291.85/187.59 tff(196,plain,
% 291.85/187.59 (implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))) = implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(symmetry,[status(thm)],[195])).
% 291.85/187.59 tff(197,plain,
% 291.85/187.59 (implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))) = implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[184, 186])).
% 291.85/187.59 tff(198,plain,
% 291.85/187.59 (implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))),
% 291.85/187.59 inference(symmetry,[status(thm)],[197])).
% 291.85/187.59 tff(199,plain,
% 291.85/187.59 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))))),
% 291.85/187.59 inference(quant_inst,[status(thm)],[])).
% 291.85/187.59 tff(200,plain,
% 291.85/187.59 (implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))))),
% 291.85/187.59 inference(unit_resolution,[status(thm)],[199, 41])).
% 291.85/187.59 tff(201,plain,
% 291.85/187.59 (not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) = implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(symmetry,[status(thm)],[200])).
% 291.85/187.59 tff(202,plain,
% 291.85/187.59 (not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))))),
% 291.85/187.59 inference(symmetry,[status(thm)],[192])).
% 291.85/187.59 tff(203,plain,
% 291.85/187.59 (and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))) = and(not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[202])).
% 291.85/187.59 tff(204,plain,
% 291.85/187.59 (not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[203])).
% 291.85/187.59 tff(205,plain,
% 291.85/187.59 (not(and(not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))))),
% 291.85/187.59 inference(symmetry,[status(thm)],[204])).
% 291.85/187.59 tff(206,plain,
% 291.85/187.59 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))))),
% 291.85/187.59 inference(quant_inst,[status(thm)],[])).
% 291.85/187.59 tff(207,plain,
% 291.85/187.59 (or(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))))),
% 291.85/187.59 inference(unit_resolution,[status(thm)],[206, 63])).
% 291.85/187.59 tff(208,plain,
% 291.85/187.59 (or(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[170, 162])).
% 291.85/187.59 tff(209,plain,
% 291.85/187.59 (or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))) = or(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(symmetry,[status(thm)],[208])).
% 291.85/187.59 tff(210,plain,
% 291.85/187.59 (or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))) = or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[161])).
% 291.85/187.59 tff(211,plain,
% 291.85/187.59 (or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(symmetry,[status(thm)],[210])).
% 291.85/187.59 tff(212,plain,
% 291.85/187.59 (or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(transitivity,[status(thm)],[211, 209, 207, 205, 201, 198, 196])).
% 291.85/187.59 tff(213,plain,
% 291.85/187.59 (and(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))))) = and(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2))))))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[212, 194])).
% 291.85/187.59 tff(214,plain,
% 291.85/187.59 (or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(symmetry,[status(thm)],[193])).
% 291.85/187.59 tff(215,plain,
% 291.85/187.59 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.85/187.59 inference(quant_inst,[status(thm)],[])).
% 291.85/187.59 tff(216,plain,
% 291.85/187.59 (implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(unit_resolution,[status(thm)],[215, 41])).
% 291.85/187.59 tff(217,plain,
% 291.85/187.59 (not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.85/187.59 inference(symmetry,[status(thm)],[216])).
% 291.85/187.59 tff(218,plain,
% 291.85/187.59 (and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = and(not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[162])).
% 291.85/187.59 tff(219,plain,
% 291.85/187.59 (and(not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.85/187.59 inference(symmetry,[status(thm)],[218])).
% 291.85/187.59 tff(220,plain,
% 291.85/187.59 (not(and(not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[219])).
% 291.85/187.59 tff(221,plain,
% 291.85/187.59 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.85/187.59 inference(quant_inst,[status(thm)],[])).
% 291.85/187.59 tff(222,plain,
% 291.85/187.59 (or(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.85/187.59 inference(unit_resolution,[status(thm)],[221, 63])).
% 291.85/187.59 tff(223,plain,
% 291.85/187.59 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(Q!1, R!0)), not(and(R!0, P!2))) = not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))),
% 291.85/187.59 inference(quant_inst,[status(thm)],[])).
% 291.85/187.59 tff(224,plain,
% 291.85/187.59 (implies(not(and(Q!1, R!0)), not(and(R!0, P!2))) = not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))),
% 291.85/187.59 inference(unit_resolution,[status(thm)],[223, 41])).
% 291.85/187.59 tff(225,plain,
% 291.85/187.59 (not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))) = implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))),
% 291.85/187.59 inference(symmetry,[status(thm)],[224])).
% 291.85/187.59 tff(226,plain,
% 291.85/187.59 (or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))) = or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[72, 225])).
% 291.85/187.59 tff(227,plain,
% 291.85/187.59 (not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))) = not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.85/187.59 inference(monotonicity,[status(thm)],[226])).
% 291.85/187.59 tff(228,plain,
% 291.85/187.59 (not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))),
% 291.85/187.60 inference(symmetry,[status(thm)],[227])).
% 291.85/187.60 tff(229,plain,
% 291.85/187.60 (or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.85/187.60 inference(monotonicity,[status(thm)],[228])).
% 291.85/187.60 tff(230,plain,
% 291.85/187.60 (or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))))),
% 291.85/187.60 inference(transitivity,[status(thm)],[229, 222, 220, 217, 190, 214])).
% 291.85/187.60 tff(231,plain,
% 291.85/187.60 (and(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))), or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = and(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))))))),
% 291.85/187.60 inference(monotonicity,[status(thm)],[210, 230])).
% 291.85/187.60 tff(232,plain,
% 291.85/187.60 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))), or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))),
% 291.85/187.60 inference(quant_inst,[status(thm)],[])).
% 291.85/187.60 tff(233,plain,
% 291.85/187.60 (and(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))), or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.85/187.60 inference(unit_resolution,[status(thm)],[232, 100])).
% 291.85/187.60 tff(234,plain,
% 291.85/187.60 (not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))) = and(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))), or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.85/187.60 inference(symmetry,[status(thm)],[233])).
% 291.85/187.60 tff(235,plain,
% 291.85/187.60 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.85/187.60 inference(quant_inst,[status(thm)],[])).
% 291.85/187.60 tff(236,plain,
% 291.85/187.60 (and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.85/187.60 inference(unit_resolution,[status(thm)],[235, 100])).
% 291.85/187.60 tff(237,plain,
% 291.85/187.60 (not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.85/187.60 inference(symmetry,[status(thm)],[236])).
% 291.85/187.60 tff(238,plain,
% 291.85/187.60 (and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))) = and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 291.85/187.60 inference(monotonicity,[status(thm)],[227])).
% 291.85/187.60 tff(239,plain,
% 291.85/187.60 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))) = not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))))),
% 291.85/187.60 inference(quant_inst,[status(thm)],[])).
% 291.85/187.60 tff(240,plain,
% 291.85/187.60 (and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))) = not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))))),
% 291.85/187.60 inference(unit_resolution,[status(thm)],[239, 100])).
% 291.85/187.60 tff(241,plain,
% 291.85/187.60 (not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))) = and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))),
% 291.85/187.60 inference(symmetry,[status(thm)],[240])).
% 291.85/187.60 tff(242,plain,
% 291.85/187.60 (not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))) = and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 291.85/187.60 inference(transitivity,[status(thm)],[241, 238])).
% 291.85/187.60 tff(243,plain,
% 291.85/187.60 (or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.85/187.60 inference(monotonicity,[status(thm)],[242, 237])).
% 291.85/187.60 tff(244,plain,
% 291.85/187.60 (or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.85/187.60 inference(symmetry,[status(thm)],[243])).
% 291.85/187.60 tff(245,plain,
% 291.85/187.60 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.85/187.60 inference(quant_inst,[status(thm)],[])).
% 291.85/187.60 tff(246,plain,
% 291.85/187.60 (or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.85/187.60 inference(unit_resolution,[status(thm)],[245, 63])).
% 291.85/187.60 tff(247,plain,
% 291.85/187.60 (not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.85/187.60 inference(symmetry,[status(thm)],[246])).
% 291.85/187.60 tff(248,plain,
% 291.85/187.60 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.85/187.60 inference(quant_inst,[status(thm)],[])).
% 291.85/187.60 tff(249,plain,
% 291.85/187.60 (implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.85/187.60 inference(unit_resolution,[status(thm)],[248, 41])).
% 291.85/187.60 tff(250,plain,
% 291.85/187.60 (not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.85/187.60 inference(symmetry,[status(thm)],[249])).
% 291.85/187.60 tff(251,plain,
% 291.85/187.60 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.85/187.60 inference(quant_inst,[status(thm)],[])).
% 291.85/187.60 tff(252,plain,
% 291.85/187.60 (implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.85/187.60 inference(unit_resolution,[status(thm)],[251, 41])).
% 291.85/187.60 tff(253,plain,
% 291.85/187.60 (not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.85/187.60 inference(symmetry,[status(thm)],[252])).
% 291.85/187.60 tff(254,plain,
% 291.85/187.60 (and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = and(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.85/187.60 inference(monotonicity,[status(thm)],[253, 250])).
% 291.85/187.60 tff(255,plain,
% 291.85/187.60 (and(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.85/187.60 inference(symmetry,[status(thm)],[254])).
% 291.85/187.60 tff(256,plain,
% 291.85/187.60 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 291.85/187.60 inference(quant_inst,[status(thm)],[])).
% 291.85/187.60 tff(257,plain,
% 291.85/187.60 (implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.85/187.60 inference(unit_resolution,[status(thm)],[256, 20])).
% 291.85/187.60 tff(258,plain,
% 291.85/187.60 (or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.85/187.60 inference(symmetry,[status(thm)],[257])).
% 291.85/187.60 tff(259,plain,
% 291.85/187.60 (and(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = and(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.85/187.60 inference(monotonicity,[status(thm)],[258, 250])).
% 291.85/187.60 tff(260,plain,
% 291.85/187.60 (and(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.85/187.60 inference(transitivity,[status(thm)],[259, 255])).
% 291.85/187.60 tff(261,plain,
% 291.85/187.60 (not(and(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.85/187.60 inference(monotonicity,[status(thm)],[260])).
% 291.85/187.60 tff(262,plain,
% 291.85/187.60 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.85/187.60 inference(quant_inst,[status(thm)],[])).
% 291.85/187.60 tff(263,plain,
% 291.85/187.60 (implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.61 inference(unit_resolution,[status(thm)],[262, 41])).
% 291.89/187.61 tff(264,plain,
% 291.89/187.61 (implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.89/187.61 inference(monotonicity,[status(thm)],[237])).
% 291.89/187.61 tff(265,plain,
% 291.89/187.61 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.89/187.61 inference(quant_inst,[status(thm)],[])).
% 291.89/187.61 tff(266,plain,
% 291.89/187.61 (implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.61 inference(unit_resolution,[status(thm)],[265, 20])).
% 291.89/187.61 tff(267,plain,
% 291.89/187.61 (or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.61 inference(symmetry,[status(thm)],[266])).
% 291.89/187.61 tff(268,plain,
% 291.89/187.61 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(implies(P!2, Q!1), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))) = or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.89/187.61 inference(quant_inst,[status(thm)],[])).
% 291.89/187.61 tff(269,plain,
% 291.89/187.61 (implies(implies(P!2, Q!1), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))) = or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))),
% 291.89/187.61 inference(unit_resolution,[status(thm)],[268, 20])).
% 291.89/187.61 tff(270,plain,
% 291.89/187.61 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(implies(P!2, Q!1), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))) = not(and(implies(P!2, Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.89/187.61 inference(quant_inst,[status(thm)],[])).
% 291.89/187.61 tff(271,plain,
% 291.89/187.61 (implies(implies(P!2, Q!1), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))) = not(and(implies(P!2, Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 291.89/187.61 inference(unit_resolution,[status(thm)],[270, 41])).
% 291.89/187.61 tff(272,plain,
% 291.89/187.61 (not(and(implies(P!2, Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))) = implies(implies(P!2, Q!1), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))),
% 291.89/187.61 inference(symmetry,[status(thm)],[271])).
% 291.89/187.61 tff(273,plain,
% 291.89/187.61 (and(implies(P!2, Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = and(or(not(P!2), Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.89/187.61 inference(monotonicity,[status(thm)],[70])).
% 291.89/187.61 tff(274,plain,
% 291.89/187.61 (and(or(not(P!2), Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = and(implies(P!2, Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.89/187.61 inference(symmetry,[status(thm)],[273])).
% 291.89/187.61 tff(275,plain,
% 291.89/187.61 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(P!2), Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.89/187.61 inference(quant_inst,[status(thm)],[])).
% 291.89/187.61 tff(276,plain,
% 291.89/187.61 (and(or(not(P!2), Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.89/187.61 inference(unit_resolution,[status(thm)],[275, 100])).
% 291.89/187.61 tff(277,plain,
% 291.89/187.61 (not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = and(or(not(P!2), Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.89/187.61 inference(symmetry,[status(thm)],[276])).
% 291.89/187.61 tff(278,plain,
% 291.89/187.61 (not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = and(implies(P!2, Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.89/187.61 inference(transitivity,[status(thm)],[277, 274])).
% 291.89/187.61 tff(279,plain,
% 291.89/187.61 (not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = not(and(implies(P!2, Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 291.89/187.61 inference(monotonicity,[status(thm)],[278])).
% 291.89/187.61 tff(280,plain,
% 291.89/187.61 (not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))),
% 291.89/187.61 inference(transitivity,[status(thm)],[279, 272, 269])).
% 291.89/187.61 tff(281,plain,
% 291.89/187.61 (or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) = or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.89/187.61 inference(monotonicity,[status(thm)],[280])).
% 291.89/187.61 tff(282,plain,
% 291.89/187.61 (not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) = not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 291.89/187.61 inference(monotonicity,[status(thm)],[281])).
% 291.89/187.61 tff(283,plain,
% 291.89/187.61 (or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.61 inference(monotonicity,[status(thm)],[282])).
% 291.89/187.61 tff(284,plain,
% 291.89/187.61 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = not(and(not(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))),
% 291.89/187.61 inference(quant_inst,[status(thm)],[])).
% 291.89/187.61 tff(285,plain,
% 291.89/187.61 (or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = not(and(not(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))),
% 291.89/187.61 inference(unit_resolution,[status(thm)],[284, 63])).
% 291.89/187.61 tff(286,plain,
% 291.89/187.61 (not(and(not(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) = or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.61 inference(symmetry,[status(thm)],[285])).
% 291.89/187.61 tff(287,plain,
% 291.89/187.61 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = or(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.89/187.61 inference(quant_inst,[status(thm)],[])).
% 291.89/187.61 tff(288,plain,
% 291.89/187.61 (implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = or(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.89/187.61 inference(unit_resolution,[status(thm)],[287, 20])).
% 291.89/187.61 tff(289,plain,
% 291.89/187.61 (or(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.89/187.61 inference(symmetry,[status(thm)],[288])).
% 291.89/187.61 tff(290,plain,
% 291.89/187.61 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = not(and(not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.89/187.61 inference(quant_inst,[status(thm)],[])).
% 291.89/187.61 tff(291,plain,
% 291.89/187.61 (or(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = not(and(not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.89/187.61 inference(unit_resolution,[status(thm)],[290, 63])).
% 291.89/187.61 tff(292,plain,
% 291.89/187.61 (not(and(not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.89/187.61 inference(symmetry,[status(thm)],[291])).
% 291.89/187.61 tff(293,plain,
% 291.89/187.61 (and(not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.89/187.61 inference(monotonicity,[status(thm)],[280])).
% 291.89/187.61 tff(294,plain,
% 291.89/187.61 (not(and(not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.89/187.61 inference(monotonicity,[status(thm)],[293])).
% 291.89/187.61 tff(295,plain,
% 291.89/187.61 (not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.89/187.61 inference(symmetry,[status(thm)],[294])).
% 291.89/187.61 tff(296,plain,
% 291.89/187.61 (not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.89/187.61 inference(monotonicity,[status(thm)],[237])).
% 291.89/187.61 tff(297,plain,
% 291.89/187.61 (not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.89/187.61 inference(transitivity,[status(thm)],[296, 295, 292, 289])).
% 291.89/187.61 tff(298,plain,
% 291.89/187.61 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.89/187.61 inference(quant_inst,[status(thm)],[])).
% 291.89/187.61 tff(299,plain,
% 291.89/187.61 (implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.89/187.62 inference(unit_resolution,[status(thm)],[298, 41])).
% 291.89/187.62 tff(300,plain,
% 291.89/187.62 (not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) = implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.89/187.62 inference(symmetry,[status(thm)],[299])).
% 291.89/187.62 tff(301,plain,
% 291.89/187.62 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.89/187.62 inference(quant_inst,[status(thm)],[])).
% 291.89/187.62 tff(302,plain,
% 291.89/187.62 (and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.89/187.62 inference(unit_resolution,[status(thm)],[301, 100])).
% 291.89/187.62 tff(303,plain,
% 291.89/187.62 (not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) = and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.89/187.62 inference(symmetry,[status(thm)],[302])).
% 291.89/187.62 tff(304,plain,
% 291.89/187.62 (not(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))) = not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.89/187.62 inference(monotonicity,[status(thm)],[303])).
% 291.89/187.62 tff(305,plain,
% 291.89/187.62 (not(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))) = implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.89/187.62 inference(transitivity,[status(thm)],[304, 300])).
% 291.89/187.62 tff(306,plain,
% 291.89/187.62 (and(not(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))) = and(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.89/187.62 inference(monotonicity,[status(thm)],[305, 297])).
% 291.89/187.62 tff(307,plain,
% 291.89/187.62 (and(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = and(not(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.89/187.62 inference(symmetry,[status(thm)],[306])).
% 291.89/187.62 tff(308,plain,
% 291.89/187.62 (and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))) = and(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.89/187.62 inference(monotonicity,[status(thm)],[300, 297])).
% 291.89/187.62 tff(309,plain,
% 291.89/187.62 (and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))) = and(not(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.89/187.62 inference(transitivity,[status(thm)],[308, 307])).
% 291.89/187.62 tff(310,plain,
% 291.89/187.62 (not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) = not(and(not(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))),
% 291.89/187.62 inference(monotonicity,[status(thm)],[309])).
% 291.89/187.62 tff(311,plain,
% 291.89/187.62 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))),
% 291.89/187.62 inference(quant_inst,[status(thm)],[])).
% 291.89/187.62 tff(312,plain,
% 291.89/187.62 (implies(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))),
% 291.89/187.62 inference(unit_resolution,[status(thm)],[311, 41])).
% 291.89/187.62 tff(313,plain,
% 291.89/187.62 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = or(not(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.89/187.62 inference(quant_inst,[status(thm)],[])).
% 291.89/187.62 tff(314,plain,
% 291.89/187.62 (implies(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = or(not(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.62 inference(unit_resolution,[status(thm)],[313, 20])).
% 291.89/187.62 tff(315,plain,
% 291.89/187.62 (or(not(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = implies(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.62 inference(symmetry,[status(thm)],[314])).
% 291.89/187.62 tff(316,plain,
% 291.89/187.62 (not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = not(or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))))))),
% 291.89/187.62 inference(monotonicity,[status(thm)],[230])).
% 291.89/187.62 tff(317,plain,
% 291.89/187.62 (not(or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))))) = not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.89/187.62 inference(symmetry,[status(thm)],[316])).
% 291.89/187.62 tff(318,plain,
% 291.89/187.62 (not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))))),
% 291.89/187.62 inference(transitivity,[status(thm)],[217, 190, 214])).
% 291.89/187.62 tff(319,plain,
% 291.89/187.62 (not(not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))) = not(or(not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))))))),
% 291.89/187.62 inference(monotonicity,[status(thm)],[318])).
% 291.89/187.62 tff(320,plain,
% 291.89/187.62 (not(not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))) = not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.89/187.62 inference(transitivity,[status(thm)],[319, 317])).
% 291.89/187.62 tff(321,plain,
% 291.89/187.62 (or(not(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) = or(not(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.62 inference(monotonicity,[status(thm)],[320])).
% 291.89/187.62 tff(322,plain,
% 291.89/187.62 (or(not(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) = or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.62 inference(transitivity,[status(thm)],[321, 315, 312, 310, 286, 283, 267, 264, 263, 261, 247, 244])).
% 291.89/187.62 tff(323,plain,
% 291.89/187.62 (not(or(not(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))) = not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.89/187.62 inference(monotonicity,[status(thm)],[322])).
% 291.89/187.62 tff(324,plain,
% 291.89/187.62 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))) = not(or(not(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))),
% 291.89/187.62 inference(quant_inst,[status(thm)],[])).
% 291.89/187.62 tff(325,plain,
% 291.89/187.62 (and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))) = not(or(not(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), not(not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))),
% 291.89/187.62 inference(unit_resolution,[status(thm)],[324, 100])).
% 291.89/187.62 tff(326,plain,
% 291.89/187.62 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.89/187.62 inference(quant_inst,[status(thm)],[])).
% 291.89/187.62 tff(327,plain,
% 291.89/187.62 (implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.89/187.62 inference(unit_resolution,[status(thm)],[326, 20])).
% 291.89/187.62 tff(328,plain,
% 291.89/187.62 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.89/187.62 inference(quant_inst,[status(thm)],[])).
% 291.89/187.62 tff(329,plain,
% 291.89/187.62 (implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.62 inference(unit_resolution,[status(thm)],[328, 41])).
% 291.89/187.62 tff(330,plain,
% 291.89/187.62 (not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.89/187.62 inference(symmetry,[status(thm)],[329])).
% 291.89/187.62 tff(331,plain,
% 291.89/187.62 (and(not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.89/187.63 inference(monotonicity,[status(thm)],[280])).
% 291.89/187.63 tff(332,plain,
% 291.89/187.63 (not(and(not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.63 inference(monotonicity,[status(thm)],[331])).
% 291.89/187.63 tff(333,plain,
% 291.89/187.63 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.89/187.63 inference(quant_inst,[status(thm)],[])).
% 291.89/187.63 tff(334,plain,
% 291.89/187.63 (or(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.63 inference(unit_resolution,[status(thm)],[333, 63])).
% 291.89/187.63 tff(335,plain,
% 291.89/187.63 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.89/187.63 inference(quant_inst,[status(thm)],[])).
% 291.89/187.63 tff(336,plain,
% 291.89/187.63 (implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.89/187.63 inference(unit_resolution,[status(thm)],[335, 20])).
% 291.89/187.63 tff(337,plain,
% 291.89/187.63 (implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.89/187.63 inference(transitivity,[status(thm)],[336, 334, 332, 330, 327, 229, 222, 220])).
% 291.89/187.63 tff(338,plain,
% 291.89/187.63 (not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))) = not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.89/187.63 inference(symmetry,[status(thm)],[282])).
% 291.89/187.63 tff(339,plain,
% 291.89/187.63 (or(not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) = or(not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.89/187.63 inference(monotonicity,[status(thm)],[280])).
% 291.89/187.63 tff(340,plain,
% 291.89/187.63 (or(not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = or(not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.89/187.63 inference(symmetry,[status(thm)],[339])).
% 291.89/187.63 tff(341,plain,
% 291.89/187.63 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = or(not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 291.89/187.63 inference(quant_inst,[status(thm)],[])).
% 291.89/187.63 tff(342,plain,
% 291.89/187.63 (implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = or(not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.89/187.63 inference(unit_resolution,[status(thm)],[341, 20])).
% 291.89/187.63 tff(343,plain,
% 291.89/187.63 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.89/187.63 inference(quant_inst,[status(thm)],[])).
% 291.89/187.63 tff(344,plain,
% 291.89/187.63 (implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.89/187.63 inference(unit_resolution,[status(thm)],[343, 41])).
% 291.89/187.63 tff(345,plain,
% 291.89/187.63 (not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 291.89/187.63 inference(symmetry,[status(thm)],[344])).
% 291.89/187.63 tff(346,plain,
% 291.89/187.63 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.89/187.63 inference(quant_inst,[status(thm)],[])).
% 291.89/187.63 tff(347,plain,
% 291.89/187.63 (or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.89/187.63 inference(unit_resolution,[status(thm)],[346, 63])).
% 291.89/187.63 tff(348,plain,
% 291.89/187.63 (or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = or(not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.89/187.63 inference(transitivity,[status(thm)],[347, 345, 342, 340])).
% 291.89/187.63 tff(349,plain,
% 291.89/187.63 (not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))) = not(or(not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.89/187.63 inference(monotonicity,[status(thm)],[348])).
% 291.89/187.63 tff(350,plain,
% 291.89/187.63 (not(or(not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) = not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 291.89/187.63 inference(symmetry,[status(thm)],[349])).
% 291.89/187.63 tff(351,plain,
% 291.89/187.63 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = not(or(not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.89/187.63 inference(quant_inst,[status(thm)],[])).
% 291.89/187.63 tff(352,plain,
% 291.89/187.63 (and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = not(or(not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.89/187.63 inference(unit_resolution,[status(thm)],[351, 100])).
% 291.89/187.63 tff(353,plain,
% 291.89/187.63 (and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.89/187.63 inference(transitivity,[status(thm)],[352, 350, 338, 303])).
% 291.89/187.63 tff(354,plain,
% 291.89/187.63 (not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) = not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.89/187.63 inference(monotonicity,[status(thm)],[353])).
% 291.89/187.63 tff(355,plain,
% 291.89/187.63 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.89/187.63 inference(quant_inst,[status(thm)],[])).
% 291.89/187.63 tff(356,plain,
% 291.89/187.63 (implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.89/187.63 inference(unit_resolution,[status(thm)],[355, 41])).
% 291.89/187.63 tff(357,plain,
% 291.89/187.63 (implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.89/187.63 inference(transitivity,[status(thm)],[356, 354])).
% 291.89/187.63 tff(358,plain,
% 291.89/187.63 (and(implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), not(and(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.91/187.63 inference(monotonicity,[status(thm)],[357, 337])).
% 291.91/187.63 tff(359,plain,
% 291.91/187.63 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = and(implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.91/187.63 inference(quant_inst,[status(thm)],[])).
% 291.91/187.63 tff(360,plain,
% 291.91/187.63 (equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = and(implies(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), implies(or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 291.91/187.63 inference(unit_resolution,[status(thm)],[359, 133])).
% 291.91/187.63 tff(361,plain,
% 291.91/187.63 (equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = equiv(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.91/187.63 inference(transitivity,[status(thm)],[360, 358, 325, 323, 234, 231, 213, 136, 114])).
% 291.91/187.63 tff(362,plain,
% 291.91/187.63 (is_a_theorem(equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) <=> is_a_theorem(equiv(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))),
% 291.91/187.63 inference(monotonicity,[status(thm)],[361])).
% 291.91/187.63 tff(363,plain,
% 291.91/187.63 (is_a_theorem(equiv(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))) <=> is_a_theorem(equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.91/187.63 inference(symmetry,[status(thm)],[362])).
% 291.91/187.63 tff(364,plain,
% 291.91/187.63 (not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))) = equiv(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.91/187.63 inference(transitivity,[status(thm)],[234, 231, 213, 136, 114])).
% 291.91/187.63 tff(365,plain,
% 291.91/187.63 (is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) <=> is_a_theorem(equiv(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))),
% 291.91/187.64 inference(monotonicity,[status(thm)],[364])).
% 291.91/187.64 tff(366,plain,
% 291.91/187.64 (is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) <=> is_a_theorem(equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.91/187.64 inference(transitivity,[status(thm)],[365, 363])).
% 291.91/187.64 tff(367,plain,
% 291.91/187.64 (not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))) = not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))))),
% 291.91/187.64 inference(monotonicity,[status(thm)],[211])).
% 291.91/187.64 tff(368,plain,
% 291.91/187.64 (not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))) = not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))),
% 291.91/187.64 inference(symmetry,[status(thm)],[367])).
% 291.91/187.64 tff(369,plain,
% 291.91/187.64 (and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))) = and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))),
% 291.91/187.64 inference(symmetry,[status(thm)],[238])).
% 291.91/187.64 tff(370,plain,
% 291.91/187.64 (and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))) = not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))),
% 291.91/187.64 inference(transitivity,[status(thm)],[369, 240, 368])).
% 291.91/187.64 tff(371,plain,
% 291.91/187.64 (or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) = or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))),
% 291.91/187.64 inference(monotonicity,[status(thm)],[370])).
% 291.91/187.64 tff(372,plain,
% 291.91/187.64 (or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) = or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))),
% 291.91/187.64 inference(symmetry,[status(thm)],[371])).
% 291.91/187.64 tff(373,plain,
% 291.91/187.64 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) = or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))),
% 291.91/187.64 inference(quant_inst,[status(thm)],[])).
% 291.91/187.64 tff(374,plain,
% 291.91/187.64 (implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) = or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))),
% 291.91/187.64 inference(unit_resolution,[status(thm)],[373, 20])).
% 291.91/187.64 tff(375,plain,
% 291.91/187.64 (implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) = or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))),
% 291.91/187.64 inference(transitivity,[status(thm)],[374, 372])).
% 291.91/187.64 tff(376,plain,
% 291.91/187.64 (is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))) <=> is_a_theorem(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))),
% 291.91/187.64 inference(monotonicity,[status(thm)],[375])).
% 291.91/187.64 tff(377,plain,
% 291.91/187.64 (is_a_theorem(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))) <=> is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))),
% 291.91/187.64 inference(symmetry,[status(thm)],[376])).
% 291.91/187.64 tff(378,plain,
% 291.91/187.64 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.64 inference(quant_inst,[status(thm)],[])).
% 291.91/187.64 tff(379,plain,
% 291.91/187.64 (or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.64 inference(unit_resolution,[status(thm)],[378, 63])).
% 291.91/187.64 tff(380,plain,
% 291.91/187.64 (not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) = or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.91/187.64 inference(symmetry,[status(thm)],[379])).
% 291.91/187.64 tff(381,plain,
% 291.91/187.64 (implies(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))) = implies(or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))),
% 291.91/187.65 inference(monotonicity,[status(thm)],[380])).
% 291.91/187.65 tff(382,plain,
% 291.91/187.65 (implies(or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))) = implies(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))),
% 291.91/187.65 inference(symmetry,[status(thm)],[381])).
% 291.91/187.65 tff(383,plain,
% 291.91/187.65 (is_a_theorem(implies(or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))) <=> is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))),
% 291.91/187.65 inference(monotonicity,[status(thm)],[382])).
% 291.91/187.65 tff(384,plain,
% 291.91/187.65 (^[P: $i, Q: $i] : refl(is_a_theorem(implies(or(P, Q), or(Q, P))) <=> is_a_theorem(implies(or(P, Q), or(Q, P))))),
% 291.91/187.65 inference(bind,[status(th)],[])).
% 291.91/187.65 tff(385,plain,
% 291.91/187.65 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 291.91/187.65 inference(quant_intro,[status(thm)],[384])).
% 291.91/187.65 tff(386,plain,
% 291.91/187.65 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 291.91/187.65 inference(rewrite,[status(thm)],[])).
% 291.91/187.65 tff(387,plain,
% 291.91/187.65 (($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 291.91/187.65 inference(rewrite,[status(thm)],[])).
% 291.91/187.65 tff(388,axiom,(r3), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_r3')).
% 291.91/187.65 tff(389,plain,
% 291.91/187.65 (r3 <=> $true),
% 291.91/187.65 inference(iff_true,[status(thm)],[388])).
% 291.91/187.65 tff(390,plain,
% 291.91/187.65 ((r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> ($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))))),
% 291.91/187.65 inference(monotonicity,[status(thm)],[389])).
% 291.91/187.65 tff(391,plain,
% 291.91/187.65 ((r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 291.91/187.65 inference(transitivity,[status(thm)],[390, 387])).
% 291.91/187.65 tff(392,plain,
% 291.91/187.65 ((r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))))),
% 291.91/187.65 inference(rewrite,[status(thm)],[])).
% 291.91/187.65 tff(393,axiom,(r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','r3')).
% 291.91/187.65 tff(394,plain,
% 291.91/187.65 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 291.91/187.65 inference(modus_ponens,[status(thm)],[393, 392])).
% 291.91/187.65 tff(395,plain,
% 291.91/187.65 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 291.91/187.65 inference(modus_ponens,[status(thm)],[394, 392])).
% 291.91/187.65 tff(396,plain,
% 291.91/187.65 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 291.91/187.65 inference(modus_ponens,[status(thm)],[395, 391])).
% 291.91/187.65 tff(397,plain,
% 291.91/187.65 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 291.91/187.65 inference(modus_ponens,[status(thm)],[396, 386])).
% 291.91/187.65 tff(398,plain,(
% 291.91/187.65 ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 291.91/187.65 inference(skolemize,[status(sab)],[397])).
% 291.91/187.65 tff(399,plain,
% 291.91/187.65 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 291.91/187.65 inference(modus_ponens,[status(thm)],[398, 385])).
% 291.91/187.65 tff(400,plain,
% 291.91/187.65 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))),
% 291.91/187.65 inference(quant_inst,[status(thm)],[])).
% 291.91/187.65 tff(401,plain,
% 291.91/187.65 (is_a_theorem(implies(or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))),
% 291.91/187.65 inference(unit_resolution,[status(thm)],[400, 399])).
% 291.91/187.65 tff(402,plain,
% 291.91/187.65 (is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))),
% 291.91/187.65 inference(modus_ponens,[status(thm)],[401, 383])).
% 291.91/187.65 tff(403,plain,
% 291.91/187.65 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))) = not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.91/187.65 inference(quant_inst,[status(thm)],[])).
% 291.91/187.65 tff(404,plain,
% 291.91/187.65 (or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))) = not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.91/187.65 inference(unit_resolution,[status(thm)],[403, 63])).
% 291.91/187.65 tff(405,plain,
% 291.91/187.65 (not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))),
% 291.91/187.65 inference(symmetry,[status(thm)],[404])).
% 291.91/187.65 tff(406,plain,
% 291.91/187.65 (or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) = or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.91/187.65 inference(monotonicity,[status(thm)],[405])).
% 291.91/187.65 tff(407,plain,
% 291.91/187.65 (not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) = not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.91/187.65 inference(monotonicity,[status(thm)],[406])).
% 291.91/187.65 tff(408,plain,
% 291.91/187.65 (or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.91/187.65 inference(monotonicity,[status(thm)],[407])).
% 291.91/187.65 tff(409,plain,
% 291.91/187.65 (or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.91/187.65 inference(symmetry,[status(thm)],[408])).
% 291.91/187.65 tff(410,plain,
% 291.91/187.65 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.65 inference(quant_inst,[status(thm)],[])).
% 291.91/187.65 tff(411,plain,
% 291.91/187.65 (implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.91/187.65 inference(unit_resolution,[status(thm)],[410, 20])).
% 291.91/187.65 tff(412,plain,
% 291.91/187.65 (implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.66 inference(monotonicity,[status(thm)],[379])).
% 291.91/187.66 tff(413,plain,
% 291.91/187.66 (implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) = implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.91/187.66 inference(symmetry,[status(thm)],[412])).
% 291.91/187.66 tff(414,plain,
% 291.91/187.66 (implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) = or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.91/187.66 inference(transitivity,[status(thm)],[413, 411, 409])).
% 291.91/187.66 tff(415,plain,
% 291.91/187.66 (is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))) <=> is_a_theorem(or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.66 inference(monotonicity,[status(thm)],[414])).
% 291.91/187.66 tff(416,plain,
% 291.91/187.66 (is_a_theorem(or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) <=> is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.91/187.66 inference(symmetry,[status(thm)],[415])).
% 291.91/187.66 tff(417,plain,
% 291.91/187.66 (and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = and(implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 291.91/187.66 inference(monotonicity,[status(thm)],[250, 253])).
% 291.91/187.66 tff(418,plain,
% 291.91/187.66 (and(implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))) = and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.91/187.66 inference(symmetry,[status(thm)],[417])).
% 291.91/187.66 tff(419,plain,
% 291.91/187.66 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.91/187.66 inference(quant_inst,[status(thm)],[])).
% 291.91/187.66 tff(420,plain,
% 291.91/187.66 (implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.91/187.66 inference(unit_resolution,[status(thm)],[419, 20])).
% 291.91/187.66 tff(421,plain,
% 291.91/187.66 (or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.91/187.66 inference(symmetry,[status(thm)],[420])).
% 291.91/187.66 tff(422,plain,
% 291.91/187.66 (and(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = and(implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 291.91/187.66 inference(monotonicity,[status(thm)],[421, 253])).
% 291.91/187.66 tff(423,plain,
% 291.91/187.66 (and(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.91/187.66 inference(transitivity,[status(thm)],[422, 418])).
% 291.91/187.66 tff(424,plain,
% 291.91/187.66 (not(and(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) = not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.66 inference(monotonicity,[status(thm)],[423])).
% 291.91/187.66 tff(425,plain,
% 291.91/187.66 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.66 inference(quant_inst,[status(thm)],[])).
% 291.91/187.66 tff(426,plain,
% 291.91/187.66 (implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.66 inference(unit_resolution,[status(thm)],[425, 41])).
% 291.91/187.66 tff(427,plain,
% 291.91/187.66 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.91/187.66 inference(quant_inst,[status(thm)],[])).
% 291.91/187.66 tff(428,plain,
% 291.91/187.66 (implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.91/187.66 inference(unit_resolution,[status(thm)],[427, 20])).
% 291.91/187.66 tff(429,plain,
% 291.91/187.66 (or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.91/187.66 inference(symmetry,[status(thm)],[428])).
% 291.91/187.66 tff(430,plain,
% 291.91/187.66 (or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.91/187.66 inference(monotonicity,[status(thm)],[407])).
% 291.91/187.66 tff(431,plain,
% 291.91/187.66 (or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.67 inference(transitivity,[status(thm)],[430, 429, 426, 424])).
% 291.91/187.67 tff(432,plain,
% 291.91/187.67 (not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.91/187.67 inference(transitivity,[status(thm)],[247, 244])).
% 291.91/187.67 tff(433,plain,
% 291.91/187.67 (not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))) = not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.91/187.67 inference(monotonicity,[status(thm)],[432])).
% 291.91/187.67 tff(434,plain,
% 291.91/187.67 (not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))) = not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))),
% 291.91/187.67 inference(symmetry,[status(thm)],[433])).
% 291.91/187.67 tff(435,plain,
% 291.91/187.67 (or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.67 inference(monotonicity,[status(thm)],[434, 431])).
% 291.91/187.67 tff(436,plain,
% 291.91/187.67 (or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) = or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 291.91/187.67 inference(symmetry,[status(thm)],[435])).
% 291.91/187.67 tff(437,plain,
% 291.91/187.67 (implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) = implies(or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.67 inference(monotonicity,[status(thm)],[436])).
% 291.91/187.67 tff(438,plain,
% 291.91/187.67 (implies(or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) = implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.67 inference(symmetry,[status(thm)],[437])).
% 291.91/187.67 tff(439,plain,
% 291.91/187.67 (is_a_theorem(implies(or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) <=> is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.67 inference(monotonicity,[status(thm)],[438])).
% 291.91/187.67 tff(440,plain,
% 291.91/187.67 (^[P: $i, Q: $i, R: $i] : refl(is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))) <=> is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))))),
% 291.91/187.67 inference(bind,[status(th)],[])).
% 291.91/187.67 tff(441,plain,
% 291.91/187.67 (![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))))),
% 291.91/187.67 inference(quant_intro,[status(thm)],[440])).
% 291.91/187.67 tff(442,plain,
% 291.91/187.67 (![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: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 291.91/187.67 inference(rewrite,[status(thm)],[])).
% 291.91/187.67 tff(443,plain,
% 291.91/187.67 (($true <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 291.91/187.67 inference(rewrite,[status(thm)],[])).
% 291.91/187.67 tff(444,axiom,(r4), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_r4')).
% 291.91/187.67 tff(445,plain,
% 291.91/187.67 (r4 <=> $true),
% 291.91/187.67 inference(iff_true,[status(thm)],[444])).
% 291.91/187.67 tff(446,plain,
% 291.91/187.67 ((r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) <=> ($true <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))))),
% 291.91/187.67 inference(monotonicity,[status(thm)],[445])).
% 291.91/187.67 tff(447,plain,
% 291.91/187.67 ((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))))),
% 291.91/187.67 inference(transitivity,[status(thm)],[446, 443])).
% 291.91/187.67 tff(448,plain,
% 291.91/187.67 ((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)))))),
% 291.91/187.67 inference(rewrite,[status(thm)],[])).
% 291.91/187.67 tff(449,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')).
% 291.91/187.67 tff(450,plain,
% 291.91/187.67 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 291.91/187.67 inference(modus_ponens,[status(thm)],[449, 448])).
% 291.91/187.67 tff(451,plain,
% 291.91/187.67 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 291.91/187.67 inference(modus_ponens,[status(thm)],[450, 448])).
% 291.91/187.67 tff(452,plain,
% 291.91/187.67 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 291.91/187.67 inference(modus_ponens,[status(thm)],[451, 447])).
% 291.91/187.67 tff(453,plain,
% 291.91/187.67 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 291.91/187.67 inference(modus_ponens,[status(thm)],[452, 442])).
% 291.91/187.67 tff(454,plain,(
% 291.91/187.67 ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 291.91/187.67 inference(skolemize,[status(sab)],[453])).
% 291.91/187.67 tff(455,plain,
% 291.91/187.67 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 291.91/187.67 inference(modus_ponens,[status(thm)],[454, 441])).
% 291.91/187.67 tff(456,plain,
% 291.91/187.67 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) | is_a_theorem(implies(or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.67 inference(quant_inst,[status(thm)],[])).
% 291.91/187.67 tff(457,plain,
% 291.91/187.67 (is_a_theorem(implies(or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.68 inference(unit_resolution,[status(thm)],[456, 455])).
% 291.91/187.68 tff(458,plain,
% 291.91/187.68 (is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.68 inference(modus_ponens,[status(thm)],[457, 439])).
% 291.91/187.68 tff(459,plain,
% 291.91/187.68 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) = or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.91/187.68 inference(quant_inst,[status(thm)],[])).
% 291.91/187.68 tff(460,plain,
% 291.91/187.68 (implies(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) = or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.68 inference(unit_resolution,[status(thm)],[459, 20])).
% 291.91/187.68 tff(461,plain,
% 291.91/187.68 (or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) = implies(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.68 inference(symmetry,[status(thm)],[460])).
% 291.91/187.68 tff(462,plain,
% 291.91/187.68 (is_a_theorem(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))) <=> is_a_theorem(implies(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.91/187.68 inference(monotonicity,[status(thm)],[461])).
% 291.91/187.68 tff(463,plain,
% 291.91/187.68 (is_a_theorem(implies(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))) <=> is_a_theorem(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.91/187.68 inference(symmetry,[status(thm)],[462])).
% 291.91/187.68 tff(464,plain,
% 291.91/187.68 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.68 inference(quant_inst,[status(thm)],[])).
% 291.91/187.68 tff(465,plain,
% 291.91/187.68 (or(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.68 inference(unit_resolution,[status(thm)],[464, 63])).
% 291.91/187.68 tff(466,plain,
% 291.91/187.68 (or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = or(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 291.91/187.68 inference(monotonicity,[status(thm)],[237])).
% 291.91/187.68 tff(467,plain,
% 291.91/187.68 (or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))) = not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.68 inference(transitivity,[status(thm)],[466, 465])).
% 291.91/187.68 tff(468,plain,
% 291.91/187.68 (or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 291.91/187.68 inference(monotonicity,[status(thm)],[237])).
% 291.91/187.68 tff(469,plain,
% 291.91/187.68 (or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))) = not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))),
% 291.91/187.68 inference(transitivity,[status(thm)],[468, 246])).
% 291.91/187.68 tff(470,plain,
% 291.91/187.68 (implies(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))) = implies(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.68 inference(monotonicity,[status(thm)],[469, 467])).
% 291.91/187.68 tff(471,plain,
% 291.91/187.68 (is_a_theorem(implies(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) <=> is_a_theorem(implies(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.91/187.69 inference(monotonicity,[status(thm)],[470])).
% 291.91/187.69 tff(472,plain,
% 291.91/187.69 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.69 inference(quant_inst,[status(thm)],[])).
% 291.91/187.69 tff(473,plain,
% 291.91/187.69 (is_a_theorem(implies(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.69 inference(unit_resolution,[status(thm)],[472, 399])).
% 291.91/187.69 tff(474,plain,
% 291.91/187.69 (is_a_theorem(implies(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.91/187.69 inference(modus_ponens,[status(thm)],[473, 471])).
% 291.91/187.69 tff(475,plain,
% 291.91/187.69 (is_a_theorem(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.91/187.69 inference(modus_ponens,[status(thm)],[474, 463])).
% 291.91/187.69 tff(476,plain,
% 291.91/187.69 (^[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)))))),
% 291.91/187.69 inference(bind,[status(th)],[])).
% 291.91/187.69 tff(477,plain,
% 291.91/187.69 (![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))))),
% 291.91/187.69 inference(quant_intro,[status(thm)],[476])).
% 291.91/187.69 tff(478,plain,
% 291.91/187.69 (^[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))))))),
% 291.91/187.69 inference(bind,[status(th)],[])).
% 291.91/187.69 tff(479,plain,
% 291.91/187.69 (![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))))),
% 291.91/187.69 inference(quant_intro,[status(thm)],[478])).
% 291.91/187.69 tff(480,plain,
% 291.91/187.69 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 291.91/187.69 inference(rewrite,[status(thm)],[])).
% 291.91/187.69 tff(481,plain,
% 291.91/187.69 (($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)))))),
% 291.91/187.69 inference(rewrite,[status(thm)],[])).
% 291.91/187.69 tff(482,axiom,(modus_ponens), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_modus_ponens')).
% 291.91/187.69 tff(483,plain,
% 291.91/187.69 (modus_ponens <=> $true),
% 291.91/187.69 inference(iff_true,[status(thm)],[482])).
% 291.91/187.69 tff(484,plain,
% 291.91/187.69 ((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))))))),
% 291.91/187.69 inference(monotonicity,[status(thm)],[483])).
% 291.91/187.69 tff(485,plain,
% 291.91/187.69 ((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)))))),
% 291.91/187.69 inference(transitivity,[status(thm)],[484, 481])).
% 291.91/187.69 tff(486,plain,
% 291.91/187.69 ((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))))))),
% 291.91/187.69 inference(rewrite,[status(thm)],[])).
% 291.91/187.69 tff(487,plain,
% 291.91/187.69 ((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))))))),
% 291.91/187.69 inference(rewrite,[status(thm)],[])).
% 291.91/187.69 tff(488,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')).
% 291.91/187.69 tff(489,plain,
% 291.91/187.69 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 291.91/187.69 inference(modus_ponens,[status(thm)],[488, 487])).
% 291.91/187.69 tff(490,plain,
% 291.91/187.69 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 291.91/187.69 inference(modus_ponens,[status(thm)],[489, 486])).
% 291.91/187.69 tff(491,plain,
% 291.91/187.69 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 291.91/187.69 inference(modus_ponens,[status(thm)],[490, 485])).
% 291.91/187.69 tff(492,plain,
% 291.91/187.69 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 291.91/187.69 inference(modus_ponens,[status(thm)],[491, 480])).
% 291.91/187.69 tff(493,plain,(
% 291.91/187.69 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 291.91/187.69 inference(skolemize,[status(sab)],[492])).
% 291.91/187.69 tff(494,plain,
% 291.91/187.69 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 291.91/187.69 inference(modus_ponens,[status(thm)],[493, 479])).
% 291.91/187.69 tff(495,plain,
% 291.91/187.69 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 291.91/187.69 inference(modus_ponens,[status(thm)],[494, 477])).
% 291.91/187.69 tff(496,plain,
% 291.91/187.69 (((~![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(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) | is_a_theorem(or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))))) <=> ((~![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(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) | is_a_theorem(or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))))),
% 291.91/187.69 inference(rewrite,[status(thm)],[])).
% 291.91/187.69 tff(497,plain,
% 291.91/187.69 ((is_a_theorem(or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) <=> ((~is_a_theorem(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) | is_a_theorem(or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))))),
% 291.91/187.70 inference(rewrite,[status(thm)],[])).
% 291.91/187.70 tff(498,plain,
% 291.91/187.70 (((~![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(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))))) <=> ((~![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(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) | is_a_theorem(or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))))),
% 291.91/187.70 inference(monotonicity,[status(thm)],[497])).
% 291.91/187.70 tff(499,plain,
% 291.91/187.70 (((~![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(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))))) <=> ((~![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(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) | is_a_theorem(or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))))),
% 291.91/187.70 inference(transitivity,[status(thm)],[498, 496])).
% 291.91/187.70 tff(500,plain,
% 291.91/187.70 ((~![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(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))))),
% 291.91/187.70 inference(quant_inst,[status(thm)],[])).
% 291.91/187.70 tff(501,plain,
% 291.91/187.70 ((~![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(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) | is_a_theorem(or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.91/187.71 inference(modus_ponens,[status(thm)],[500, 499])).
% 291.91/187.71 tff(502,plain,
% 291.91/187.71 ((~is_a_theorem(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))) | is_a_theorem(or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))), not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), not(and(not(and(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))), or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.91/187.71 inference(unit_resolution,[status(thm)],[501, 495])).
% 291.91/187.71 tff(503,plain,
% 291.91/187.71 (is_a_theorem(or(not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(and(not(not(not(and(Q!1, R!0)))), not(or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))), or(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))), and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))),
% 291.91/187.71 inference(unit_resolution,[status(thm)],[502, 475, 458])).
% 291.91/187.71 tff(504,plain,
% 291.91/187.71 (is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))),
% 291.91/187.71 inference(modus_ponens,[status(thm)],[503, 416])).
% 291.91/187.71 tff(505,plain,
% 291.91/187.71 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(Q!1, R!0)), not(and(R!0, P!2))) = or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))))),
% 291.91/187.71 inference(quant_inst,[status(thm)],[])).
% 291.91/187.71 tff(506,plain,
% 291.91/187.71 (implies(not(and(Q!1, R!0)), not(and(R!0, P!2))) = or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))),
% 291.91/187.71 inference(unit_resolution,[status(thm)],[505, 20])).
% 291.91/187.71 tff(507,plain,
% 291.91/187.71 (or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))) = implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))),
% 291.91/187.71 inference(symmetry,[status(thm)],[506])).
% 291.91/187.71 tff(508,plain,
% 291.91/187.71 (or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))) = or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))),
% 291.91/187.71 inference(monotonicity,[status(thm)],[507])).
% 291.91/187.71 tff(509,plain,
% 291.91/187.71 (or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))) = or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))))),
% 291.91/187.71 inference(symmetry,[status(thm)],[508])).
% 291.91/187.71 tff(510,plain,
% 291.91/187.71 (implies(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = implies(or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.91/187.71 inference(monotonicity,[status(thm)],[509])).
% 291.91/187.71 tff(511,plain,
% 291.91/187.71 (or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))) = implies(or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))),
% 291.91/187.71 inference(transitivity,[status(thm)],[421, 510])).
% 291.91/187.71 tff(512,plain,
% 291.91/187.71 (is_a_theorem(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) <=> is_a_theorem(implies(or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.91/187.71 inference(monotonicity,[status(thm)],[511])).
% 291.91/187.71 tff(513,plain,
% 291.91/187.71 (is_a_theorem(implies(or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) <=> is_a_theorem(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.91/187.71 inference(symmetry,[status(thm)],[512])).
% 291.91/187.71 tff(514,plain,
% 291.91/187.71 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) | is_a_theorem(implies(or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.91/187.71 inference(quant_inst,[status(thm)],[])).
% 291.91/187.71 tff(515,plain,
% 291.91/187.71 (is_a_theorem(implies(or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.91/187.71 inference(unit_resolution,[status(thm)],[514, 455])).
% 291.91/187.71 tff(516,plain,
% 291.91/187.71 (is_a_theorem(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 291.91/187.71 inference(modus_ponens,[status(thm)],[515, 513])).
% 291.91/187.71 tff(517,plain,
% 291.91/187.71 (((~![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(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))))) <=> ((~![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(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))))),
% 291.91/187.71 inference(rewrite,[status(thm)],[])).
% 291.91/187.71 tff(518,plain,
% 291.91/187.71 ((is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) | (~is_a_theorem(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) | (~is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))))) <=> ((~is_a_theorem(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))))),
% 291.91/187.71 inference(rewrite,[status(thm)],[])).
% 291.91/187.71 tff(519,plain,
% 291.91/187.71 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) | (~is_a_theorem(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) | (~is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))))) <=> ((~![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(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))))))),
% 291.91/187.71 inference(monotonicity,[status(thm)],[518])).
% 291.91/187.71 tff(520,plain,
% 291.91/187.71 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) | (~is_a_theorem(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) | (~is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))))) <=> ((~![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(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))))),
% 291.91/187.72 inference(transitivity,[status(thm)],[519, 517])).
% 291.91/187.72 tff(521,plain,
% 291.91/187.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) | (~is_a_theorem(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) | (~is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))))))),
% 291.91/187.72 inference(quant_inst,[status(thm)],[])).
% 291.91/187.72 tff(522,plain,
% 291.91/187.72 ((~![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(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))))),
% 291.91/187.72 inference(modus_ponens,[status(thm)],[521, 520])).
% 291.91/187.72 tff(523,plain,
% 291.91/187.72 (is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))))),
% 291.91/187.72 inference(unit_resolution,[status(thm)],[522, 495, 516])).
% 291.91/187.72 tff(524,plain,
% 291.91/187.72 (is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))),
% 291.91/187.72 inference(unit_resolution,[status(thm)],[523, 504])).
% 291.91/187.72 tff(525,plain,
% 291.91/187.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))))),
% 291.91/187.72 inference(rewrite,[status(thm)],[])).
% 291.91/187.72 tff(526,plain,
% 291.91/187.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))))),
% 291.91/187.72 inference(quant_inst,[status(thm)],[])).
% 291.91/187.72 tff(527,plain,
% 291.91/187.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))))),
% 291.91/187.73 inference(modus_ponens,[status(thm)],[526, 525])).
% 291.91/187.73 tff(528,plain,
% 291.91/187.73 (is_a_theorem(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))), not(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))), or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))))),
% 291.91/187.73 inference(unit_resolution,[status(thm)],[527, 495])).
% 291.91/187.73 tff(529,plain,
% 291.91/187.73 (is_a_theorem(or(and(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))), not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))),
% 291.91/187.73 inference(unit_resolution,[status(thm)],[528, 524, 402])).
% 291.91/187.73 tff(530,plain,
% 291.91/187.73 (is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))),
% 291.91/187.73 inference(modus_ponens,[status(thm)],[529, 377])).
% 291.91/187.73 tff(531,plain,
% 291.91/187.73 (not(and(not(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2)))))))), not(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) = or(not(or(not(not(and(Q!1, R!0))), not(and(not(not(implies(P!2, Q!1))), not(not(and(R!0, P!2))))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.91/187.73 inference(symmetry,[status(thm)],[207])).
% 291.91/187.73 tff(532,plain,
% 291.91/187.73 (implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 291.91/187.73 inference(transitivity,[status(thm)],[195, 197, 200, 204, 531, 208, 210])).
% 291.91/187.73 tff(533,plain,
% 291.91/187.73 (is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))) <=> is_a_theorem(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))),
% 291.91/187.73 inference(monotonicity,[status(thm)],[532])).
% 291.91/187.73 tff(534,plain,
% 291.91/187.73 (is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))) <=> is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))),
% 291.91/187.73 inference(monotonicity,[status(thm)],[196])).
% 291.91/187.73 tff(535,plain,
% 291.91/187.73 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) | is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 291.91/187.73 inference(quant_inst,[status(thm)],[])).
% 291.91/187.73 tff(536,plain,
% 291.91/187.73 (is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), or(not(implies(P!2, Q!1)), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 291.91/187.73 inference(unit_resolution,[status(thm)],[535, 455])).
% 291.91/187.73 tff(537,plain,
% 291.91/187.73 (is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))),
% 291.91/187.73 inference(modus_ponens,[status(thm)],[536, 534])).
% 291.91/187.73 tff(538,plain,
% 291.91/187.73 (is_a_theorem(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))),
% 291.91/187.73 inference(modus_ponens,[status(thm)],[537, 533])).
% 291.91/187.73 tff(539,plain,
% 291.91/187.73 (((~![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(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) | is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))))) <=> ((~![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(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) | is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))))),
% 291.91/187.73 inference(rewrite,[status(thm)],[])).
% 291.91/187.73 tff(540,plain,
% 291.91/187.73 ((is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))) <=> ((~is_a_theorem(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) | is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))))),
% 291.91/187.73 inference(rewrite,[status(thm)],[])).
% 291.91/187.73 tff(541,plain,
% 291.91/187.73 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))))) <=> ((~![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(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) | is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))))),
% 291.91/187.73 inference(monotonicity,[status(thm)],[540])).
% 291.91/187.73 tff(542,plain,
% 292.02/187.74 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))))) <=> ((~![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(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) | is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))))),
% 292.02/187.74 inference(transitivity,[status(thm)],[541, 539])).
% 292.02/187.74 tff(543,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(544,plain,
% 292.02/187.74 ((~![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(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))) | is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))),
% 292.02/187.74 inference(modus_ponens,[status(thm)],[543, 542])).
% 292.02/187.74 tff(545,plain,
% 292.02/187.74 (is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))), not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[544, 495, 538])).
% 292.02/187.74 tff(546,plain,
% 292.02/187.74 (is_a_theorem(not(or(not(or(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))), not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))))), not(or(not(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))), not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[545, 530])).
% 292.02/187.74 tff(547,plain,
% 292.02/187.74 (is_a_theorem(equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 292.02/187.74 inference(modus_ponens,[status(thm)],[546, 366])).
% 292.02/187.74 tff(548,plain,
% 292.02/187.74 (^[X: $i, Y: $i] : refl(((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 292.02/187.74 inference(bind,[status(th)],[])).
% 292.02/187.74 tff(549,plain,
% 292.02/187.74 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 292.02/187.74 inference(quant_intro,[status(thm)],[548])).
% 292.02/187.74 tff(550,plain,
% 292.02/187.74 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 292.02/187.74 inference(rewrite,[status(thm)],[])).
% 292.02/187.74 tff(551,plain,
% 292.02/187.74 (($true <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 292.02/187.74 inference(rewrite,[status(thm)],[])).
% 292.02/187.74 tff(552,axiom,(substitution_of_equivalents), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','substitution_of_equivalents')).
% 292.02/187.74 tff(553,plain,
% 292.02/187.74 (substitution_of_equivalents <=> $true),
% 292.02/187.74 inference(iff_true,[status(thm)],[552])).
% 292.02/187.74 tff(554,plain,
% 292.02/187.74 ((substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) <=> ($true <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[553])).
% 292.02/187.74 tff(555,plain,
% 292.02/187.74 ((substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 292.02/187.74 inference(transitivity,[status(thm)],[554, 551])).
% 292.02/187.74 tff(556,plain,
% 292.02/187.74 ((substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) <=> (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 292.02/187.74 inference(rewrite,[status(thm)],[])).
% 292.02/187.74 tff(557,plain,
% 292.02/187.74 ((substitution_of_equivalents <=> ![X: $i, Y: $i] : (is_a_theorem(equiv(X, Y)) => (X = Y))) <=> (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 292.02/187.74 inference(rewrite,[status(thm)],[])).
% 292.02/187.74 tff(558,axiom,(substitution_of_equivalents <=> ![X: $i, Y: $i] : (is_a_theorem(equiv(X, Y)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','substitution_of_equivalents')).
% 292.02/187.74 tff(559,plain,
% 292.02/187.74 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 292.02/187.74 inference(modus_ponens,[status(thm)],[558, 557])).
% 292.02/187.74 tff(560,plain,
% 292.02/187.74 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 292.02/187.74 inference(modus_ponens,[status(thm)],[559, 556])).
% 292.02/187.74 tff(561,plain,
% 292.02/187.74 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 292.02/187.74 inference(modus_ponens,[status(thm)],[560, 555])).
% 292.02/187.74 tff(562,plain,
% 292.02/187.74 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 292.02/187.74 inference(modus_ponens,[status(thm)],[561, 550])).
% 292.02/187.74 tff(563,plain,(
% 292.02/187.74 ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 292.02/187.74 inference(skolemize,[status(sab)],[562])).
% 292.02/187.74 tff(564,plain,
% 292.02/187.74 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 292.02/187.74 inference(modus_ponens,[status(thm)],[563, 549])).
% 292.02/187.74 tff(565,plain,
% 292.02/187.74 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 292.02/187.74 inference(rewrite,[status(thm)],[])).
% 292.02/187.74 tff(566,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(567,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 292.02/187.74 inference(modus_ponens,[status(thm)],[566, 565])).
% 292.02/187.74 tff(568,plain,
% 292.02/187.74 ((~is_a_theorem(equiv(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))), or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) | (not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[567, 564])).
% 292.02/187.74 tff(569,plain,
% 292.02/187.74 (not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))) = or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[568, 547])).
% 292.02/187.74 tff(570,plain,
% 292.02/187.74 (or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))) = not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 292.02/187.74 inference(symmetry,[status(thm)],[569])).
% 292.02/187.74 tff(571,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(P!2), Q!1), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))) = or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(572,plain,
% 292.02/187.74 (implies(or(not(P!2), Q!1), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))) = or(not(or(not(P!2), Q!1)), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[571, 20])).
% 292.02/187.74 tff(573,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))) = not(or(not(not(and(Q!1, R!0))), not(not(or(not(R!0), not(P!2)))))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(574,plain,
% 292.02/187.74 (and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))) = not(or(not(not(and(Q!1, R!0))), not(not(or(not(R!0), not(P!2))))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[573, 100])).
% 292.02/187.74 tff(575,plain,
% 292.02/187.74 (not(or(not(not(and(Q!1, R!0))), not(not(or(not(R!0), not(P!2)))))) = and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2))))),
% 292.02/187.74 inference(symmetry,[status(thm)],[574])).
% 292.02/187.74 tff(576,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(R!0, P!2) = not(or(not(R!0), not(P!2))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(577,plain,
% 292.02/187.74 (and(R!0, P!2) = not(or(not(R!0), not(P!2)))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[576, 100])).
% 292.02/187.74 tff(578,plain,
% 292.02/187.74 (not(or(not(R!0), not(P!2))) = and(R!0, P!2)),
% 292.02/187.74 inference(symmetry,[status(thm)],[577])).
% 292.02/187.74 tff(579,plain,
% 292.02/187.74 (not(not(or(not(R!0), not(P!2)))) = not(and(R!0, P!2))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[578])).
% 292.02/187.74 tff(580,plain,
% 292.02/187.74 (or(not(not(and(Q!1, R!0))), not(not(or(not(R!0), not(P!2))))) = or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[579])).
% 292.02/187.74 tff(581,plain,
% 292.02/187.74 (or(not(not(and(Q!1, R!0))), not(not(or(not(R!0), not(P!2))))) = implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))),
% 292.02/187.74 inference(transitivity,[status(thm)],[580, 507])).
% 292.02/187.74 tff(582,plain,
% 292.02/187.74 (not(or(not(not(and(Q!1, R!0))), not(not(or(not(R!0), not(P!2)))))) = not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[581])).
% 292.02/187.74 tff(583,plain,
% 292.02/187.74 (not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))) = not(or(not(not(and(Q!1, R!0))), not(not(or(not(R!0), not(P!2))))))),
% 292.02/187.74 inference(symmetry,[status(thm)],[582])).
% 292.02/187.74 tff(584,plain,
% 292.02/187.74 (not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))) = and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2))))),
% 292.02/187.74 inference(transitivity,[status(thm)],[583, 575])).
% 292.02/187.74 tff(585,plain,
% 292.02/187.74 (not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) = not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[584])).
% 292.02/187.74 tff(586,plain,
% 292.02/187.74 (not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2))))) = not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 292.02/187.74 inference(symmetry,[status(thm)],[585])).
% 292.02/187.74 tff(587,plain,
% 292.02/187.74 (implies(or(not(P!2), Q!1), not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))) = implies(or(not(P!2), Q!1), not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[586])).
% 292.02/187.74 tff(588,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(P!2), Q!1), not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))) = not(and(or(not(P!2), Q!1), not(not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(589,plain,
% 292.02/187.74 (implies(or(not(P!2), Q!1), not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))) = not(and(or(not(P!2), Q!1), not(not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2))))))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[588, 41])).
% 292.02/187.74 tff(590,plain,
% 292.02/187.74 (not(and(or(not(P!2), Q!1), not(not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))))) = implies(or(not(P!2), Q!1), not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2))))))),
% 292.02/187.74 inference(symmetry,[status(thm)],[589])).
% 292.02/187.74 tff(591,plain,
% 292.02/187.74 (and(not(not(or(not(P!2), not(not(Q!1))))), not(not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2))))))) = and(or(not(P!2), Q!1), not(not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[105])).
% 292.02/187.74 tff(592,plain,
% 292.02/187.74 (not(and(not(not(or(not(P!2), not(not(Q!1))))), not(not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))))) = not(and(or(not(P!2), Q!1), not(not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2))))))))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[591])).
% 292.02/187.74 tff(593,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(P!2), not(not(Q!1)))), not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))) = not(and(not(not(or(not(P!2), not(not(Q!1))))), not(not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(594,plain,
% 292.02/187.74 (or(not(or(not(P!2), not(not(Q!1)))), not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))) = not(and(not(not(or(not(P!2), not(not(Q!1))))), not(not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2))))))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[593, 63])).
% 292.02/187.74 tff(595,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(P!2), not(not(Q!1))), not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))) = or(not(or(not(P!2), not(not(Q!1)))), not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(596,plain,
% 292.02/187.74 (implies(or(not(P!2), not(not(Q!1))), not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))) = or(not(or(not(P!2), not(not(Q!1)))), not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2))))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[595, 20])).
% 292.02/187.74 tff(597,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(Q!1, R!0) = not(or(not(Q!1), not(R!0))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(598,plain,
% 292.02/187.74 (and(Q!1, R!0) = not(or(not(Q!1), not(R!0)))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[597, 100])).
% 292.02/187.74 tff(599,plain,
% 292.02/187.74 (not(or(not(Q!1), not(R!0))) = and(Q!1, R!0)),
% 292.02/187.74 inference(symmetry,[status(thm)],[598])).
% 292.02/187.74 tff(600,plain,
% 292.02/187.74 (not(not(or(not(Q!1), not(R!0)))) = not(and(Q!1, R!0))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[599])).
% 292.02/187.74 tff(601,plain,
% 292.02/187.74 (and(not(not(or(not(Q!1), not(R!0)))), not(or(not(R!0), not(P!2)))) = and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2))))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[600])).
% 292.02/187.74 tff(602,plain,
% 292.02/187.74 (and(not(not(or(not(Q!1), not(R!0)))), not(or(not(R!0), not(P!2)))) = not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))),
% 292.02/187.74 inference(transitivity,[status(thm)],[601, 574, 582])).
% 292.02/187.74 tff(603,plain,
% 292.02/187.74 (not(and(not(not(or(not(Q!1), not(R!0)))), not(or(not(R!0), not(P!2))))) = not(not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[602])).
% 292.02/187.74 tff(604,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(P!2))) = not(and(not(not(or(not(Q!1), not(R!0)))), not(or(not(R!0), not(P!2))))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(605,plain,
% 292.02/187.74 (or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(P!2))) = not(and(not(not(or(not(Q!1), not(R!0)))), not(or(not(R!0), not(P!2)))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[604, 63])).
% 292.02/187.74 tff(606,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(Q!1), not(R!0)), or(not(R!0), not(P!2))) = or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(P!2))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(607,plain,
% 292.02/187.74 (implies(or(not(Q!1), not(R!0)), or(not(R!0), not(P!2))) = or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(P!2)))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[606, 20])).
% 292.02/187.74 tff(608,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))) = and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(609,plain,
% 292.02/187.74 (equiv(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))) = and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[608, 133])).
% 292.02/187.74 tff(610,plain,
% 292.02/187.74 (and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))) = equiv(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1)))),
% 292.02/187.74 inference(symmetry,[status(thm)],[609])).
% 292.02/187.74 tff(611,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))) = or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(612,plain,
% 292.02/187.74 (implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))) = or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[611, 20])).
% 292.02/187.74 tff(613,plain,
% 292.02/187.74 (or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))) = implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))),
% 292.02/187.74 inference(symmetry,[status(thm)],[612])).
% 292.02/187.74 tff(614,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))) = or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(615,plain,
% 292.02/187.74 (implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))) = or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[614, 20])).
% 292.02/187.74 tff(616,plain,
% 292.02/187.74 (or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))) = implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1)))),
% 292.02/187.74 inference(symmetry,[status(thm)],[615])).
% 292.02/187.74 tff(617,plain,
% 292.02/187.74 (and(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))) = and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))),
% 292.02/187.74 inference(monotonicity,[status(thm)],[616, 613])).
% 292.02/187.74 tff(618,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))) = not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))))))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.74 tff(619,plain,
% 292.02/187.74 (and(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))) = not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))))),
% 292.02/187.74 inference(unit_resolution,[status(thm)],[618, 100])).
% 292.02/187.74 tff(620,plain,
% 292.02/187.74 (not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))))) = and(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))),
% 292.02/187.74 inference(symmetry,[status(thm)],[619])).
% 292.02/187.74 tff(621,plain,
% 292.02/187.74 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(Q!1, not(R!0)) = or(not(Q!1), not(R!0)))),
% 292.02/187.74 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(622,plain,
% 292.02/187.75 (implies(Q!1, not(R!0)) = or(not(Q!1), not(R!0))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[621, 20])).
% 292.02/187.75 tff(623,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(Q!1, not(R!0)) = not(and(Q!1, not(not(R!0)))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(624,plain,
% 292.02/187.75 (implies(Q!1, not(R!0)) = not(and(Q!1, not(not(R!0))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[623, 41])).
% 292.02/187.75 tff(625,plain,
% 292.02/187.75 (not(and(Q!1, not(not(R!0)))) = implies(Q!1, not(R!0))),
% 292.02/187.75 inference(symmetry,[status(thm)],[624])).
% 292.02/187.75 tff(626,plain,
% 292.02/187.75 (not(and(Q!1, not(not(R!0)))) = or(not(Q!1), not(R!0))),
% 292.02/187.75 inference(transitivity,[status(thm)],[625, 622])).
% 292.02/187.75 tff(627,plain,
% 292.02/187.75 (or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))) = or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[626])).
% 292.02/187.75 tff(628,plain,
% 292.02/187.75 (not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))) = not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[627])).
% 292.02/187.75 tff(629,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(R!0), not(Q!1)) = not(and(not(not(R!0)), not(not(Q!1)))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(630,plain,
% 292.02/187.75 (or(not(R!0), not(Q!1)) = not(and(not(not(R!0)), not(not(Q!1))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[629, 63])).
% 292.02/187.75 tff(631,plain,
% 292.02/187.75 (not(and(not(not(R!0)), not(not(Q!1)))) = or(not(R!0), not(Q!1))),
% 292.02/187.75 inference(symmetry,[status(thm)],[630])).
% 292.02/187.75 tff(632,plain,
% 292.02/187.75 (or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))) = or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[631])).
% 292.02/187.75 tff(633,plain,
% 292.02/187.75 (not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))) = not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[632])).
% 292.02/187.75 tff(634,plain,
% 292.02/187.75 (or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[633, 628])).
% 292.02/187.75 tff(635,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = not(and(not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(636,plain,
% 292.02/187.75 (or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = not(and(not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[635, 63])).
% 292.02/187.75 tff(637,plain,
% 292.02/187.75 (not(and(not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))) = or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[636])).
% 292.02/187.75 tff(638,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(R!0)), not(not(Q!1))) = not(or(not(not(not(R!0))), not(not(not(Q!1))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(639,plain,
% 292.02/187.75 (and(not(not(R!0)), not(not(Q!1))) = not(or(not(not(not(R!0))), not(not(not(Q!1)))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[638, 100])).
% 292.02/187.75 tff(640,plain,
% 292.02/187.75 (not(or(not(not(not(R!0))), not(not(not(Q!1))))) = and(not(not(R!0)), not(not(Q!1)))),
% 292.02/187.75 inference(symmetry,[status(thm)],[639])).
% 292.02/187.75 tff(641,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(Q!1), not(R!0)) = not(and(not(not(Q!1)), not(not(R!0)))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(642,plain,
% 292.02/187.75 (or(not(Q!1), not(R!0)) = not(and(not(not(Q!1)), not(not(R!0))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[641, 63])).
% 292.02/187.75 tff(643,plain,
% 292.02/187.75 (not(and(not(not(Q!1)), not(not(R!0)))) = or(not(Q!1), not(R!0))),
% 292.02/187.75 inference(symmetry,[status(thm)],[642])).
% 292.02/187.75 tff(644,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(Q!1)), not(not(R!0))) = not(or(not(not(not(Q!1))), not(not(not(R!0))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(645,plain,
% 292.02/187.75 (and(not(not(Q!1)), not(not(R!0))) = not(or(not(not(not(Q!1))), not(not(not(R!0)))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[644, 100])).
% 292.02/187.75 tff(646,plain,
% 292.02/187.75 (not(or(not(not(not(Q!1))), not(not(not(R!0))))) = and(not(not(Q!1)), not(not(R!0)))),
% 292.02/187.75 inference(symmetry,[status(thm)],[645])).
% 292.02/187.75 tff(647,plain,
% 292.02/187.75 (not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))) = not(and(not(not(Q!1)), not(not(R!0))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[646])).
% 292.02/187.75 tff(648,plain,
% 292.02/187.75 (not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))) = or(not(Q!1), not(R!0))),
% 292.02/187.75 inference(transitivity,[status(thm)],[647, 643])).
% 292.02/187.75 tff(649,plain,
% 292.02/187.75 (and(not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))), not(or(not(not(not(R!0))), not(not(not(Q!1)))))) = and(or(not(Q!1), not(R!0)), and(not(not(R!0)), not(not(Q!1))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[648, 640])).
% 292.02/187.75 tff(650,plain,
% 292.02/187.75 (and(or(not(Q!1), not(R!0)), and(not(not(R!0)), not(not(Q!1)))) = and(not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))), not(or(not(not(not(R!0))), not(not(not(Q!1))))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[649])).
% 292.02/187.75 tff(651,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(Q!1), not(R!0)), and(not(not(R!0)), not(not(Q!1)))) = not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(652,plain,
% 292.02/187.75 (and(or(not(Q!1), not(R!0)), and(not(not(R!0)), not(not(Q!1)))) = not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[651, 100])).
% 292.02/187.75 tff(653,plain,
% 292.02/187.75 (not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))) = and(or(not(Q!1), not(R!0)), and(not(not(R!0)), not(not(Q!1))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[652])).
% 292.02/187.75 tff(654,plain,
% 292.02/187.75 (not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))) = and(not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))), not(or(not(not(not(R!0))), not(not(not(Q!1))))))),
% 292.02/187.75 inference(transitivity,[status(thm)],[653, 650])).
% 292.02/187.75 tff(655,plain,
% 292.02/187.75 (not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))) = not(and(not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))), not(or(not(not(not(R!0))), not(not(not(Q!1)))))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[654])).
% 292.02/187.75 tff(656,plain,
% 292.02/187.75 (not(and(not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))), not(or(not(not(not(R!0))), not(not(not(Q!1))))))) = not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[655])).
% 292.02/187.75 tff(657,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))) = not(and(not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))), not(or(not(not(not(R!0))), not(not(not(Q!1))))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(658,plain,
% 292.02/187.75 (or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))) = not(and(not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))), not(or(not(not(not(R!0))), not(not(not(Q!1)))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[657, 63])).
% 292.02/187.75 tff(659,plain,
% 292.02/187.75 (or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))) = not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))),
% 292.02/187.75 inference(transitivity,[status(thm)],[658, 656])).
% 292.02/187.75 tff(660,plain,
% 292.02/187.75 (and(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))) = and(not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[659])).
% 292.02/187.75 tff(661,plain,
% 292.02/187.75 (not(and(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))) = not(and(not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[660])).
% 292.02/187.75 tff(662,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = not(and(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(663,plain,
% 292.02/187.75 (implies(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = not(and(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[662, 41])).
% 292.02/187.75 tff(664,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = or(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(665,plain,
% 292.02/187.75 (implies(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = or(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[664, 20])).
% 292.02/187.75 tff(666,plain,
% 292.02/187.75 (or(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = implies(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[665])).
% 292.02/187.75 tff(667,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(not(not(R!0))), not(not(not(Q!1)))) = not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(668,plain,
% 292.02/187.75 (or(not(not(not(R!0))), not(not(not(Q!1)))) = not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[667, 63])).
% 292.02/187.75 tff(669,plain,
% 292.02/187.75 (not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))) = or(not(not(not(R!0))), not(not(not(Q!1))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[668])).
% 292.02/187.75 tff(670,plain,
% 292.02/187.75 (or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))) = or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1)))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[669])).
% 292.02/187.75 tff(671,plain,
% 292.02/187.75 (not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))) = not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[670])).
% 292.02/187.75 tff(672,plain,
% 292.02/187.75 (or(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = or(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[671])).
% 292.02/187.75 tff(673,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = not(and(not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(674,plain,
% 292.02/187.75 (or(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = not(and(not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[673, 63])).
% 292.02/187.75 tff(675,plain,
% 292.02/187.75 (not(and(not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))) = or(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[674])).
% 292.02/187.75 tff(676,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(not(not(Q!1))), not(not(not(R!0))))) = or(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(not(not(Q!1))), not(not(not(R!0))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(677,plain,
% 292.02/187.75 (implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(not(not(Q!1))), not(not(not(R!0))))) = or(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(not(not(Q!1))), not(not(not(R!0)))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[676, 20])).
% 292.02/187.75 tff(678,plain,
% 292.02/187.75 (or(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(not(not(Q!1))), not(not(not(R!0))))) = implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(not(not(Q!1))), not(not(not(R!0)))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[677])).
% 292.02/187.75 tff(679,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))) = not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(680,plain,
% 292.02/187.75 (and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))) = not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[679, 100])).
% 292.02/187.75 tff(681,plain,
% 292.02/187.75 (not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[680])).
% 292.02/187.75 tff(682,plain,
% 292.02/187.75 (or(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(not(not(Q!1))), not(not(not(R!0))))) = or(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))), or(not(not(not(Q!1))), not(not(not(R!0)))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[681])).
% 292.02/187.75 tff(683,plain,
% 292.02/187.75 (or(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))), or(not(not(not(Q!1))), not(not(not(R!0))))) = or(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(not(not(Q!1))), not(not(not(R!0)))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[682])).
% 292.02/187.75 tff(684,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))), or(not(not(not(Q!1))), not(not(not(R!0))))) = not(and(not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))), not(or(not(not(not(Q!1))), not(not(not(R!0))))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(685,plain,
% 292.02/187.75 (or(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))), or(not(not(not(Q!1))), not(not(not(R!0))))) = not(and(not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))), not(or(not(not(not(Q!1))), not(not(not(R!0)))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[684, 63])).
% 292.02/187.75 tff(686,plain,
% 292.02/187.75 (not(and(not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))), not(or(not(not(not(Q!1))), not(not(not(R!0))))))) = or(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))), or(not(not(not(Q!1))), not(not(not(R!0)))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[685])).
% 292.02/187.75 tff(687,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(R!0), not(Q!1)), not(or(not(not(not(Q!1))), not(not(not(R!0)))))) = not(or(not(or(not(R!0), not(Q!1))), not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(688,plain,
% 292.02/187.75 (and(or(not(R!0), not(Q!1)), not(or(not(not(not(Q!1))), not(not(not(R!0)))))) = not(or(not(or(not(R!0), not(Q!1))), not(not(or(not(not(not(Q!1))), not(not(not(R!0))))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[687, 100])).
% 292.02/187.75 tff(689,plain,
% 292.02/187.75 (not(or(not(or(not(R!0), not(Q!1))), not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))))) = and(or(not(R!0), not(Q!1)), not(or(not(not(not(Q!1))), not(not(not(R!0))))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[688])).
% 292.02/187.75 tff(690,plain,
% 292.02/187.75 (or(not(or(not(R!0), not(Q!1))), not(not(or(not(not(not(Q!1))), not(not(not(R!0))))))) = or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[648])).
% 292.02/187.75 tff(691,plain,
% 292.02/187.75 (not(or(not(or(not(R!0), not(Q!1))), not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))))) = not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[690])).
% 292.02/187.75 tff(692,plain,
% 292.02/187.75 (not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))) = not(or(not(or(not(R!0), not(Q!1))), not(not(or(not(not(not(Q!1))), not(not(not(R!0))))))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[691])).
% 292.02/187.75 tff(693,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))) = not(and(or(not(R!0), not(Q!1)), not(or(not(Q!1), not(R!0))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(694,plain,
% 292.02/187.75 (implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))) = not(and(or(not(R!0), not(Q!1)), not(or(not(Q!1), not(R!0)))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[693, 41])).
% 292.02/187.75 tff(695,plain,
% 292.02/187.75 (not(and(or(not(R!0), not(Q!1)), not(or(not(Q!1), not(R!0))))) = implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))),
% 292.02/187.75 inference(symmetry,[status(thm)],[694])).
% 292.02/187.75 tff(696,plain,
% 292.02/187.75 (and(not(and(not(not(R!0)), not(not(Q!1)))), not(or(not(Q!1), not(R!0)))) = and(or(not(R!0), not(Q!1)), not(or(not(Q!1), not(R!0))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[631])).
% 292.02/187.75 tff(697,plain,
% 292.02/187.75 (not(and(not(and(not(not(R!0)), not(not(Q!1)))), not(or(not(Q!1), not(R!0))))) = not(and(or(not(R!0), not(Q!1)), not(or(not(Q!1), not(R!0)))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[696])).
% 292.02/187.75 tff(698,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(not(not(R!0)), not(not(Q!1))), or(not(Q!1), not(R!0))) = not(and(not(and(not(not(R!0)), not(not(Q!1)))), not(or(not(Q!1), not(R!0))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(699,plain,
% 292.02/187.75 (or(and(not(not(R!0)), not(not(Q!1))), or(not(Q!1), not(R!0))) = not(and(not(and(not(not(R!0)), not(not(Q!1)))), not(or(not(Q!1), not(R!0)))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[698, 63])).
% 292.02/187.75 tff(700,plain,
% 292.02/187.75 (or(not(or(not(not(not(R!0))), not(not(not(Q!1))))), not(not(or(not(not(not(Q!1))), not(not(not(R!0))))))) = or(and(not(not(R!0)), not(not(Q!1))), or(not(Q!1), not(R!0)))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[640, 648])).
% 292.02/187.75 tff(701,plain,
% 292.02/187.75 (or(not(or(not(not(not(R!0))), not(not(not(Q!1))))), not(not(or(not(not(not(Q!1))), not(not(not(R!0))))))) = or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))),
% 292.02/187.75 inference(transitivity,[status(thm)],[700, 699, 697, 695, 612])).
% 292.02/187.75 tff(702,plain,
% 292.02/187.75 (not(or(not(or(not(not(not(R!0))), not(not(not(Q!1))))), not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))))) = not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[701])).
% 292.02/187.75 tff(703,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(not(not(R!0))), not(not(not(Q!1)))), not(or(not(not(not(Q!1))), not(not(not(R!0)))))) = not(or(not(or(not(not(not(R!0))), not(not(not(Q!1))))), not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(704,plain,
% 292.02/187.75 (and(or(not(not(not(R!0))), not(not(not(Q!1)))), not(or(not(not(not(Q!1))), not(not(not(R!0)))))) = not(or(not(or(not(not(not(R!0))), not(not(not(Q!1))))), not(not(or(not(not(not(Q!1))), not(not(not(R!0))))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[703, 100])).
% 292.02/187.75 tff(705,plain,
% 292.02/187.75 (and(not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))), not(or(not(not(not(Q!1))), not(not(not(R!0)))))) = and(or(not(not(not(R!0))), not(not(not(Q!1)))), not(or(not(not(not(Q!1))), not(not(not(R!0))))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[669])).
% 292.02/187.75 tff(706,plain,
% 292.02/187.75 (and(not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))), not(or(not(not(not(Q!1))), not(not(not(R!0)))))) = and(or(not(R!0), not(Q!1)), not(or(not(not(not(Q!1))), not(not(not(R!0))))))),
% 292.02/187.75 inference(transitivity,[status(thm)],[705, 704, 702, 692, 689])).
% 292.02/187.75 tff(707,plain,
% 292.02/187.75 (not(and(not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))), not(or(not(not(not(Q!1))), not(not(not(R!0))))))) = not(and(or(not(R!0), not(Q!1)), not(or(not(not(not(Q!1))), not(not(not(R!0)))))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[706])).
% 292.02/187.75 tff(708,plain,
% 292.02/187.75 (not(and(or(not(R!0), not(Q!1)), not(or(not(not(not(Q!1))), not(not(not(R!0))))))) = not(and(not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))), not(or(not(not(not(Q!1))), not(not(not(R!0)))))))),
% 292.02/187.75 inference(symmetry,[status(thm)],[707])).
% 292.02/187.75 tff(709,plain,
% 292.02/187.75 (not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))) = and(or(not(R!0), not(Q!1)), not(or(not(not(not(Q!1))), not(not(not(R!0))))))),
% 292.02/187.75 inference(transitivity,[status(thm)],[628, 692, 689])).
% 292.02/187.75 tff(710,plain,
% 292.02/187.75 (not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = not(and(or(not(R!0), not(Q!1)), not(or(not(not(not(Q!1))), not(not(not(R!0)))))))),
% 292.02/187.75 inference(monotonicity,[status(thm)],[709])).
% 292.02/187.75 tff(711,plain,
% 292.02/187.75 (not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(not(not(Q!1))), not(not(not(R!0)))))),
% 292.02/187.75 inference(transitivity,[status(thm)],[710, 708, 686, 683, 678])).
% 292.02/187.75 tff(712,plain,
% 292.02/187.75 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(not(not(Q!1))), not(not(not(R!0)))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = not(and(or(not(not(not(Q!1))), not(not(not(R!0)))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))))),
% 292.02/187.75 inference(quant_inst,[status(thm)],[])).
% 292.02/187.75 tff(713,plain,
% 292.02/187.75 (implies(or(not(not(not(Q!1))), not(not(not(R!0)))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = not(and(or(not(not(not(Q!1))), not(not(not(R!0)))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))))),
% 292.02/187.75 inference(unit_resolution,[status(thm)],[712, 41])).
% 292.02/187.75 tff(714,plain,
% 292.02/187.75 (not(and(or(not(not(not(Q!1))), not(not(not(R!0)))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) = implies(or(not(not(not(Q!1))), not(not(not(R!0)))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[713])).
% 292.02/187.76 tff(715,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(not(not(Q!1))), not(not(not(R!0)))), and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))) = not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(716,plain,
% 292.02/187.76 (and(or(not(not(not(Q!1))), not(not(not(R!0)))), and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))) = not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[715, 100])).
% 292.02/187.76 tff(717,plain,
% 292.02/187.76 (and(or(not(not(not(Q!1))), not(not(not(R!0)))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))) = and(or(not(not(not(Q!1))), not(not(not(R!0)))), and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[681])).
% 292.02/187.76 tff(718,plain,
% 292.02/187.76 (and(or(not(not(not(Q!1))), not(not(not(R!0)))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))) = not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))),
% 292.02/187.76 inference(transitivity,[status(thm)],[717, 716])).
% 292.02/187.76 tff(719,plain,
% 292.02/187.76 (not(and(or(not(not(not(Q!1))), not(not(not(R!0)))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) = not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[718])).
% 292.02/187.76 tff(720,plain,
% 292.02/187.76 (not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))) = not(and(or(not(not(not(Q!1))), not(not(not(R!0)))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[719])).
% 292.02/187.76 tff(721,plain,
% 292.02/187.76 (not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))) = implies(or(not(not(not(Q!1))), not(not(not(R!0)))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))),
% 292.02/187.76 inference(transitivity,[status(thm)],[720, 714])).
% 292.02/187.76 tff(722,plain,
% 292.02/187.76 (and(not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))) = and(implies(or(not(not(not(Q!1))), not(not(not(R!0)))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(not(not(Q!1))), not(not(not(R!0))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[721, 711])).
% 292.02/187.76 tff(723,plain,
% 292.02/187.76 (and(implies(or(not(not(not(Q!1))), not(not(not(R!0)))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(not(not(Q!1))), not(not(not(R!0)))))) = and(not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[722])).
% 292.02/187.76 tff(724,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(not(not(Q!1))), not(not(not(R!0)))) = not(and(not(not(not(not(Q!1)))), not(not(not(not(R!0)))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(725,plain,
% 292.02/187.76 (or(not(not(not(Q!1))), not(not(not(R!0)))) = not(and(not(not(not(not(Q!1)))), not(not(not(not(R!0))))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[724, 63])).
% 292.02/187.76 tff(726,plain,
% 292.02/187.76 (not(and(not(not(not(not(Q!1)))), not(not(not(not(R!0)))))) = or(not(not(not(Q!1))), not(not(not(R!0))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[725])).
% 292.02/187.76 tff(727,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(not(not(Q!1)))), not(not(not(not(R!0))))) = not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(728,plain,
% 292.02/187.76 (and(not(not(not(not(Q!1)))), not(not(not(not(R!0))))) = not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0)))))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[727, 100])).
% 292.02/187.76 tff(729,plain,
% 292.02/187.76 (not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))) = and(not(not(not(not(Q!1)))), not(not(not(not(R!0)))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[728])).
% 292.02/187.76 tff(730,plain,
% 292.02/187.76 (not(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0)))))))) = not(and(not(not(not(not(Q!1)))), not(not(not(not(R!0))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[729])).
% 292.02/187.76 tff(731,plain,
% 292.02/187.76 (not(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0)))))))) = or(not(not(not(Q!1))), not(not(not(R!0))))),
% 292.02/187.76 inference(transitivity,[status(thm)],[730, 726])).
% 292.02/187.76 tff(732,plain,
% 292.02/187.76 (and(not(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0)))))))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))) = and(or(not(not(not(Q!1))), not(not(not(R!0)))), and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[731, 681])).
% 292.02/187.76 tff(733,plain,
% 292.02/187.76 (and(or(not(not(not(Q!1))), not(not(not(R!0)))), and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))) = and(not(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0)))))))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[732])).
% 292.02/187.76 tff(734,plain,
% 292.02/187.76 (not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))) = and(or(not(not(not(Q!1))), not(not(not(R!0)))), and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[716])).
% 292.02/187.76 tff(735,plain,
% 292.02/187.76 (not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))) = and(not(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0)))))))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))),
% 292.02/187.76 inference(transitivity,[status(thm)],[734, 733])).
% 292.02/187.76 tff(736,plain,
% 292.02/187.76 (not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))) = not(and(not(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0)))))))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[735])).
% 292.02/187.76 tff(737,plain,
% 292.02/187.76 (not(and(not(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0)))))))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) = not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[736])).
% 292.02/187.76 tff(738,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = not(and(not(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0)))))))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(739,plain,
% 292.02/187.76 (or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = not(and(not(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0)))))))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[738, 63])).
% 292.02/187.76 tff(740,plain,
% 292.02/187.76 (or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = implies(or(not(not(not(Q!1))), not(not(not(R!0)))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))),
% 292.02/187.76 inference(transitivity,[status(thm)],[739, 737, 720, 714])).
% 292.02/187.76 tff(741,plain,
% 292.02/187.76 (and(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))) = and(implies(or(not(not(not(Q!1))), not(not(not(R!0)))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(not(not(Q!1))), not(not(not(R!0))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[740, 711])).
% 292.02/187.76 tff(742,plain,
% 292.02/187.76 (and(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))) = and(not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))),
% 292.02/187.76 inference(transitivity,[status(thm)],[741, 723])).
% 292.02/187.76 tff(743,plain,
% 292.02/187.76 (not(and(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))) = not(and(not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[742])).
% 292.02/187.76 tff(744,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = not(and(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(745,plain,
% 292.02/187.76 (implies(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = not(and(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[744, 41])).
% 292.02/187.76 tff(746,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = or(not(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(747,plain,
% 292.02/187.76 (implies(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = or(not(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[746, 20])).
% 292.02/187.76 tff(748,plain,
% 292.02/187.76 (or(not(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = implies(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[747])).
% 292.02/187.76 tff(749,plain,
% 292.02/187.76 (not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))) = not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[628])).
% 292.02/187.76 tff(750,plain,
% 292.02/187.76 (or(not(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) = or(not(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[749])).
% 292.02/187.76 tff(751,plain,
% 292.02/187.76 (or(not(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) = or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))))),
% 292.02/187.76 inference(transitivity,[status(thm)],[750, 748, 745, 743, 675, 672, 666, 663, 661, 637, 634])).
% 292.02/187.76 tff(752,plain,
% 292.02/187.76 (not(or(not(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))))) = not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[751])).
% 292.02/187.76 tff(753,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))) = not(or(not(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(754,plain,
% 292.02/187.76 (and(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))) = not(or(not(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[753, 100])).
% 292.02/187.76 tff(755,plain,
% 292.02/187.76 (or(not(or(not(not(not(R!0))), not(not(not(Q!1))))), or(not(Q!1), not(R!0))) = or(and(not(not(R!0)), not(not(Q!1))), or(not(Q!1), not(R!0)))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[640])).
% 292.02/187.76 tff(756,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(not(R!0))), not(not(not(Q!1)))), or(not(Q!1), not(R!0))) = or(not(or(not(not(not(R!0))), not(not(not(Q!1))))), or(not(Q!1), not(R!0))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(757,plain,
% 292.02/187.76 (implies(or(not(not(not(R!0))), not(not(not(Q!1)))), or(not(Q!1), not(R!0))) = or(not(or(not(not(not(R!0))), not(not(not(Q!1))))), or(not(Q!1), not(R!0)))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[756, 20])).
% 292.02/187.76 tff(758,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(not(not(R!0))), not(not(not(Q!1)))), or(not(Q!1), not(R!0))) = not(and(or(not(not(not(R!0))), not(not(not(Q!1)))), not(or(not(Q!1), not(R!0))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(759,plain,
% 292.02/187.76 (implies(or(not(not(not(R!0))), not(not(not(Q!1)))), or(not(Q!1), not(R!0))) = not(and(or(not(not(not(R!0))), not(not(not(Q!1)))), not(or(not(Q!1), not(R!0)))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[758, 41])).
% 292.02/187.76 tff(760,plain,
% 292.02/187.76 (not(and(or(not(not(not(R!0))), not(not(not(Q!1)))), not(or(not(Q!1), not(R!0))))) = implies(or(not(not(not(R!0))), not(not(not(Q!1)))), or(not(Q!1), not(R!0)))),
% 292.02/187.76 inference(symmetry,[status(thm)],[759])).
% 292.02/187.76 tff(761,plain,
% 292.02/187.76 (not(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))) = not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[681])).
% 292.02/187.76 tff(762,plain,
% 292.02/187.76 (not(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))) = or(not(not(not(R!0))), not(not(not(Q!1))))),
% 292.02/187.76 inference(transitivity,[status(thm)],[761, 669])).
% 292.02/187.76 tff(763,plain,
% 292.02/187.76 (and(not(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(Q!1), not(R!0)))) = and(or(not(not(not(R!0))), not(not(not(Q!1)))), not(or(not(Q!1), not(R!0))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[762])).
% 292.02/187.76 tff(764,plain,
% 292.02/187.76 (not(and(not(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(Q!1), not(R!0))))) = not(and(or(not(not(not(R!0))), not(not(not(Q!1)))), not(or(not(Q!1), not(R!0)))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[763])).
% 292.02/187.76 tff(765,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(Q!1), not(R!0))) = not(and(not(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(Q!1), not(R!0))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(766,plain,
% 292.02/187.76 (or(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(Q!1), not(R!0))) = not(and(not(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))), not(or(not(Q!1), not(R!0)))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[765, 63])).
% 292.02/187.76 tff(767,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(Q!1), not(R!0))) = or(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(Q!1), not(R!0))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(768,plain,
% 292.02/187.76 (implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(Q!1), not(R!0))) = or(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(Q!1), not(R!0)))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[767, 20])).
% 292.02/187.76 tff(769,plain,
% 292.02/187.76 (implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(Q!1), not(R!0))) = or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))),
% 292.02/187.76 inference(transitivity,[status(thm)],[768, 766, 764, 760, 757, 755, 699, 697, 695, 612])).
% 292.02/187.76 tff(770,plain,
% 292.02/187.76 (not(and(not(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0)))))))), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) = or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[739])).
% 292.02/187.76 tff(771,plain,
% 292.02/187.76 (not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1)))))) = not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[671])).
% 292.02/187.76 tff(772,plain,
% 292.02/187.76 (not(and(not(not(or(not(not(not(Q!1))), not(not(not(R!0)))))), not(or(not(not(not(R!0))), not(not(not(Q!1))))))) = or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1)))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[658])).
% 292.02/187.76 tff(773,plain,
% 292.02/187.76 (and(or(not(Q!1), not(R!0)), not(or(not(not(not(R!0))), not(not(not(Q!1)))))) = and(or(not(Q!1), not(R!0)), and(not(not(R!0)), not(not(Q!1))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[640])).
% 292.02/187.76 tff(774,plain,
% 292.02/187.76 (and(or(not(Q!1), not(R!0)), not(or(not(not(not(R!0))), not(not(not(Q!1)))))) = not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))),
% 292.02/187.76 inference(transitivity,[status(thm)],[773, 652])).
% 292.02/187.76 tff(775,plain,
% 292.02/187.76 (not(and(or(not(Q!1), not(R!0)), not(or(not(not(not(R!0))), not(not(not(Q!1))))))) = not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[774])).
% 292.02/187.76 tff(776,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(Q!1), not(R!0)), or(not(not(not(R!0))), not(not(not(Q!1))))) = not(and(or(not(Q!1), not(R!0)), not(or(not(not(not(R!0))), not(not(not(Q!1))))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(777,plain,
% 292.02/187.76 (implies(or(not(Q!1), not(R!0)), or(not(not(not(R!0))), not(not(not(Q!1))))) = not(and(or(not(Q!1), not(R!0)), not(or(not(not(not(R!0))), not(not(not(Q!1)))))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[776, 41])).
% 292.02/187.76 tff(778,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(Q!1), not(R!0)), or(not(not(not(R!0))), not(not(not(Q!1))))) = or(not(or(not(Q!1), not(R!0))), or(not(not(not(R!0))), not(not(not(Q!1))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(779,plain,
% 292.02/187.76 (implies(or(not(Q!1), not(R!0)), or(not(not(not(R!0))), not(not(not(Q!1))))) = or(not(or(not(Q!1), not(R!0))), or(not(not(not(R!0))), not(not(not(Q!1)))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[778, 20])).
% 292.02/187.76 tff(780,plain,
% 292.02/187.76 (or(not(or(not(Q!1), not(R!0))), or(not(not(not(R!0))), not(not(not(Q!1))))) = implies(or(not(Q!1), not(R!0)), or(not(not(not(R!0))), not(not(not(Q!1)))))),
% 292.02/187.76 inference(symmetry,[status(thm)],[779])).
% 292.02/187.76 tff(781,plain,
% 292.02/187.76 (or(not(or(not(Q!1), not(R!0))), not(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) = or(not(or(not(Q!1), not(R!0))), or(not(not(not(R!0))), not(not(not(Q!1)))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[762])).
% 292.02/187.76 tff(782,plain,
% 292.02/187.76 (or(not(or(not(Q!1), not(R!0))), not(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) = or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1)))))),
% 292.02/187.76 inference(transitivity,[status(thm)],[781, 780, 777, 775, 655, 772])).
% 292.02/187.76 tff(783,plain,
% 292.02/187.76 (not(or(not(or(not(Q!1), not(R!0))), not(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))))) = not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), or(not(not(not(R!0))), not(not(not(Q!1))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[782])).
% 292.02/187.76 tff(784,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(Q!1), not(R!0)), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))) = not(or(not(or(not(Q!1), not(R!0))), not(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(785,plain,
% 292.02/187.76 (and(or(not(Q!1), not(R!0)), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))) = not(or(not(or(not(Q!1), not(R!0))), not(not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[784, 100])).
% 292.02/187.76 tff(786,plain,
% 292.02/187.76 (and(or(not(Q!1), not(R!0)), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))) = not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1))))))))),
% 292.02/187.76 inference(transitivity,[status(thm)],[785, 783, 771])).
% 292.02/187.76 tff(787,plain,
% 292.02/187.76 (not(and(or(not(Q!1), not(R!0)), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) = not(not(or(not(or(not(not(not(Q!1))), not(not(not(R!0))))), not(and(not(not(not(not(R!0)))), not(not(not(not(Q!1)))))))))),
% 292.02/187.76 inference(monotonicity,[status(thm)],[786])).
% 292.02/187.76 tff(788,plain,
% 292.02/187.76 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = not(and(or(not(Q!1), not(R!0)), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))))),
% 292.02/187.76 inference(quant_inst,[status(thm)],[])).
% 292.02/187.76 tff(789,plain,
% 292.02/187.76 (implies(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = not(and(or(not(Q!1), not(R!0)), not(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))))),
% 292.02/187.76 inference(unit_resolution,[status(thm)],[788, 41])).
% 292.02/187.76 tff(790,plain,
% 292.02/187.76 (implies(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))),
% 292.02/187.77 inference(transitivity,[status(thm)],[789, 787, 736, 770])).
% 292.02/187.77 tff(791,plain,
% 292.02/187.77 (and(implies(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(Q!1), not(R!0)))) = and(or(not(or(not(not(not(not(not(Q!1))))), not(not(not(not(not(R!0))))))), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[790, 769])).
% 292.02/187.77 tff(792,plain,
% 292.02/187.77 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = and(implies(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(Q!1), not(R!0)))))),
% 292.02/187.77 inference(quant_inst,[status(thm)],[])).
% 292.02/187.77 tff(793,plain,
% 292.02/187.77 (equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = and(implies(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))), implies(or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))), or(not(Q!1), not(R!0))))),
% 292.02/187.77 inference(unit_resolution,[status(thm)],[792, 133])).
% 292.02/187.77 tff(794,plain,
% 292.02/187.77 (equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))) = equiv(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1)))),
% 292.02/187.77 inference(transitivity,[status(thm)],[793, 791, 754, 752, 620, 617, 610])).
% 292.02/187.77 tff(795,plain,
% 292.02/187.77 (is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))) <=> is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[794])).
% 292.02/187.77 tff(796,plain,
% 292.02/187.77 (is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1)))) <=> is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))),
% 292.02/187.77 inference(symmetry,[status(thm)],[795])).
% 292.02/187.77 tff(797,plain,
% 292.02/187.77 (is_a_theorem(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) <=> is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[610])).
% 292.02/187.77 tff(798,plain,
% 292.02/187.77 (is_a_theorem(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) <=> is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))),
% 292.02/187.77 inference(transitivity,[status(thm)],[797, 796])).
% 292.02/187.77 tff(799,plain,
% 292.02/187.77 (or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) = or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[633])).
% 292.02/187.77 tff(800,plain,
% 292.02/187.77 (or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) = or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))),
% 292.02/187.77 inference(symmetry,[status(thm)],[799])).
% 292.02/187.77 tff(801,plain,
% 292.02/187.77 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) = or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))),
% 292.02/187.77 inference(quant_inst,[status(thm)],[])).
% 292.02/187.77 tff(802,plain,
% 292.02/187.77 (implies(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) = or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))),
% 292.02/187.77 inference(unit_resolution,[status(thm)],[801, 20])).
% 292.02/187.77 tff(803,plain,
% 292.02/187.77 (implies(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) = or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))),
% 292.02/187.77 inference(transitivity,[status(thm)],[802, 800])).
% 292.02/187.77 tff(804,plain,
% 292.02/187.77 (is_a_theorem(implies(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))) <=> is_a_theorem(or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[803])).
% 292.02/187.77 tff(805,plain,
% 292.02/187.77 (is_a_theorem(or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))) <=> is_a_theorem(implies(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))),
% 292.02/187.77 inference(symmetry,[status(thm)],[804])).
% 292.02/187.77 tff(806,plain,
% 292.02/187.77 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))) = not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.77 inference(quant_inst,[status(thm)],[])).
% 292.02/187.77 tff(807,plain,
% 292.02/187.77 (or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))) = not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))),
% 292.02/187.77 inference(unit_resolution,[status(thm)],[806, 63])).
% 292.02/187.77 tff(808,plain,
% 292.02/187.77 (implies(or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))) = implies(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[807])).
% 292.02/187.77 tff(809,plain,
% 292.02/187.77 (is_a_theorem(implies(or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))) <=> is_a_theorem(implies(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[808])).
% 292.02/187.77 tff(810,plain,
% 292.02/187.77 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))))),
% 292.02/187.77 inference(quant_inst,[status(thm)],[])).
% 292.02/187.77 tff(811,plain,
% 292.02/187.77 (is_a_theorem(implies(or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))))),
% 292.02/187.77 inference(unit_resolution,[status(thm)],[810, 399])).
% 292.02/187.77 tff(812,plain,
% 292.02/187.77 (is_a_theorem(implies(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))))),
% 292.02/187.77 inference(modus_ponens,[status(thm)],[811, 809])).
% 292.02/187.77 tff(813,plain,
% 292.02/187.77 (or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))) = or(not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[628])).
% 292.02/187.77 tff(814,plain,
% 292.02/187.77 (or(not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))) = or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))),
% 292.02/187.77 inference(symmetry,[status(thm)],[813])).
% 292.02/187.77 tff(815,plain,
% 292.02/187.77 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))) = or(not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))),
% 292.02/187.77 inference(quant_inst,[status(thm)],[])).
% 292.02/187.77 tff(816,plain,
% 292.02/187.77 (implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))) = or(not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))),
% 292.02/187.77 inference(unit_resolution,[status(thm)],[815, 20])).
% 292.02/187.77 tff(817,plain,
% 292.02/187.77 (implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))) = implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[807])).
% 292.02/187.77 tff(818,plain,
% 292.02/187.77 (implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) = implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))),
% 292.02/187.77 inference(symmetry,[status(thm)],[817])).
% 292.02/187.77 tff(819,plain,
% 292.02/187.77 (implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) = or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))),
% 292.02/187.77 inference(transitivity,[status(thm)],[818, 816, 814])).
% 292.02/187.77 tff(820,plain,
% 292.02/187.77 (is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))) <=> is_a_theorem(or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[819])).
% 292.02/187.77 tff(821,plain,
% 292.02/187.77 (is_a_theorem(or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))) <=> is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))),
% 292.02/187.77 inference(symmetry,[status(thm)],[820])).
% 292.02/187.77 tff(822,plain,
% 292.02/187.77 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))) = not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.77 inference(quant_inst,[status(thm)],[])).
% 292.02/187.77 tff(823,plain,
% 292.02/187.77 (or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))) = not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))),
% 292.02/187.77 inference(unit_resolution,[status(thm)],[822, 63])).
% 292.02/187.77 tff(824,plain,
% 292.02/187.77 (or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) = or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[749])).
% 292.02/187.77 tff(825,plain,
% 292.02/187.77 (or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))))),
% 292.02/187.77 inference(symmetry,[status(thm)],[824])).
% 292.02/187.77 tff(826,plain,
% 292.02/187.77 (not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))) = not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[825])).
% 292.02/187.77 tff(827,plain,
% 292.02/187.77 (not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))))) = not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))),
% 292.02/187.77 inference(symmetry,[status(thm)],[826])).
% 292.02/187.77 tff(828,plain,
% 292.02/187.77 (and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))) = and(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))),
% 292.02/187.77 inference(symmetry,[status(thm)],[617])).
% 292.02/187.77 tff(829,plain,
% 292.02/187.77 (and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))) = not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))))),
% 292.02/187.77 inference(transitivity,[status(thm)],[828, 619, 827])).
% 292.02/187.77 tff(830,plain,
% 292.02/187.77 (or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))) = or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.77 inference(monotonicity,[status(thm)],[829, 823])).
% 292.02/187.77 tff(831,plain,
% 292.02/187.77 (implies(or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))) = implies(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))),
% 292.02/187.78 inference(monotonicity,[status(thm)],[830])).
% 292.02/187.78 tff(832,plain,
% 292.02/187.78 (is_a_theorem(implies(or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) <=> is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.78 inference(monotonicity,[status(thm)],[831])).
% 292.02/187.78 tff(833,plain,
% 292.02/187.78 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) | is_a_theorem(implies(or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.78 inference(quant_inst,[status(thm)],[])).
% 292.02/187.78 tff(834,plain,
% 292.02/187.78 (is_a_theorem(implies(or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.78 inference(unit_resolution,[status(thm)],[833, 455])).
% 292.02/187.78 tff(835,plain,
% 292.02/187.78 (is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.78 inference(modus_ponens,[status(thm)],[834, 832])).
% 292.02/187.78 tff(836,plain,
% 292.02/187.78 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) = or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))),
% 292.02/187.78 inference(quant_inst,[status(thm)],[])).
% 292.02/187.78 tff(837,plain,
% 292.02/187.78 (implies(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) = or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.78 inference(unit_resolution,[status(thm)],[836, 20])).
% 292.02/187.78 tff(838,plain,
% 292.02/187.78 (or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) = implies(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.78 inference(symmetry,[status(thm)],[837])).
% 292.02/187.78 tff(839,plain,
% 292.02/187.78 (is_a_theorem(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))) <=> is_a_theorem(implies(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))),
% 292.02/187.78 inference(monotonicity,[status(thm)],[838])).
% 292.02/187.78 tff(840,plain,
% 292.02/187.78 (is_a_theorem(implies(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))) <=> is_a_theorem(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))),
% 292.02/187.78 inference(symmetry,[status(thm)],[839])).
% 292.02/187.78 tff(841,plain,
% 292.02/187.78 (or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))) = or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))),
% 292.02/187.78 inference(transitivity,[status(thm)],[634, 824])).
% 292.02/187.78 tff(842,plain,
% 292.02/187.78 (implies(or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))) = implies(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.78 inference(monotonicity,[status(thm)],[841, 823])).
% 292.02/187.78 tff(843,plain,
% 292.02/187.78 (is_a_theorem(implies(or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))) <=> is_a_theorem(implies(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))),
% 292.02/187.78 inference(monotonicity,[status(thm)],[842])).
% 292.02/187.78 tff(844,plain,
% 292.02/187.78 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))),
% 292.02/187.78 inference(quant_inst,[status(thm)],[])).
% 292.02/187.78 tff(845,plain,
% 292.02/187.78 (is_a_theorem(implies(or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))),
% 292.02/187.78 inference(unit_resolution,[status(thm)],[844, 399])).
% 292.02/187.78 tff(846,plain,
% 292.02/187.78 (is_a_theorem(implies(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))),
% 292.02/187.78 inference(modus_ponens,[status(thm)],[845, 843])).
% 292.02/187.78 tff(847,plain,
% 292.02/187.78 (is_a_theorem(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))),
% 292.02/187.78 inference(modus_ponens,[status(thm)],[846, 840])).
% 292.02/187.78 tff(848,plain,
% 292.02/187.78 (((~![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(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))) | (~is_a_theorem(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))) | (~is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))))) <=> ((~![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(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))) | (~is_a_theorem(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))) | (~is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))))),
% 292.02/187.78 inference(rewrite,[status(thm)],[])).
% 292.02/187.78 tff(849,plain,
% 292.02/187.78 ((~![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(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))) | (~is_a_theorem(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))) | (~is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))))),
% 292.02/187.78 inference(quant_inst,[status(thm)],[])).
% 292.02/187.78 tff(850,plain,
% 292.02/187.78 ((~![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(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))) | (~is_a_theorem(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))) | (~is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))),
% 292.02/187.78 inference(modus_ponens,[status(thm)],[849, 848])).
% 292.02/187.78 tff(851,plain,
% 292.02/187.78 (is_a_theorem(or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))) | (~is_a_theorem(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))) | (~is_a_theorem(implies(or(not(or(not(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))), not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))))), not(and(not(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0))))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))), or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))),
% 292.02/187.78 inference(unit_resolution,[status(thm)],[850, 495])).
% 292.02/187.78 tff(852,plain,
% 292.02/187.78 (is_a_theorem(or(not(or(not(or(not(R!0), not(Q!1))), not(and(Q!1, not(not(R!0)))))), or(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))), not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))),
% 292.02/187.78 inference(unit_resolution,[status(thm)],[851, 847, 835])).
% 292.02/187.78 tff(853,plain,
% 292.02/187.78 (is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))),
% 292.02/187.78 inference(modus_ponens,[status(thm)],[852, 821])).
% 292.02/187.78 tff(854,plain,
% 292.02/187.78 (is_a_theorem(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0)))) <=> is_a_theorem(implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))),
% 292.02/187.78 inference(monotonicity,[status(thm)],[613])).
% 292.02/187.78 tff(855,plain,
% 292.02/187.78 (is_a_theorem(implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))) <=> is_a_theorem(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))),
% 292.02/187.78 inference(symmetry,[status(thm)],[854])).
% 292.02/187.78 tff(856,plain,
% 292.02/187.78 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))),
% 292.02/187.78 inference(quant_inst,[status(thm)],[])).
% 292.02/187.78 tff(857,plain,
% 292.02/187.78 (is_a_theorem(implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))),
% 292.02/187.78 inference(unit_resolution,[status(thm)],[856, 399])).
% 292.02/187.78 tff(858,plain,
% 292.02/187.78 (is_a_theorem(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))),
% 292.02/187.78 inference(modus_ponens,[status(thm)],[857, 855])).
% 292.02/187.78 tff(859,plain,
% 292.02/187.78 (((~![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(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) | is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) | (~is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))))) <=> ((~![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(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) | is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) | (~is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))))),
% 292.02/187.79 inference(rewrite,[status(thm)],[])).
% 292.02/187.79 tff(860,plain,
% 292.02/187.79 ((is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) | (~is_a_theorem(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) | (~is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))))) <=> ((~is_a_theorem(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) | is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) | (~is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))))),
% 292.02/187.79 inference(rewrite,[status(thm)],[])).
% 292.02/187.79 tff(861,plain,
% 292.02/187.79 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) | (~is_a_theorem(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) | (~is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))))) <=> ((~![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(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) | is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) | (~is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))))))),
% 292.02/187.79 inference(monotonicity,[status(thm)],[860])).
% 292.02/187.79 tff(862,plain,
% 292.02/187.79 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) | (~is_a_theorem(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) | (~is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))))) <=> ((~![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(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) | is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) | (~is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))))),
% 292.02/187.79 inference(transitivity,[status(thm)],[861, 859])).
% 292.02/187.79 tff(863,plain,
% 292.02/187.79 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) | (~is_a_theorem(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) | (~is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))))))),
% 292.02/187.79 inference(quant_inst,[status(thm)],[])).
% 292.02/187.79 tff(864,plain,
% 292.02/187.79 ((~![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(R!0), not(Q!1))), or(not(Q!1), not(R!0))))) | is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) | (~is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))))),
% 292.02/187.79 inference(modus_ponens,[status(thm)],[863, 862])).
% 292.02/187.79 tff(865,plain,
% 292.02/187.79 (is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))))))) | (~is_a_theorem(implies(or(not(or(not(R!0), not(Q!1))), or(not(Q!1), not(R!0))), not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[864, 495, 858])).
% 292.02/187.79 tff(866,plain,
% 292.02/187.79 (is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[865, 853])).
% 292.02/187.79 tff(867,plain,
% 292.02/187.79 (((~![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(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))) | (~is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(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(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))) | (~is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))))))),
% 292.02/187.79 inference(rewrite,[status(thm)],[])).
% 292.02/187.79 tff(868,plain,
% 292.02/187.79 ((~![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(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))) | (~is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))))))),
% 292.02/187.79 inference(quant_inst,[status(thm)],[])).
% 292.02/187.79 tff(869,plain,
% 292.02/187.79 ((~![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(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))) | (~is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))))),
% 292.02/187.79 inference(modus_ponens,[status(thm)],[868, 867])).
% 292.02/187.79 tff(870,plain,
% 292.02/187.79 (is_a_theorem(or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))) | (~is_a_theorem(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))), not(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1))))))))), or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[869, 495])).
% 292.02/187.79 tff(871,plain,
% 292.02/187.79 (is_a_theorem(or(not(or(not(or(not(Q!1), not(R!0))), not(and(not(not(R!0)), not(not(Q!1)))))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[870, 866, 812])).
% 292.02/187.79 tff(872,plain,
% 292.02/187.79 (is_a_theorem(implies(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))),
% 292.02/187.79 inference(modus_ponens,[status(thm)],[871, 805])).
% 292.02/187.79 tff(873,plain,
% 292.02/187.79 (is_a_theorem(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1)))) <=> is_a_theorem(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))))),
% 292.02/187.79 inference(monotonicity,[status(thm)],[616])).
% 292.02/187.79 tff(874,plain,
% 292.02/187.79 (is_a_theorem(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1)))) <=> is_a_theorem(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))))),
% 292.02/187.79 inference(symmetry,[status(thm)],[873])).
% 292.02/187.79 tff(875,plain,
% 292.02/187.79 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))))),
% 292.02/187.79 inference(quant_inst,[status(thm)],[])).
% 292.02/187.79 tff(876,plain,
% 292.02/187.79 (is_a_theorem(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[875, 399])).
% 292.02/187.79 tff(877,plain,
% 292.02/187.79 (is_a_theorem(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))))),
% 292.02/187.79 inference(modus_ponens,[status(thm)],[876, 874])).
% 292.02/187.79 tff(878,plain,
% 292.02/187.79 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) | (~is_a_theorem(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) | (~is_a_theorem(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))))),
% 292.02/187.79 inference(rewrite,[status(thm)],[])).
% 292.02/187.79 tff(879,plain,
% 292.02/187.79 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) | (~is_a_theorem(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))))))),
% 292.02/187.79 inference(quant_inst,[status(thm)],[])).
% 292.02/187.79 tff(880,plain,
% 292.02/187.79 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) | (~is_a_theorem(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))))) | (~is_a_theorem(implies(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))))),
% 292.02/187.79 inference(modus_ponens,[status(thm)],[879, 878])).
% 292.02/187.79 tff(881,plain,
% 292.02/187.79 (is_a_theorem(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0))))) | (~is_a_theorem(implies(or(not(or(not(Q!1), not(R!0))), or(not(R!0), not(Q!1))), and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[880, 495, 877])).
% 292.02/187.79 tff(882,plain,
% 292.02/187.79 (is_a_theorem(and(implies(or(not(Q!1), not(R!0)), or(not(R!0), not(Q!1))), implies(or(not(R!0), not(Q!1)), or(not(Q!1), not(R!0)))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[881, 872])).
% 292.02/187.79 tff(883,plain,
% 292.02/187.79 (is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))),
% 292.02/187.79 inference(modus_ponens,[status(thm)],[882, 798])).
% 292.02/187.79 tff(884,plain,
% 292.02/187.79 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) | (or(not(Q!1), not(R!0)) = or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) | (or(not(Q!1), not(R!0)) = or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))),
% 292.02/187.79 inference(rewrite,[status(thm)],[])).
% 292.02/187.79 tff(885,plain,
% 292.02/187.79 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) | (or(not(Q!1), not(R!0)) = or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))),
% 292.02/187.79 inference(quant_inst,[status(thm)],[])).
% 292.02/187.79 tff(886,plain,
% 292.02/187.79 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) | (or(not(Q!1), not(R!0)) = or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))),
% 292.02/187.79 inference(modus_ponens,[status(thm)],[885, 884])).
% 292.02/187.79 tff(887,plain,
% 292.02/187.79 ((~is_a_theorem(equiv(or(not(Q!1), not(R!0)), or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))))) | (or(not(Q!1), not(R!0)) = or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[886, 564])).
% 292.02/187.79 tff(888,plain,
% 292.02/187.79 (or(not(Q!1), not(R!0)) = or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[887, 883])).
% 292.02/187.79 tff(889,plain,
% 292.02/187.79 (or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))) = or(not(Q!1), not(R!0))),
% 292.02/187.79 inference(symmetry,[status(thm)],[888])).
% 292.02/187.79 tff(890,plain,
% 292.02/187.79 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(not(not(R!0)))), not(not(not(not(not(Q!1)))))) = or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1)))))))),
% 292.02/187.79 inference(quant_inst,[status(thm)],[])).
% 292.02/187.79 tff(891,plain,
% 292.02/187.79 (implies(not(not(not(not(R!0)))), not(not(not(not(not(Q!1)))))) = or(not(not(not(not(not(R!0))))), not(not(not(not(not(Q!1))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[890, 20])).
% 292.02/187.79 tff(892,plain,
% 292.02/187.79 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(not(not(R!0)))), not(not(not(not(not(Q!1)))))) = not(and(not(not(not(not(R!0)))), not(not(not(not(not(not(Q!1)))))))))),
% 292.02/187.79 inference(quant_inst,[status(thm)],[])).
% 292.02/187.79 tff(893,plain,
% 292.02/187.79 (implies(not(not(not(not(R!0)))), not(not(not(not(not(Q!1)))))) = not(and(not(not(not(not(R!0)))), not(not(not(not(not(not(Q!1))))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[892, 41])).
% 292.02/187.79 tff(894,plain,
% 292.02/187.79 (not(and(not(not(not(not(R!0)))), not(not(not(not(not(not(Q!1)))))))) = implies(not(not(not(not(R!0)))), not(not(not(not(not(Q!1))))))),
% 292.02/187.79 inference(symmetry,[status(thm)],[893])).
% 292.02/187.79 tff(895,plain,
% 292.02/187.79 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(not(not(R!0))), not(not(not(not(not(Q!1)))))) = not(and(not(not(not(not(R!0)))), not(not(not(not(not(not(Q!1)))))))))),
% 292.02/187.79 inference(quant_inst,[status(thm)],[])).
% 292.02/187.79 tff(896,plain,
% 292.02/187.79 (or(not(not(not(R!0))), not(not(not(not(not(Q!1)))))) = not(and(not(not(not(not(R!0)))), not(not(not(not(not(not(Q!1))))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[895, 63])).
% 292.02/187.79 tff(897,plain,
% 292.02/187.79 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(R!0)), not(not(not(not(not(Q!1)))))) = or(not(not(not(R!0))), not(not(not(not(not(Q!1)))))))),
% 292.02/187.79 inference(quant_inst,[status(thm)],[])).
% 292.02/187.79 tff(898,plain,
% 292.02/187.79 (implies(not(not(R!0)), not(not(not(not(not(Q!1)))))) = or(not(not(not(R!0))), not(not(not(not(not(Q!1))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[897, 20])).
% 292.02/187.79 tff(899,plain,
% 292.02/187.79 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(R!0)), not(not(not(not(not(Q!1)))))) = not(and(not(not(R!0)), not(not(not(not(not(not(Q!1)))))))))),
% 292.02/187.79 inference(quant_inst,[status(thm)],[])).
% 292.02/187.79 tff(900,plain,
% 292.02/187.79 (implies(not(not(R!0)), not(not(not(not(not(Q!1)))))) = not(and(not(not(R!0)), not(not(not(not(not(not(Q!1))))))))),
% 292.02/187.79 inference(unit_resolution,[status(thm)],[899, 41])).
% 292.02/187.79 tff(901,plain,
% 292.02/187.79 (not(and(not(not(R!0)), not(not(not(not(not(not(Q!1)))))))) = implies(not(not(R!0)), not(not(not(not(not(Q!1))))))),
% 292.02/187.79 inference(symmetry,[status(thm)],[900])).
% 292.02/187.79 tff(902,plain,
% 292.02/187.79 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(R!0), not(not(not(not(not(Q!1)))))) = not(and(not(not(R!0)), not(not(not(not(not(not(Q!1)))))))))),
% 292.02/187.79 inference(quant_inst,[status(thm)],[])).
% 292.02/187.79 tff(903,plain,
% 292.02/187.79 (or(not(R!0), not(not(not(not(not(Q!1)))))) = not(and(not(not(R!0)), not(not(not(not(not(not(Q!1))))))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[902, 63])).
% 292.02/187.80 tff(904,plain,
% 292.02/187.80 (or(not(R!0), not(not(not(not(not(Q!1)))))) = or(not(Q!1), not(R!0))),
% 292.02/187.80 inference(transitivity,[status(thm)],[903, 901, 898, 896, 894, 891, 889])).
% 292.02/187.80 tff(905,plain,
% 292.02/187.80 (implies(or(not(R!0), not(not(not(not(not(Q!1)))))), or(not(R!0), not(P!2))) = implies(or(not(Q!1), not(R!0)), or(not(R!0), not(P!2)))),
% 292.02/187.80 inference(monotonicity,[status(thm)],[904])).
% 292.02/187.80 tff(906,plain,
% 292.02/187.80 (implies(or(not(R!0), not(not(not(not(not(Q!1)))))), or(not(R!0), not(P!2))) = not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2)))))),
% 292.02/187.80 inference(transitivity,[status(thm)],[905, 607, 605, 603, 585])).
% 292.02/187.80 tff(907,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)) = and(implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)), implies(or(not(P!2), Q!1), not(not(or(Q!1, not(P!2)))))))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(908,plain,
% 292.02/187.80 (equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)) = and(implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)), implies(or(not(P!2), Q!1), not(not(or(Q!1, not(P!2))))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[907, 133])).
% 292.02/187.80 tff(909,plain,
% 292.02/187.80 (and(implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)), implies(or(not(P!2), Q!1), not(not(or(Q!1, not(P!2)))))) = equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1))),
% 292.02/187.80 inference(symmetry,[status(thm)],[908])).
% 292.02/187.80 tff(910,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(P!2), Q!1), not(not(or(Q!1, not(P!2))))) = or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(911,plain,
% 292.02/187.80 (implies(or(not(P!2), Q!1), not(not(or(Q!1, not(P!2))))) = or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[910, 20])).
% 292.02/187.80 tff(912,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)) = not(and(not(not(or(Q!1, not(P!2)))), not(or(not(P!2), Q!1)))))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(913,plain,
% 292.02/187.80 (or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)) = not(and(not(not(or(Q!1, not(P!2)))), not(or(not(P!2), Q!1))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[912, 63])).
% 292.02/187.80 tff(914,plain,
% 292.02/187.80 (not(and(not(not(or(Q!1, not(P!2)))), not(or(not(P!2), Q!1)))) = or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))),
% 292.02/187.80 inference(symmetry,[status(thm)],[913])).
% 292.02/187.80 tff(915,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)) = not(and(not(not(or(Q!1, not(P!2)))), not(or(not(P!2), Q!1)))))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(916,plain,
% 292.02/187.80 (implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)) = not(and(not(not(or(Q!1, not(P!2)))), not(or(not(P!2), Q!1))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[915, 41])).
% 292.02/187.80 tff(917,plain,
% 292.02/187.80 (implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)) = or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))),
% 292.02/187.80 inference(transitivity,[status(thm)],[916, 914])).
% 292.02/187.80 tff(918,plain,
% 292.02/187.80 (and(implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)), implies(or(not(P!2), Q!1), not(not(or(Q!1, not(P!2)))))) = and(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.02/187.80 inference(monotonicity,[status(thm)],[917, 911])).
% 292.02/187.80 tff(919,plain,
% 292.02/187.80 (and(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) = and(implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)), implies(or(not(P!2), Q!1), not(not(or(Q!1, not(P!2))))))),
% 292.02/187.80 inference(symmetry,[status(thm)],[918])).
% 292.02/187.80 tff(920,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) = not(or(not(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(921,plain,
% 292.02/187.80 (and(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) = not(or(not(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[920, 100])).
% 292.02/187.80 tff(922,plain,
% 292.02/187.80 (not(or(not(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = and(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.02/187.80 inference(symmetry,[status(thm)],[921])).
% 292.02/187.80 tff(923,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))) = not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(924,plain,
% 292.02/187.80 (and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))) = not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[923, 100])).
% 292.02/187.80 tff(925,plain,
% 292.02/187.80 (not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) = and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))),
% 292.02/187.80 inference(symmetry,[status(thm)],[924])).
% 292.02/187.80 tff(926,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(Q!1, not(P!2)) = not(and(not(Q!1), not(not(P!2)))))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(927,plain,
% 292.02/187.80 (or(Q!1, not(P!2)) = not(and(not(Q!1), not(not(P!2))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[926, 63])).
% 292.02/187.80 tff(928,plain,
% 292.02/187.80 (and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))) = and(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))),
% 292.02/187.80 inference(monotonicity,[status(thm)],[927, 72])).
% 292.02/187.80 tff(929,plain,
% 292.02/187.80 (and(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1))) = and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))),
% 292.02/187.80 inference(symmetry,[status(thm)],[928])).
% 292.02/187.80 tff(930,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1))) = not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(931,plain,
% 292.02/187.80 (and(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1))) = not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[930, 100])).
% 292.02/187.80 tff(932,plain,
% 292.02/187.80 (not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))) = and(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))),
% 292.02/187.80 inference(symmetry,[status(thm)],[931])).
% 292.02/187.80 tff(933,plain,
% 292.02/187.80 (not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))) = and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))),
% 292.02/187.80 inference(transitivity,[status(thm)],[932, 929])).
% 292.02/187.80 tff(934,plain,
% 292.02/187.80 (or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))),
% 292.02/187.80 inference(monotonicity,[status(thm)],[933, 925])).
% 292.02/187.80 tff(935,plain,
% 292.02/187.80 (or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) = or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.02/187.80 inference(symmetry,[status(thm)],[934])).
% 292.02/187.80 tff(936,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) = not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(937,plain,
% 292.02/187.80 (or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) = not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[936, 63])).
% 292.02/187.80 tff(938,plain,
% 292.02/187.80 (not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))) = or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))),
% 292.02/187.80 inference(symmetry,[status(thm)],[937])).
% 292.02/187.80 tff(939,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(P!2), Q!1), or(Q!1, not(P!2))) = not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(940,plain,
% 292.02/187.80 (implies(or(not(P!2), Q!1), or(Q!1, not(P!2))) = not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[939, 41])).
% 292.02/187.80 tff(941,plain,
% 292.02/187.80 (not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) = implies(or(not(P!2), Q!1), or(Q!1, not(P!2)))),
% 292.02/187.80 inference(symmetry,[status(thm)],[940])).
% 292.02/187.80 tff(942,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)) = not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(943,plain,
% 292.02/187.80 (implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)) = not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[942, 41])).
% 292.02/187.80 tff(944,plain,
% 292.02/187.80 (not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = implies(or(Q!1, not(P!2)), or(not(P!2), Q!1))),
% 292.02/187.80 inference(symmetry,[status(thm)],[943])).
% 292.02/187.80 tff(945,plain,
% 292.02/187.80 (and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))) = and(implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)), implies(or(not(P!2), Q!1), or(Q!1, not(P!2))))),
% 292.02/187.80 inference(monotonicity,[status(thm)],[944, 941])).
% 292.02/187.80 tff(946,plain,
% 292.02/187.80 (and(implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)), implies(or(not(P!2), Q!1), or(Q!1, not(P!2)))) = and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))),
% 292.02/187.80 inference(symmetry,[status(thm)],[945])).
% 292.02/187.80 tff(947,plain,
% 292.02/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)) = or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)))),
% 292.02/187.80 inference(quant_inst,[status(thm)],[])).
% 292.02/187.80 tff(948,plain,
% 292.02/187.80 (implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)) = or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))),
% 292.02/187.80 inference(unit_resolution,[status(thm)],[947, 20])).
% 292.02/187.80 tff(949,plain,
% 292.02/187.80 (or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)) = implies(or(Q!1, not(P!2)), or(not(P!2), Q!1))),
% 292.02/187.80 inference(symmetry,[status(thm)],[948])).
% 292.02/187.80 tff(950,plain,
% 292.02/187.80 (and(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))) = and(implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)), implies(or(not(P!2), Q!1), or(Q!1, not(P!2))))),
% 292.02/187.80 inference(monotonicity,[status(thm)],[949, 941])).
% 292.02/187.80 tff(951,plain,
% 292.02/187.80 (and(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))) = and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))),
% 292.08/187.80 inference(transitivity,[status(thm)],[950, 946])).
% 292.08/187.80 tff(952,plain,
% 292.08/187.80 (not(and(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))) = not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))),
% 292.08/187.80 inference(monotonicity,[status(thm)],[951])).
% 292.08/187.80 tff(953,plain,
% 292.08/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) = not(and(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))),
% 292.08/187.80 inference(quant_inst,[status(thm)],[])).
% 292.08/187.80 tff(954,plain,
% 292.08/187.80 (implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) = not(and(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))),
% 292.08/187.80 inference(unit_resolution,[status(thm)],[953, 41])).
% 292.08/187.80 tff(955,plain,
% 292.08/187.80 (implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))),
% 292.08/187.80 inference(monotonicity,[status(thm)],[925])).
% 292.08/187.80 tff(956,plain,
% 292.08/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = or(not(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.80 inference(quant_inst,[status(thm)],[])).
% 292.08/187.80 tff(957,plain,
% 292.08/187.80 (implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = or(not(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.80 inference(unit_resolution,[status(thm)],[956, 20])).
% 292.08/187.80 tff(958,plain,
% 292.08/187.80 (or(not(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.80 inference(symmetry,[status(thm)],[957])).
% 292.08/187.80 tff(959,plain,
% 292.08/187.80 (or(not(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.80 inference(transitivity,[status(thm)],[958, 955, 954, 952, 938, 935])).
% 292.08/187.80 tff(960,plain,
% 292.08/187.80 (not(or(not(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.80 inference(monotonicity,[status(thm)],[959])).
% 292.08/187.80 tff(961,plain,
% 292.08/187.80 (not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = not(or(not(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.80 inference(symmetry,[status(thm)],[960])).
% 292.08/187.80 tff(962,plain,
% 292.08/187.80 (not(and(not(Q!1), not(not(P!2)))) = or(Q!1, not(P!2))),
% 292.08/187.80 inference(symmetry,[status(thm)],[927])).
% 292.08/187.80 tff(963,plain,
% 292.08/187.80 (not(not(and(not(Q!1), not(not(P!2))))) = not(or(Q!1, not(P!2)))),
% 292.08/187.80 inference(monotonicity,[status(thm)],[962])).
% 292.08/187.80 tff(964,plain,
% 292.08/187.80 (or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1)))))) = or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))),
% 292.08/187.80 inference(monotonicity,[status(thm)],[963, 105])).
% 292.08/187.80 tff(965,plain,
% 292.08/187.80 (not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1))))))) = not(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)))),
% 292.08/187.80 inference(monotonicity,[status(thm)],[964])).
% 292.08/187.80 tff(966,plain,
% 292.08/187.80 (or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = or(not(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.80 inference(monotonicity,[status(thm)],[965])).
% 292.08/187.80 tff(967,plain,
% 292.08/187.80 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = not(and(not(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.80 inference(quant_inst,[status(thm)],[])).
% 292.08/187.80 tff(968,plain,
% 292.08/187.80 (or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = not(and(not(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.80 inference(unit_resolution,[status(thm)],[967, 63])).
% 292.08/187.80 tff(969,plain,
% 292.08/187.80 (not(and(not(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) = or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.80 inference(symmetry,[status(thm)],[968])).
% 292.08/187.80 tff(970,plain,
% 292.08/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(Q!1)), not(P!2)), or(not(P!2), not(not(Q!1)))) = or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))),
% 292.08/187.80 inference(quant_inst,[status(thm)],[])).
% 292.08/187.80 tff(971,plain,
% 292.08/187.80 (implies(or(not(not(Q!1)), not(P!2)), or(not(P!2), not(not(Q!1)))) = or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))),
% 292.08/187.80 inference(unit_resolution,[status(thm)],[970, 20])).
% 292.08/187.80 tff(972,plain,
% 292.08/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(not(Q!1)), not(P!2)), or(not(P!2), not(not(Q!1)))) = not(and(or(not(not(Q!1)), not(P!2)), not(or(not(P!2), not(not(Q!1)))))))),
% 292.08/187.80 inference(quant_inst,[status(thm)],[])).
% 292.08/187.80 tff(973,plain,
% 292.08/187.80 (implies(or(not(not(Q!1)), not(P!2)), or(not(P!2), not(not(Q!1)))) = not(and(or(not(not(Q!1)), not(P!2)), not(or(not(P!2), not(not(Q!1))))))),
% 292.08/187.80 inference(unit_resolution,[status(thm)],[972, 41])).
% 292.08/187.80 tff(974,plain,
% 292.08/187.80 (not(and(or(not(not(Q!1)), not(P!2)), not(or(not(P!2), not(not(Q!1)))))) = implies(or(not(not(Q!1)), not(P!2)), or(not(P!2), not(not(Q!1))))),
% 292.08/187.80 inference(symmetry,[status(thm)],[973])).
% 292.08/187.80 tff(975,plain,
% 292.08/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(Q!1), not(P!2)) = not(and(not(Q!1), not(not(P!2)))))),
% 292.08/187.80 inference(quant_inst,[status(thm)],[])).
% 292.08/187.80 tff(976,plain,
% 292.08/187.80 (implies(not(Q!1), not(P!2)) = not(and(not(Q!1), not(not(P!2))))),
% 292.08/187.80 inference(unit_resolution,[status(thm)],[975, 41])).
% 292.08/187.80 tff(977,plain,
% 292.08/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(Q!1), not(P!2)) = or(not(not(Q!1)), not(P!2)))),
% 292.08/187.80 inference(quant_inst,[status(thm)],[])).
% 292.08/187.80 tff(978,plain,
% 292.08/187.80 (implies(not(Q!1), not(P!2)) = or(not(not(Q!1)), not(P!2))),
% 292.08/187.80 inference(unit_resolution,[status(thm)],[977, 20])).
% 292.08/187.80 tff(979,plain,
% 292.08/187.80 (or(not(not(Q!1)), not(P!2)) = implies(not(Q!1), not(P!2))),
% 292.08/187.80 inference(symmetry,[status(thm)],[978])).
% 292.08/187.80 tff(980,plain,
% 292.08/187.80 (or(not(not(Q!1)), not(P!2)) = not(and(not(Q!1), not(not(P!2))))),
% 292.08/187.80 inference(transitivity,[status(thm)],[979, 976])).
% 292.08/187.80 tff(981,plain,
% 292.08/187.80 (and(or(not(not(Q!1)), not(P!2)), not(or(not(P!2), not(not(Q!1))))) = and(not(and(not(Q!1), not(not(P!2)))), not(or(not(P!2), not(not(Q!1)))))),
% 292.08/187.80 inference(monotonicity,[status(thm)],[980])).
% 292.08/187.80 tff(982,plain,
% 292.08/187.80 (and(not(and(not(Q!1), not(not(P!2)))), not(or(not(P!2), not(not(Q!1))))) = and(or(not(not(Q!1)), not(P!2)), not(or(not(P!2), not(not(Q!1)))))),
% 292.08/187.80 inference(symmetry,[status(thm)],[981])).
% 292.08/187.80 tff(983,plain,
% 292.08/187.80 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(Q!1), not(not(P!2)))), not(or(not(P!2), not(not(Q!1))))) = not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1))))))))),
% 292.08/187.80 inference(quant_inst,[status(thm)],[])).
% 292.08/187.80 tff(984,plain,
% 292.08/187.80 (and(not(and(not(Q!1), not(not(P!2)))), not(or(not(P!2), not(not(Q!1))))) = not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1)))))))),
% 292.08/187.80 inference(unit_resolution,[status(thm)],[983, 100])).
% 292.08/187.80 tff(985,plain,
% 292.08/187.80 (not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1))))))) = and(not(and(not(Q!1), not(not(P!2)))), not(or(not(P!2), not(not(Q!1)))))),
% 292.08/187.80 inference(symmetry,[status(thm)],[984])).
% 292.08/187.80 tff(986,plain,
% 292.08/187.80 (not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1))))))) = and(or(not(not(Q!1)), not(P!2)), not(or(not(P!2), not(not(Q!1)))))),
% 292.08/187.80 inference(transitivity,[status(thm)],[985, 982])).
% 292.08/187.80 tff(987,plain,
% 292.08/187.80 (not(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1)))))))) = not(and(or(not(not(Q!1)), not(P!2)), not(or(not(P!2), not(not(Q!1))))))),
% 292.08/187.80 inference(monotonicity,[status(thm)],[986])).
% 292.08/187.80 tff(988,plain,
% 292.08/187.80 (not(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1)))))))) = or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))),
% 292.08/187.80 inference(transitivity,[status(thm)],[987, 974, 971])).
% 292.08/187.80 tff(989,plain,
% 292.08/187.80 (and(not(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = and(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.80 inference(monotonicity,[status(thm)],[988])).
% 292.08/187.80 tff(990,plain,
% 292.08/187.80 (and(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = and(not(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.80 inference(symmetry,[status(thm)],[989])).
% 292.08/187.80 tff(991,plain,
% 292.08/187.80 (not(and(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) = not(and(not(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(or(not(P!2), not(not(Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.80 inference(monotonicity,[status(thm)],[990])).
% 292.08/187.80 tff(992,plain,
% 292.08/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = not(and(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.80 inference(quant_inst,[status(thm)],[])).
% 292.08/187.80 tff(993,plain,
% 292.08/187.80 (implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = not(and(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.80 inference(unit_resolution,[status(thm)],[992, 41])).
% 292.08/187.80 tff(994,plain,
% 292.08/187.80 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = or(not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.80 inference(quant_inst,[status(thm)],[])).
% 292.08/187.80 tff(995,plain,
% 292.08/187.80 (implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = or(not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.80 inference(unit_resolution,[status(thm)],[994, 20])).
% 292.08/187.80 tff(996,plain,
% 292.08/187.80 (or(not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.81 inference(symmetry,[status(thm)],[995])).
% 292.08/187.81 tff(997,plain,
% 292.08/187.81 (or(not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.81 inference(transitivity,[status(thm)],[996, 993, 991, 969, 966, 958, 955, 954, 952, 938, 935])).
% 292.08/187.81 tff(998,plain,
% 292.08/187.81 (not(or(not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[997])).
% 292.08/187.81 tff(999,plain,
% 292.08/187.81 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) = not(or(not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.81 inference(quant_inst,[status(thm)],[])).
% 292.08/187.81 tff(1000,plain,
% 292.08/187.81 (and(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) = not(or(not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.81 inference(unit_resolution,[status(thm)],[999, 100])).
% 292.08/187.81 tff(1001,plain,
% 292.08/187.81 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(P!2), Q!1), not(not(or(Q!1, not(P!2))))) = not(and(or(not(P!2), Q!1), not(not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.81 inference(quant_inst,[status(thm)],[])).
% 292.08/187.81 tff(1002,plain,
% 292.08/187.81 (implies(or(not(P!2), Q!1), not(not(or(Q!1, not(P!2))))) = not(and(or(not(P!2), Q!1), not(not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.81 inference(unit_resolution,[status(thm)],[1001, 41])).
% 292.08/187.81 tff(1003,plain,
% 292.08/187.81 (not(and(or(not(P!2), Q!1), not(not(not(or(Q!1, not(P!2))))))) = implies(or(not(P!2), Q!1), not(not(or(Q!1, not(P!2)))))),
% 292.08/187.81 inference(symmetry,[status(thm)],[1002])).
% 292.08/187.81 tff(1004,plain,
% 292.08/187.81 (and(not(not(or(not(P!2), not(not(Q!1))))), not(not(not(or(Q!1, not(P!2)))))) = and(or(not(P!2), Q!1), not(not(not(or(Q!1, not(P!2))))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[105])).
% 292.08/187.81 tff(1005,plain,
% 292.08/187.81 (not(and(not(not(or(not(P!2), not(not(Q!1))))), not(not(not(or(Q!1, not(P!2))))))) = not(and(or(not(P!2), Q!1), not(not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1004])).
% 292.08/187.81 tff(1006,plain,
% 292.08/187.81 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(P!2), not(not(Q!1)))), not(not(or(Q!1, not(P!2))))) = not(and(not(not(or(not(P!2), not(not(Q!1))))), not(not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.81 inference(quant_inst,[status(thm)],[])).
% 292.08/187.81 tff(1007,plain,
% 292.08/187.81 (or(not(or(not(P!2), not(not(Q!1)))), not(not(or(Q!1, not(P!2))))) = not(and(not(not(or(not(P!2), not(not(Q!1))))), not(not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.81 inference(unit_resolution,[status(thm)],[1006, 63])).
% 292.08/187.81 tff(1008,plain,
% 292.08/187.81 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(P!2), not(not(Q!1))), not(not(or(Q!1, not(P!2))))) = or(not(or(not(P!2), not(not(Q!1)))), not(not(or(Q!1, not(P!2))))))),
% 292.08/187.81 inference(quant_inst,[status(thm)],[])).
% 292.08/187.81 tff(1009,plain,
% 292.08/187.81 (implies(or(not(P!2), not(not(Q!1))), not(not(or(Q!1, not(P!2))))) = or(not(or(not(P!2), not(not(Q!1)))), not(not(or(Q!1, not(P!2)))))),
% 292.08/187.81 inference(unit_resolution,[status(thm)],[1008, 20])).
% 292.08/187.81 tff(1010,plain,
% 292.08/187.81 (implies(or(not(P!2), not(not(Q!1))), not(not(or(Q!1, not(P!2))))) = or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))),
% 292.08/187.81 inference(transitivity,[status(thm)],[1009, 1007, 1005, 1003, 911])).
% 292.08/187.81 tff(1011,plain,
% 292.08/187.81 (or(not(not(Q!1)), not(P!2)) = or(Q!1, not(P!2))),
% 292.08/187.81 inference(transitivity,[status(thm)],[979, 976, 962])).
% 292.08/187.81 tff(1012,plain,
% 292.08/187.81 (not(or(not(not(Q!1)), not(P!2))) = not(or(Q!1, not(P!2)))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1011])).
% 292.08/187.81 tff(1013,plain,
% 292.08/187.81 (not(or(Q!1, not(P!2))) = not(or(not(not(Q!1)), not(P!2)))),
% 292.08/187.81 inference(symmetry,[status(thm)],[1012])).
% 292.08/187.81 tff(1014,plain,
% 292.08/187.81 (or(not(or(Q!1, not(P!2))), or(not(P!2), not(not(Q!1)))) = or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1013])).
% 292.08/187.81 tff(1015,plain,
% 292.08/187.81 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(Q!1, not(P!2))), or(not(P!2), not(not(Q!1)))) = not(and(not(not(or(Q!1, not(P!2)))), not(or(not(P!2), not(not(Q!1)))))))),
% 292.08/187.81 inference(quant_inst,[status(thm)],[])).
% 292.08/187.81 tff(1016,plain,
% 292.08/187.81 (or(not(or(Q!1, not(P!2))), or(not(P!2), not(not(Q!1)))) = not(and(not(not(or(Q!1, not(P!2)))), not(or(not(P!2), not(not(Q!1))))))),
% 292.08/187.81 inference(unit_resolution,[status(thm)],[1015, 63])).
% 292.08/187.81 tff(1017,plain,
% 292.08/187.81 (not(and(not(not(or(Q!1, not(P!2)))), not(or(not(P!2), not(not(Q!1)))))) = or(not(or(Q!1, not(P!2))), or(not(P!2), not(not(Q!1))))),
% 292.08/187.81 inference(symmetry,[status(thm)],[1016])).
% 292.08/187.81 tff(1018,plain,
% 292.08/187.81 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))) = not(and(not(not(or(Q!1, not(P!2)))), not(or(not(P!2), not(not(Q!1)))))))),
% 292.08/187.81 inference(quant_inst,[status(thm)],[])).
% 292.08/187.81 tff(1019,plain,
% 292.08/187.81 (implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))) = not(and(not(not(or(Q!1, not(P!2)))), not(or(not(P!2), not(not(Q!1))))))),
% 292.08/187.81 inference(unit_resolution,[status(thm)],[1018, 41])).
% 292.08/187.81 tff(1020,plain,
% 292.08/187.81 (implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))) = or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))),
% 292.08/187.81 inference(transitivity,[status(thm)],[1019, 1017, 1014])).
% 292.08/187.81 tff(1021,plain,
% 292.08/187.81 (and(implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))), implies(or(not(P!2), not(not(Q!1))), not(not(or(Q!1, not(P!2)))))) = and(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1020, 1010])).
% 292.08/187.81 tff(1022,plain,
% 292.08/187.81 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))) = and(implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))), implies(or(not(P!2), not(not(Q!1))), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.81 inference(quant_inst,[status(thm)],[])).
% 292.08/187.81 tff(1023,plain,
% 292.08/187.81 (equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))) = and(implies(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))), implies(or(not(P!2), not(not(Q!1))), not(not(or(Q!1, not(P!2))))))),
% 292.08/187.81 inference(unit_resolution,[status(thm)],[1022, 133])).
% 292.08/187.81 tff(1024,plain,
% 292.08/187.81 (equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))) = equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1))),
% 292.08/187.81 inference(transitivity,[status(thm)],[1023, 1021, 1000, 998, 961, 922, 919, 909])).
% 292.08/187.81 tff(1025,plain,
% 292.08/187.81 (is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1))))) <=> is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1024])).
% 292.08/187.81 tff(1026,plain,
% 292.08/187.81 (is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1))) <=> is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))))),
% 292.08/187.81 inference(symmetry,[status(thm)],[1025])).
% 292.08/187.81 tff(1027,plain,
% 292.08/187.81 (not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1))),
% 292.08/187.81 inference(transitivity,[status(thm)],[961, 922, 919, 909])).
% 292.08/187.81 tff(1028,plain,
% 292.08/187.81 (is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) <=> is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1027])).
% 292.08/187.81 tff(1029,plain,
% 292.08/187.81 (is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) <=> is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))))),
% 292.08/187.81 inference(transitivity,[status(thm)],[1028, 1026])).
% 292.08/187.81 tff(1030,plain,
% 292.08/187.81 (or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) = or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[933])).
% 292.08/187.81 tff(1031,plain,
% 292.08/187.81 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) = or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.81 inference(quant_inst,[status(thm)],[])).
% 292.08/187.81 tff(1032,plain,
% 292.08/187.81 (implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) = or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.81 inference(unit_resolution,[status(thm)],[1031, 20])).
% 292.08/187.81 tff(1033,plain,
% 292.08/187.81 (implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) = or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.81 inference(transitivity,[status(thm)],[1032, 1030])).
% 292.08/187.81 tff(1034,plain,
% 292.08/187.81 (is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) <=> is_a_theorem(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1033])).
% 292.08/187.81 tff(1035,plain,
% 292.08/187.81 (is_a_theorem(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) <=> is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.81 inference(symmetry,[status(thm)],[1034])).
% 292.08/187.81 tff(1036,plain,
% 292.08/187.81 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.81 inference(quant_inst,[status(thm)],[])).
% 292.08/187.81 tff(1037,plain,
% 292.08/187.81 (or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.81 inference(unit_resolution,[status(thm)],[1036, 63])).
% 292.08/187.81 tff(1038,plain,
% 292.08/187.81 (implies(or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) = implies(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1037])).
% 292.08/187.81 tff(1039,plain,
% 292.08/187.81 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))) <=> is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1038])).
% 292.08/187.81 tff(1040,plain,
% 292.08/187.81 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))),
% 292.08/187.81 inference(quant_inst,[status(thm)],[])).
% 292.08/187.81 tff(1041,plain,
% 292.08/187.81 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))),
% 292.08/187.81 inference(unit_resolution,[status(thm)],[1040, 399])).
% 292.08/187.81 tff(1042,plain,
% 292.08/187.81 (is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))),
% 292.08/187.81 inference(modus_ponens,[status(thm)],[1041, 1039])).
% 292.08/187.81 tff(1043,plain,
% 292.08/187.81 (or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2))))) = or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[962])).
% 292.08/187.81 tff(1044,plain,
% 292.08/187.81 (not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))) = not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1043])).
% 292.08/187.81 tff(1045,plain,
% 292.08/187.81 (or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))) = or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1044])).
% 292.08/187.81 tff(1046,plain,
% 292.08/187.81 (or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))) = or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))),
% 292.08/187.81 inference(symmetry,[status(thm)],[1045])).
% 292.08/187.81 tff(1047,plain,
% 292.08/187.81 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))) = or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.81 inference(quant_inst,[status(thm)],[])).
% 292.08/187.81 tff(1048,plain,
% 292.08/187.81 (implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))) = or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))),
% 292.08/187.81 inference(unit_resolution,[status(thm)],[1047, 20])).
% 292.08/187.81 tff(1049,plain,
% 292.08/187.81 (implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))) = implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.81 inference(monotonicity,[status(thm)],[1037])).
% 292.08/187.81 tff(1050,plain,
% 292.08/187.81 (implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) = implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))),
% 292.08/187.81 inference(symmetry,[status(thm)],[1049])).
% 292.08/187.81 tff(1051,plain,
% 292.08/187.81 (implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) = or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))),
% 292.08/187.82 inference(transitivity,[status(thm)],[1050, 1048, 1046])).
% 292.08/187.82 tff(1052,plain,
% 292.08/187.82 (is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))) <=> is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.82 inference(monotonicity,[status(thm)],[1051])).
% 292.08/187.82 tff(1053,plain,
% 292.08/187.82 (is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) <=> is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))),
% 292.08/187.82 inference(symmetry,[status(thm)],[1052])).
% 292.08/187.82 tff(1054,plain,
% 292.08/187.82 (and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))) = and(implies(or(not(P!2), Q!1), or(Q!1, not(P!2))), implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)))),
% 292.08/187.82 inference(monotonicity,[status(thm)],[941, 944])).
% 292.08/187.82 tff(1055,plain,
% 292.08/187.82 (and(implies(or(not(P!2), Q!1), or(Q!1, not(P!2))), implies(or(Q!1, not(P!2)), or(not(P!2), Q!1))) = and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))),
% 292.08/187.82 inference(symmetry,[status(thm)],[1054])).
% 292.08/187.82 tff(1056,plain,
% 292.08/187.82 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(P!2), Q!1), or(Q!1, not(P!2))) = or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))),
% 292.08/187.82 inference(quant_inst,[status(thm)],[])).
% 292.08/187.82 tff(1057,plain,
% 292.08/187.82 (implies(or(not(P!2), Q!1), or(Q!1, not(P!2))) = or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))),
% 292.08/187.82 inference(unit_resolution,[status(thm)],[1056, 20])).
% 292.08/187.82 tff(1058,plain,
% 292.08/187.82 (or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))) = implies(or(not(P!2), Q!1), or(Q!1, not(P!2)))),
% 292.08/187.82 inference(symmetry,[status(thm)],[1057])).
% 292.08/187.82 tff(1059,plain,
% 292.08/187.82 (and(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))) = and(implies(or(not(P!2), Q!1), or(Q!1, not(P!2))), implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)))),
% 292.08/187.82 inference(monotonicity,[status(thm)],[1058, 944])).
% 292.08/187.82 tff(1060,plain,
% 292.08/187.82 (and(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))) = and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))),
% 292.08/187.82 inference(transitivity,[status(thm)],[1059, 1055])).
% 292.08/187.82 tff(1061,plain,
% 292.08/187.82 (not(and(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) = not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.82 inference(monotonicity,[status(thm)],[1060])).
% 292.08/187.82 tff(1062,plain,
% 292.08/187.82 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = not(and(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.82 inference(quant_inst,[status(thm)],[])).
% 292.08/187.82 tff(1063,plain,
% 292.08/187.82 (implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = not(and(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.82 inference(unit_resolution,[status(thm)],[1062, 41])).
% 292.08/187.82 tff(1064,plain,
% 292.08/187.82 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))),
% 292.08/187.82 inference(quant_inst,[status(thm)],[])).
% 292.08/187.82 tff(1065,plain,
% 292.08/187.82 (implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))),
% 292.08/187.82 inference(unit_resolution,[status(thm)],[1064, 20])).
% 292.08/187.82 tff(1066,plain,
% 292.08/187.82 (or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))),
% 292.08/187.82 inference(symmetry,[status(thm)],[1065])).
% 292.08/187.82 tff(1067,plain,
% 292.08/187.82 (or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))),
% 292.08/187.82 inference(monotonicity,[status(thm)],[1044])).
% 292.08/187.82 tff(1068,plain,
% 292.08/187.82 (or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.82 inference(transitivity,[status(thm)],[1067, 1066, 1063, 1061])).
% 292.08/187.82 tff(1069,plain,
% 292.08/187.82 (not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))) = or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.82 inference(transitivity,[status(thm)],[938, 935])).
% 292.08/187.82 tff(1070,plain,
% 292.08/187.82 (not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))) = not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.82 inference(monotonicity,[status(thm)],[1069])).
% 292.08/187.82 tff(1071,plain,
% 292.08/187.82 (not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))),
% 292.08/187.82 inference(symmetry,[status(thm)],[1070])).
% 292.08/187.82 tff(1072,plain,
% 292.08/187.82 (or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))) = or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.82 inference(monotonicity,[status(thm)],[1071, 1068])).
% 292.08/187.82 tff(1073,plain,
% 292.08/187.82 (or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) = or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))),
% 292.08/187.82 inference(symmetry,[status(thm)],[1072])).
% 292.08/187.82 tff(1074,plain,
% 292.08/187.82 (implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) = implies(or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.82 inference(monotonicity,[status(thm)],[1073])).
% 292.08/187.82 tff(1075,plain,
% 292.08/187.82 (implies(or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) = implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.82 inference(symmetry,[status(thm)],[1074])).
% 292.08/187.82 tff(1076,plain,
% 292.08/187.82 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) <=> is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.82 inference(monotonicity,[status(thm)],[1075])).
% 292.08/187.82 tff(1077,plain,
% 292.08/187.82 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) | is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.82 inference(quant_inst,[status(thm)],[])).
% 292.08/187.82 tff(1078,plain,
% 292.08/187.82 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.82 inference(unit_resolution,[status(thm)],[1077, 455])).
% 292.08/187.82 tff(1079,plain,
% 292.08/187.82 (is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.82 inference(modus_ponens,[status(thm)],[1078, 1076])).
% 292.08/187.82 tff(1080,plain,
% 292.08/187.82 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) = or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))),
% 292.08/187.82 inference(quant_inst,[status(thm)],[])).
% 292.08/187.82 tff(1081,plain,
% 292.08/187.82 (implies(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) = or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.82 inference(unit_resolution,[status(thm)],[1080, 20])).
% 292.08/187.82 tff(1082,plain,
% 292.08/187.82 (or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) = implies(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.82 inference(symmetry,[status(thm)],[1081])).
% 292.08/187.82 tff(1083,plain,
% 292.08/187.82 (is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))) <=> is_a_theorem(implies(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))),
% 292.08/187.82 inference(monotonicity,[status(thm)],[1082])).
% 292.08/187.82 tff(1084,plain,
% 292.08/187.82 (is_a_theorem(implies(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))) <=> is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))),
% 292.08/187.83 inference(symmetry,[status(thm)],[1083])).
% 292.08/187.83 tff(1085,plain,
% 292.08/187.83 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.83 inference(quant_inst,[status(thm)],[])).
% 292.08/187.83 tff(1086,plain,
% 292.08/187.83 (or(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.83 inference(unit_resolution,[status(thm)],[1085, 63])).
% 292.08/187.83 tff(1087,plain,
% 292.08/187.83 (or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = or(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))),
% 292.08/187.83 inference(monotonicity,[status(thm)],[925])).
% 292.08/187.83 tff(1088,plain,
% 292.08/187.83 (or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.83 inference(transitivity,[status(thm)],[1087, 1086])).
% 292.08/187.83 tff(1089,plain,
% 292.08/187.83 (or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))),
% 292.08/187.83 inference(monotonicity,[status(thm)],[925])).
% 292.08/187.83 tff(1090,plain,
% 292.08/187.83 (or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))),
% 292.08/187.83 inference(transitivity,[status(thm)],[1089, 937])).
% 292.08/187.83 tff(1091,plain,
% 292.08/187.83 (implies(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))) = implies(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.83 inference(monotonicity,[status(thm)],[1090, 1088])).
% 292.08/187.83 tff(1092,plain,
% 292.08/187.83 (is_a_theorem(implies(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) <=> is_a_theorem(implies(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))),
% 292.08/187.83 inference(monotonicity,[status(thm)],[1091])).
% 292.08/187.83 tff(1093,plain,
% 292.08/187.83 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.83 inference(quant_inst,[status(thm)],[])).
% 292.08/187.83 tff(1094,plain,
% 292.08/187.83 (is_a_theorem(implies(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.83 inference(unit_resolution,[status(thm)],[1093, 399])).
% 292.08/187.83 tff(1095,plain,
% 292.08/187.83 (is_a_theorem(implies(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))),
% 292.08/187.83 inference(modus_ponens,[status(thm)],[1094, 1092])).
% 292.08/187.83 tff(1096,plain,
% 292.08/187.83 (is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))),
% 292.08/187.83 inference(modus_ponens,[status(thm)],[1095, 1084])).
% 292.08/187.83 tff(1097,plain,
% 292.08/187.83 (((~![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(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) | is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) | is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))))),
% 292.08/187.83 inference(rewrite,[status(thm)],[])).
% 292.08/187.83 tff(1098,plain,
% 292.08/187.83 ((is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) | (~is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) <=> ((~is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) | is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))))),
% 292.08/187.83 inference(rewrite,[status(thm)],[])).
% 292.08/187.83 tff(1099,plain,
% 292.08/187.83 (((~![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(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) | (~is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) | is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))))),
% 292.08/187.83 inference(monotonicity,[status(thm)],[1098])).
% 292.08/187.83 tff(1100,plain,
% 292.08/187.83 (((~![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(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) | (~is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) | is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))))),
% 292.08/187.83 inference(transitivity,[status(thm)],[1099, 1097])).
% 292.08/187.83 tff(1101,plain,
% 292.08/187.83 ((~![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(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) | (~is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))))),
% 292.08/187.83 inference(quant_inst,[status(thm)],[])).
% 292.08/187.83 tff(1102,plain,
% 292.08/187.83 ((~![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(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) | is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))),
% 292.08/187.83 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 292.08/187.83 tff(1103,plain,
% 292.08/187.83 ((~is_a_theorem(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))) | is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))),
% 292.08/187.83 inference(unit_resolution,[status(thm)],[1102, 495])).
% 292.08/187.83 tff(1104,plain,
% 292.08/187.83 (is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(and(not(Q!1), not(not(P!2)))))), or(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.83 inference(unit_resolution,[status(thm)],[1103, 1096, 1079])).
% 292.08/187.83 tff(1105,plain,
% 292.08/187.83 (is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))),
% 292.08/187.83 inference(modus_ponens,[status(thm)],[1104, 1053])).
% 292.08/187.83 tff(1106,plain,
% 292.08/187.83 (is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))) <=> is_a_theorem(implies(or(not(P!2), Q!1), or(Q!1, not(P!2))))),
% 292.08/187.83 inference(monotonicity,[status(thm)],[1058])).
% 292.08/187.83 tff(1107,plain,
% 292.08/187.83 (is_a_theorem(implies(or(not(P!2), Q!1), or(Q!1, not(P!2)))) <=> is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))),
% 292.08/187.83 inference(symmetry,[status(thm)],[1106])).
% 292.08/187.83 tff(1108,plain,
% 292.08/187.83 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(P!2), Q!1), or(Q!1, not(P!2))))),
% 292.08/187.83 inference(quant_inst,[status(thm)],[])).
% 292.08/187.83 tff(1109,plain,
% 292.08/187.83 (is_a_theorem(implies(or(not(P!2), Q!1), or(Q!1, not(P!2))))),
% 292.08/187.83 inference(unit_resolution,[status(thm)],[1108, 399])).
% 292.08/187.83 tff(1110,plain,
% 292.08/187.83 (is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))),
% 292.08/187.83 inference(modus_ponens,[status(thm)],[1109, 1107])).
% 292.08/187.83 tff(1111,plain,
% 292.08/187.83 (((~![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(P!2), Q!1)), or(Q!1, not(P!2))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))))) <=> ((~![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(P!2), Q!1)), or(Q!1, not(P!2))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))))),
% 292.08/187.84 inference(rewrite,[status(thm)],[])).
% 292.08/187.84 tff(1112,plain,
% 292.08/187.84 ((is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))))) <=> ((~is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))))),
% 292.08/187.84 inference(rewrite,[status(thm)],[])).
% 292.08/187.84 tff(1113,plain,
% 292.08/187.84 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))))) <=> ((~![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(P!2), Q!1)), or(Q!1, not(P!2))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))))))),
% 292.08/187.84 inference(monotonicity,[status(thm)],[1112])).
% 292.08/187.84 tff(1114,plain,
% 292.08/187.84 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))))) <=> ((~![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(P!2), Q!1)), or(Q!1, not(P!2))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))))),
% 292.08/187.84 inference(transitivity,[status(thm)],[1113, 1111])).
% 292.08/187.84 tff(1115,plain,
% 292.08/187.84 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))))))),
% 292.08/187.84 inference(quant_inst,[status(thm)],[])).
% 292.08/187.84 tff(1116,plain,
% 292.08/187.84 ((~![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(P!2), Q!1)), or(Q!1, not(P!2))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))))),
% 292.08/187.84 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 292.08/187.84 tff(1117,plain,
% 292.08/187.84 (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))))),
% 292.08/187.84 inference(unit_resolution,[status(thm)],[1116, 495, 1110])).
% 292.08/187.84 tff(1118,plain,
% 292.08/187.84 (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.84 inference(unit_resolution,[status(thm)],[1117, 1105])).
% 292.08/187.84 tff(1119,plain,
% 292.08/187.84 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))),
% 292.08/187.84 inference(rewrite,[status(thm)],[])).
% 292.08/187.84 tff(1120,plain,
% 292.08/187.84 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))),
% 292.08/187.84 inference(quant_inst,[status(thm)],[])).
% 292.08/187.84 tff(1121,plain,
% 292.08/187.84 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.08/187.84 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 292.08/187.84 tff(1122,plain,
% 292.08/187.84 (is_a_theorem(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.08/187.84 inference(unit_resolution,[status(thm)],[1121, 495])).
% 292.08/187.84 tff(1123,plain,
% 292.08/187.84 (is_a_theorem(or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.84 inference(unit_resolution,[status(thm)],[1122, 1118, 1042])).
% 292.08/187.84 tff(1124,plain,
% 292.08/187.84 (is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.84 inference(modus_ponens,[status(thm)],[1123, 1035])).
% 292.08/187.84 tff(1125,plain,
% 292.08/187.84 (not(or(Q!1, not(P!2))) = not(not(and(not(Q!1), not(not(P!2)))))),
% 292.08/187.84 inference(symmetry,[status(thm)],[963])).
% 292.08/187.84 tff(1126,plain,
% 292.08/187.84 (or(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1)))) = or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))),
% 292.08/187.84 inference(monotonicity,[status(thm)],[1125])).
% 292.08/187.84 tff(1127,plain,
% 292.08/187.84 (or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))) = or(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1))))),
% 292.08/187.84 inference(symmetry,[status(thm)],[1126])).
% 292.08/187.84 tff(1128,plain,
% 292.08/187.84 (implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))) = implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1)))))),
% 292.08/187.84 inference(monotonicity,[status(thm)],[1127])).
% 292.08/187.84 tff(1129,plain,
% 292.08/187.84 (implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1))))) = implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))),
% 292.08/187.84 inference(symmetry,[status(thm)],[1128])).
% 292.08/187.84 tff(1130,plain,
% 292.08/187.84 (is_a_theorem(implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1)))))) <=> is_a_theorem(implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))),
% 292.08/187.84 inference(monotonicity,[status(thm)],[1129])).
% 292.08/187.84 tff(1131,plain,
% 292.08/187.84 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1))))))),
% 292.08/187.84 inference(quant_inst,[status(thm)],[])).
% 292.08/187.84 tff(1132,plain,
% 292.08/187.84 (is_a_theorem(implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1))))))),
% 292.08/187.84 inference(unit_resolution,[status(thm)],[1131, 399])).
% 292.08/187.84 tff(1133,plain,
% 292.08/187.84 (is_a_theorem(implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))),
% 292.08/187.84 inference(modus_ponens,[status(thm)],[1132, 1130])).
% 292.08/187.84 tff(1134,plain,
% 292.08/187.84 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))) = not(and(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.84 inference(quant_inst,[status(thm)],[])).
% 292.08/187.84 tff(1135,plain,
% 292.08/187.84 (or(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))) = not(and(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.08/187.84 inference(unit_resolution,[status(thm)],[1134, 63])).
% 292.08/187.84 tff(1136,plain,
% 292.08/187.84 (not(and(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) = or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))),
% 292.08/187.84 inference(symmetry,[status(thm)],[1135])).
% 292.08/187.84 tff(1137,plain,
% 292.08/187.84 (and(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2))))) = and(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))),
% 292.08/187.84 inference(monotonicity,[status(thm)],[137])).
% 292.08/187.84 tff(1138,plain,
% 292.08/187.84 (and(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))) = and(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2)))))),
% 292.08/187.84 inference(symmetry,[status(thm)],[1137])).
% 292.08/187.84 tff(1139,plain,
% 292.08/187.84 (not(and(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) = not(and(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.08/187.84 inference(monotonicity,[status(thm)],[1138])).
% 292.08/187.84 tff(1140,plain,
% 292.08/187.84 (not(and(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2)))))) = not(and(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.08/187.84 inference(symmetry,[status(thm)],[1139])).
% 292.08/187.84 tff(1141,plain,
% 292.08/187.84 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(implies(P!2, Q!1)), not(or(Q!1, not(P!2)))) = not(and(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.84 inference(quant_inst,[status(thm)],[])).
% 292.08/187.84 tff(1142,plain,
% 292.08/187.84 (implies(not(implies(P!2, Q!1)), not(or(Q!1, not(P!2)))) = not(and(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.08/187.84 inference(unit_resolution,[status(thm)],[1141, 41])).
% 292.08/187.84 tff(1143,plain,
% 292.08/187.84 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(implies(P!2, Q!1)), not(or(Q!1, not(P!2)))) = or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))))),
% 292.08/187.84 inference(quant_inst,[status(thm)],[])).
% 292.08/187.84 tff(1144,plain,
% 292.08/187.84 (implies(not(implies(P!2, Q!1)), not(or(Q!1, not(P!2)))) = or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2))))),
% 292.08/187.84 inference(unit_resolution,[status(thm)],[1143, 20])).
% 292.08/187.84 tff(1145,plain,
% 292.08/187.84 (or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))) = implies(not(implies(P!2, Q!1)), not(or(Q!1, not(P!2))))),
% 292.08/187.84 inference(symmetry,[status(thm)],[1144])).
% 292.08/187.84 tff(1146,plain,
% 292.08/187.84 (or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))) = or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))),
% 292.08/187.84 inference(transitivity,[status(thm)],[1145, 1142, 1140, 1136])).
% 292.08/187.84 tff(1147,plain,
% 292.08/187.84 (is_a_theorem(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2))))) <=> is_a_theorem(or(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))),
% 292.08/187.84 inference(monotonicity,[status(thm)],[1146])).
% 292.08/187.84 tff(1148,plain,
% 292.08/187.84 (is_a_theorem(or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) <=> is_a_theorem(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))))),
% 292.08/187.84 inference(symmetry,[status(thm)],[1147])).
% 292.08/187.84 tff(1149,plain,
% 292.08/187.84 (is_a_theorem(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))) <=> is_a_theorem(implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)))),
% 292.08/187.84 inference(monotonicity,[status(thm)],[949])).
% 292.08/187.84 tff(1150,plain,
% 292.08/187.84 (is_a_theorem(implies(or(Q!1, not(P!2)), or(not(P!2), Q!1))) <=> is_a_theorem(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)))),
% 292.08/187.84 inference(symmetry,[status(thm)],[1149])).
% 292.08/187.84 tff(1151,plain,
% 292.08/187.84 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)))),
% 292.08/187.84 inference(quant_inst,[status(thm)],[])).
% 292.08/187.84 tff(1152,plain,
% 292.08/187.84 (is_a_theorem(implies(or(Q!1, not(P!2)), or(not(P!2), Q!1)))),
% 292.08/187.84 inference(unit_resolution,[status(thm)],[1151, 399])).
% 292.08/187.84 tff(1153,plain,
% 292.08/187.84 (is_a_theorem(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)))),
% 292.08/187.84 inference(modus_ponens,[status(thm)],[1152, 1150])).
% 292.08/187.84 tff(1154,plain,
% 292.08/187.84 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))),
% 292.08/187.84 inference(quant_inst,[status(thm)],[])).
% 292.08/187.84 tff(1155,plain,
% 292.08/187.84 (is_a_theorem(implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))),
% 292.08/187.84 inference(unit_resolution,[status(thm)],[1154, 399])).
% 292.08/187.84 tff(1156,plain,
% 292.08/187.84 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) | (~is_a_theorem(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)))) | (~is_a_theorem(implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) | (~is_a_theorem(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)))) | (~is_a_theorem(implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))),
% 292.08/187.84 inference(rewrite,[status(thm)],[])).
% 292.08/187.84 tff(1157,plain,
% 292.08/187.84 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) | (~is_a_theorem(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)))) | (~is_a_theorem(implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1158,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) | (~is_a_theorem(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)))) | (~is_a_theorem(implies(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1)), or(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))),
% 292.08/187.85 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 292.08/187.85 tff(1159,plain,
% 292.08/187.85 (is_a_theorem(or(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))) | (~is_a_theorem(or(not(or(Q!1, not(P!2))), or(not(P!2), Q!1))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1158, 495, 1155])).
% 292.08/187.85 tff(1160,plain,
% 292.08/187.85 (is_a_theorem(or(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1159, 1153])).
% 292.08/187.85 tff(1161,plain,
% 292.08/187.85 (is_a_theorem(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))))),
% 292.08/187.85 inference(modus_ponens,[status(thm)],[1160, 1148])).
% 292.08/187.85 tff(1162,plain,
% 292.08/187.85 (((~![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(not(P!2))))), not(not(implies(P!2, Q!1))))) | (~is_a_theorem(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))))) | (~is_a_theorem(implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))) | (~is_a_theorem(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))))) | (~is_a_theorem(implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))),
% 292.08/187.85 inference(rewrite,[status(thm)],[])).
% 292.08/187.85 tff(1163,plain,
% 292.08/187.85 ((~![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(not(P!2))))), not(not(implies(P!2, Q!1))))) | (~is_a_theorem(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))))) | (~is_a_theorem(implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1164,plain,
% 292.08/187.85 ((~![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(not(P!2))))), not(not(implies(P!2, Q!1))))) | (~is_a_theorem(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))))) | (~is_a_theorem(implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))),
% 292.08/187.85 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 292.08/187.85 tff(1165,plain,
% 292.08/187.85 (is_a_theorem(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))) | (~is_a_theorem(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))))) | (~is_a_theorem(implies(or(not(not(implies(P!2, Q!1))), not(or(Q!1, not(P!2)))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1164, 495])).
% 292.08/187.85 tff(1166,plain,
% 292.08/187.85 (is_a_theorem(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1165, 1161, 1133])).
% 292.08/187.85 tff(1167,plain,
% 292.08/187.85 (((~![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(not(P!2))))), not(not(implies(P!2, Q!1)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))) <=> ((~![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(not(P!2))))), not(not(implies(P!2, Q!1)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.08/187.85 inference(rewrite,[status(thm)],[])).
% 292.08/187.85 tff(1168,plain,
% 292.08/187.85 ((is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))) <=> ((~is_a_theorem(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.08/187.85 inference(rewrite,[status(thm)],[])).
% 292.08/187.85 tff(1169,plain,
% 292.08/187.85 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))) <=> ((~![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(not(P!2))))), not(not(implies(P!2, Q!1)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))),
% 292.08/187.85 inference(monotonicity,[status(thm)],[1168])).
% 292.08/187.85 tff(1170,plain,
% 292.08/187.85 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))) <=> ((~![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(not(P!2))))), not(not(implies(P!2, Q!1)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.08/187.85 inference(transitivity,[status(thm)],[1169, 1167])).
% 292.08/187.85 tff(1171,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1172,plain,
% 292.08/187.85 ((~![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(not(P!2))))), not(not(implies(P!2, Q!1)))))) | is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))),
% 292.08/187.85 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 292.08/187.85 tff(1173,plain,
% 292.08/187.85 (is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1172, 495, 1166])).
% 292.08/187.85 tff(1174,plain,
% 292.08/187.85 (is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1173, 1124])).
% 292.08/187.85 tff(1175,plain,
% 292.08/187.85 (is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))))),
% 292.08/187.85 inference(modus_ponens,[status(thm)],[1174, 1029])).
% 292.08/187.85 tff(1176,plain,
% 292.08/187.85 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))))) | (not(not(or(Q!1, not(P!2)))) = or(not(P!2), not(not(Q!1)))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))))) | (not(not(or(Q!1, not(P!2)))) = or(not(P!2), not(not(Q!1)))))),
% 292.08/187.85 inference(rewrite,[status(thm)],[])).
% 292.08/187.85 tff(1177,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))))) | (not(not(or(Q!1, not(P!2)))) = or(not(P!2), not(not(Q!1)))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1178,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))))) | (not(not(or(Q!1, not(P!2)))) = or(not(P!2), not(not(Q!1))))),
% 292.08/187.85 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 292.08/187.85 tff(1179,plain,
% 292.08/187.85 ((~is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), not(not(Q!1)))))) | (not(not(or(Q!1, not(P!2)))) = or(not(P!2), not(not(Q!1))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1178, 564])).
% 292.08/187.85 tff(1180,plain,
% 292.08/187.85 (not(not(or(Q!1, not(P!2)))) = or(not(P!2), not(not(Q!1)))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1179, 1175])).
% 292.08/187.85 tff(1181,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) = not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1182,plain,
% 292.08/187.85 (and(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) = not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1181, 100])).
% 292.08/187.85 tff(1183,plain,
% 292.08/187.85 (or(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2))))) = or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))),
% 292.08/187.85 inference(monotonicity,[status(thm)],[137])).
% 292.08/187.85 tff(1184,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1185,plain,
% 292.08/187.85 (or(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1184, 63])).
% 292.08/187.85 tff(1186,plain,
% 292.08/187.85 (not(and(not(not(implies(P!2, Q!1))), not(not(not(or(Q!1, not(P!2))))))) = or(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2)))))),
% 292.08/187.85 inference(symmetry,[status(thm)],[1185])).
% 292.08/187.85 tff(1187,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(implies(P!2, Q!1))), not(not(or(Q!1, not(P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1188,plain,
% 292.08/187.85 (implies(not(not(implies(P!2, Q!1))), not(not(or(Q!1, not(P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1187, 41])).
% 292.08/187.85 tff(1189,plain,
% 292.08/187.85 (implies(not(not(implies(P!2, Q!1))), not(not(or(Q!1, not(P!2))))) = or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))),
% 292.08/187.85 inference(transitivity,[status(thm)],[1188, 1186, 1183])).
% 292.08/187.85 tff(1190,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1)))) = not(and(not(not(or(Q!1, not(P!2)))), not(not(not(implies(P!2, Q!1)))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1191,plain,
% 292.08/187.85 (or(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1)))) = not(and(not(not(or(Q!1, not(P!2)))), not(not(not(implies(P!2, Q!1))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1190, 63])).
% 292.08/187.85 tff(1192,plain,
% 292.08/187.85 (not(and(not(not(or(Q!1, not(P!2)))), not(not(not(implies(P!2, Q!1)))))) = or(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1))))),
% 292.08/187.85 inference(symmetry,[status(thm)],[1191])).
% 292.08/187.85 tff(1193,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))) = not(and(not(not(or(Q!1, not(P!2)))), not(not(not(implies(P!2, Q!1)))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1194,plain,
% 292.08/187.85 (implies(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))) = not(and(not(not(or(Q!1, not(P!2)))), not(not(not(implies(P!2, Q!1))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1193, 41])).
% 292.08/187.85 tff(1195,plain,
% 292.08/187.85 (implies(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))) = or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))),
% 292.08/187.85 inference(transitivity,[status(thm)],[1194, 1192, 1126])).
% 292.08/187.85 tff(1196,plain,
% 292.08/187.85 (and(implies(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))), implies(not(not(implies(P!2, Q!1))), not(not(or(Q!1, not(P!2)))))) = and(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.08/187.85 inference(monotonicity,[status(thm)],[1195, 1189])).
% 292.08/187.85 tff(1197,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))) = and(implies(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))), implies(not(not(implies(P!2, Q!1))), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1198,plain,
% 292.08/187.85 (equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))) = and(implies(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))), implies(not(not(implies(P!2, Q!1))), not(not(or(Q!1, not(P!2))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1197, 133])).
% 292.08/187.85 tff(1199,plain,
% 292.08/187.85 (equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))) = equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1))),
% 292.08/187.85 inference(transitivity,[status(thm)],[1198, 1196, 1182, 961, 922, 919, 909])).
% 292.08/187.85 tff(1200,plain,
% 292.08/187.85 (is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1))))) <=> is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1)))),
% 292.08/187.85 inference(monotonicity,[status(thm)],[1199])).
% 292.08/187.85 tff(1201,plain,
% 292.08/187.85 (is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), or(not(P!2), Q!1))) <=> is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))))),
% 292.08/187.85 inference(symmetry,[status(thm)],[1200])).
% 292.08/187.85 tff(1202,plain,
% 292.08/187.85 (is_a_theorem(not(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) <=> is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))))),
% 292.08/187.85 inference(transitivity,[status(thm)],[1028, 1201])).
% 292.08/187.85 tff(1203,plain,
% 292.08/187.85 (is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))))),
% 292.08/187.85 inference(modus_ponens,[status(thm)],[1174, 1202])).
% 292.08/187.85 tff(1204,plain,
% 292.08/187.85 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))))) | (not(not(or(Q!1, not(P!2)))) = not(not(implies(P!2, Q!1)))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))))) | (not(not(or(Q!1, not(P!2)))) = not(not(implies(P!2, Q!1)))))),
% 292.08/187.85 inference(rewrite,[status(thm)],[])).
% 292.08/187.85 tff(1205,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))))) | (not(not(or(Q!1, not(P!2)))) = not(not(implies(P!2, Q!1)))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1206,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))))) | (not(not(or(Q!1, not(P!2)))) = not(not(implies(P!2, Q!1))))),
% 292.08/187.85 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 292.08/187.85 tff(1207,plain,
% 292.08/187.85 ((~is_a_theorem(equiv(not(not(or(Q!1, not(P!2)))), not(not(implies(P!2, Q!1)))))) | (not(not(or(Q!1, not(P!2)))) = not(not(implies(P!2, Q!1))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1206, 564])).
% 292.08/187.85 tff(1208,plain,
% 292.08/187.85 (not(not(or(Q!1, not(P!2)))) = not(not(implies(P!2, Q!1)))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1207, 1203])).
% 292.08/187.85 tff(1209,plain,
% 292.08/187.85 (not(not(implies(P!2, Q!1))) = not(not(or(Q!1, not(P!2))))),
% 292.08/187.85 inference(symmetry,[status(thm)],[1208])).
% 292.08/187.85 tff(1210,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))) = and(implies(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))), implies(not(and(not(Q!1), not(not(P!2)))), not(not(implies(P!2, Q!1))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1211,plain,
% 292.08/187.85 (equiv(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))) = and(implies(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))), implies(not(and(not(Q!1), not(not(P!2)))), not(not(implies(P!2, Q!1)))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1210, 133])).
% 292.08/187.85 tff(1212,plain,
% 292.08/187.85 (and(implies(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))), implies(not(and(not(Q!1), not(not(P!2)))), not(not(implies(P!2, Q!1))))) = equiv(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2)))))),
% 292.08/187.85 inference(symmetry,[status(thm)],[1211])).
% 292.08/187.85 tff(1213,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(Q!1), not(not(P!2)))), not(not(implies(P!2, Q!1)))) = or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1214,plain,
% 292.08/187.85 (implies(not(and(not(Q!1), not(not(P!2)))), not(not(implies(P!2, Q!1)))) = or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1213, 20])).
% 292.08/187.85 tff(1215,plain,
% 292.08/187.85 (or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))) = implies(not(and(not(Q!1), not(not(P!2)))), not(not(implies(P!2, Q!1))))),
% 292.08/187.85 inference(symmetry,[status(thm)],[1214])).
% 292.08/187.85 tff(1216,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(and(not(Q!1), not(not(P!2))))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1217,plain,
% 292.08/187.85 (implies(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(and(not(Q!1), not(not(P!2)))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1216, 41])).
% 292.08/187.85 tff(1218,plain,
% 292.08/187.85 (not(and(not(not(implies(P!2, Q!1))), not(not(and(not(Q!1), not(not(P!2))))))) = implies(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2)))))),
% 292.08/187.85 inference(symmetry,[status(thm)],[1217])).
% 292.08/187.85 tff(1219,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(implies(P!2, Q!1)), not(and(not(Q!1), not(not(P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(and(not(Q!1), not(not(P!2))))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1220,plain,
% 292.08/187.85 (or(not(implies(P!2, Q!1)), not(and(not(Q!1), not(not(P!2))))) = not(and(not(not(implies(P!2, Q!1))), not(not(and(not(Q!1), not(not(P!2)))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1219, 63])).
% 292.08/187.85 tff(1221,plain,
% 292.08/187.85 (or(not(implies(P!2, Q!1)), not(and(not(Q!1), not(not(P!2))))) = or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))),
% 292.08/187.85 inference(monotonicity,[status(thm)],[137, 962])).
% 292.08/187.85 tff(1222,plain,
% 292.08/187.85 (or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))) = or(not(implies(P!2, Q!1)), not(and(not(Q!1), not(not(P!2)))))),
% 292.08/187.85 inference(symmetry,[status(thm)],[1221])).
% 292.08/187.85 tff(1223,plain,
% 292.08/187.85 (or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))) = implies(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2)))))),
% 292.08/187.85 inference(transitivity,[status(thm)],[1222, 1220, 1218])).
% 292.08/187.85 tff(1224,plain,
% 292.08/187.85 (and(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))) = and(implies(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))), implies(not(and(not(Q!1), not(not(P!2)))), not(not(implies(P!2, Q!1)))))),
% 292.08/187.85 inference(monotonicity,[status(thm)],[1223, 1215])).
% 292.08/187.85 tff(1225,plain,
% 292.08/187.85 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))) = not(or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))),
% 292.08/187.85 inference(quant_inst,[status(thm)],[])).
% 292.08/187.85 tff(1226,plain,
% 292.08/187.85 (and(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))) = not(or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))),
% 292.08/187.85 inference(unit_resolution,[status(thm)],[1225, 100])).
% 292.08/187.85 tff(1227,plain,
% 292.08/187.85 (not(or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))) = and(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))),
% 292.08/187.85 inference(symmetry,[status(thm)],[1226])).
% 292.08/187.85 tff(1228,plain,
% 292.08/187.85 (or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))) = or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[933])).
% 292.08/187.86 tff(1229,plain,
% 292.08/187.86 (or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1228])).
% 292.08/187.86 tff(1230,plain,
% 292.08/187.86 (not(and(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) = implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1063])).
% 292.08/187.86 tff(1231,plain,
% 292.08/187.86 (not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) = not(and(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1061])).
% 292.08/187.86 tff(1232,plain,
% 292.08/187.86 (or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))) = or(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[925, 933])).
% 292.08/187.86 tff(1233,plain,
% 292.08/187.86 (or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))) = or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))),
% 292.08/187.86 inference(transitivity,[status(thm)],[1232, 1086, 1231, 1230, 1065, 1229])).
% 292.08/187.86 tff(1234,plain,
% 292.08/187.86 (not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))) = not(or(not(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2)))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1233])).
% 292.08/187.86 tff(1235,plain,
% 292.08/187.86 (not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))) = equiv(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2)))))),
% 292.08/187.86 inference(transitivity,[status(thm)],[1234, 1227, 1224, 1212])).
% 292.08/187.86 tff(1236,plain,
% 292.08/187.86 (is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) <=> is_a_theorem(equiv(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1235])).
% 292.08/187.86 tff(1237,plain,
% 292.08/187.86 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) = or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))),
% 292.08/187.86 inference(quant_inst,[status(thm)],[])).
% 292.08/187.86 tff(1238,plain,
% 292.08/187.86 (implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) = or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))),
% 292.08/187.86 inference(unit_resolution,[status(thm)],[1237, 20])).
% 292.08/187.86 tff(1239,plain,
% 292.08/187.86 (is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))) <=> is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1238])).
% 292.08/187.86 tff(1240,plain,
% 292.08/187.86 (is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))) <=> is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1239])).
% 292.08/187.86 tff(1241,plain,
% 292.08/187.86 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.86 inference(quant_inst,[status(thm)],[])).
% 292.08/187.86 tff(1242,plain,
% 292.08/187.86 (or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.86 inference(unit_resolution,[status(thm)],[1241, 63])).
% 292.08/187.86 tff(1243,plain,
% 292.08/187.86 (implies(or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))) = implies(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1242])).
% 292.08/187.86 tff(1244,plain,
% 292.08/187.86 (is_a_theorem(implies(or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))) <=> is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1243])).
% 292.08/187.86 tff(1245,plain,
% 292.08/187.86 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))))),
% 292.08/187.86 inference(quant_inst,[status(thm)],[])).
% 292.08/187.86 tff(1246,plain,
% 292.08/187.86 (is_a_theorem(implies(or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))))),
% 292.08/187.86 inference(unit_resolution,[status(thm)],[1245, 399])).
% 292.08/187.86 tff(1247,plain,
% 292.08/187.86 (is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))))),
% 292.08/187.86 inference(modus_ponens,[status(thm)],[1246, 1244])).
% 292.08/187.86 tff(1248,plain,
% 292.08/187.86 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(P!2), not(not(Q!1))) = not(and(not(not(P!2)), not(not(not(Q!1))))))),
% 292.08/187.86 inference(quant_inst,[status(thm)],[])).
% 292.08/187.86 tff(1249,plain,
% 292.08/187.86 (or(not(P!2), not(not(Q!1))) = not(and(not(not(P!2)), not(not(not(Q!1)))))),
% 292.08/187.86 inference(unit_resolution,[status(thm)],[1248, 63])).
% 292.08/187.86 tff(1250,plain,
% 292.08/187.86 (not(and(not(not(P!2)), not(not(not(Q!1))))) = or(not(P!2), not(not(Q!1)))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1249])).
% 292.08/187.86 tff(1251,plain,
% 292.08/187.86 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(P!2)), not(not(Q!1))) = not(and(not(not(P!2)), not(not(not(Q!1))))))),
% 292.08/187.86 inference(quant_inst,[status(thm)],[])).
% 292.08/187.86 tff(1252,plain,
% 292.08/187.86 (implies(not(not(P!2)), not(not(Q!1))) = not(and(not(not(P!2)), not(not(not(Q!1)))))),
% 292.08/187.86 inference(unit_resolution,[status(thm)],[1251, 41])).
% 292.08/187.86 tff(1253,plain,
% 292.08/187.86 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(P!2)), not(not(Q!1))) = or(not(not(not(P!2))), not(not(Q!1))))),
% 292.08/187.86 inference(quant_inst,[status(thm)],[])).
% 292.08/187.86 tff(1254,plain,
% 292.08/187.86 (implies(not(not(P!2)), not(not(Q!1))) = or(not(not(not(P!2))), not(not(Q!1)))),
% 292.08/187.86 inference(unit_resolution,[status(thm)],[1253, 20])).
% 292.08/187.86 tff(1255,plain,
% 292.08/187.86 (or(not(not(not(P!2))), not(not(Q!1))) = implies(not(not(P!2)), not(not(Q!1)))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1254])).
% 292.08/187.86 tff(1256,plain,
% 292.08/187.86 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(not(not(P!2))), not(not(Q!1))) = not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))),
% 292.08/187.86 inference(quant_inst,[status(thm)],[])).
% 292.08/187.86 tff(1257,plain,
% 292.08/187.86 (or(not(not(not(P!2))), not(not(Q!1))) = not(and(not(not(not(not(P!2)))), not(not(not(Q!1)))))),
% 292.08/187.86 inference(unit_resolution,[status(thm)],[1256, 63])).
% 292.08/187.86 tff(1258,plain,
% 292.08/187.86 (not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))) = or(not(not(not(P!2))), not(not(Q!1)))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1257])).
% 292.08/187.86 tff(1259,plain,
% 292.08/187.86 (not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))) = or(not(P!2), not(not(Q!1)))),
% 292.08/187.86 inference(transitivity,[status(thm)],[1258, 1255, 1252, 1250])).
% 292.08/187.86 tff(1260,plain,
% 292.08/187.86 (not(not(and(not(Q!1), not(not(P!2))))) = not(or(not(not(Q!1)), not(P!2)))),
% 292.08/187.86 inference(transitivity,[status(thm)],[963, 1013])).
% 292.08/187.86 tff(1261,plain,
% 292.08/187.86 (or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1)))))) = or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1260, 1259])).
% 292.08/187.86 tff(1262,plain,
% 292.08/187.86 (or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))) = or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1261])).
% 292.08/187.86 tff(1263,plain,
% 292.08/187.86 (not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))) = not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1)))))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1262])).
% 292.08/187.86 tff(1264,plain,
% 292.08/187.86 (or(not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1263])).
% 292.08/187.86 tff(1265,plain,
% 292.08/187.86 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = or(not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.86 inference(quant_inst,[status(thm)],[])).
% 292.08/187.86 tff(1266,plain,
% 292.08/187.86 (implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = or(not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.86 inference(unit_resolution,[status(thm)],[1265, 20])).
% 292.08/187.86 tff(1267,plain,
% 292.08/187.86 (not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) = or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1242])).
% 292.08/187.86 tff(1268,plain,
% 292.08/187.86 (implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) = implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1267])).
% 292.08/187.86 tff(1269,plain,
% 292.08/187.86 (implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) = or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.08/187.86 inference(transitivity,[status(thm)],[1268, 1266, 1264])).
% 292.08/187.86 tff(1270,plain,
% 292.08/187.86 (is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))) <=> is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1269])).
% 292.08/187.86 tff(1271,plain,
% 292.08/187.86 (is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) <=> is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1270])).
% 292.08/187.86 tff(1272,plain,
% 292.08/187.86 (not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))) = not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1263])).
% 292.08/187.86 tff(1273,plain,
% 292.08/187.86 (or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = or(not(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1272])).
% 292.08/187.86 tff(1274,plain,
% 292.08/187.86 (or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) = not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))),
% 292.08/187.86 inference(transitivity,[status(thm)],[1273, 996, 993, 991, 969, 966, 958, 955, 954, 952])).
% 292.08/187.86 tff(1275,plain,
% 292.08/187.86 (or(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))) = or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1232])).
% 292.08/187.86 tff(1276,plain,
% 292.08/187.86 (not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) = or(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))),
% 292.08/187.86 inference(symmetry,[status(thm)],[1086])).
% 292.08/187.86 tff(1277,plain,
% 292.08/187.86 (not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))) = or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))),
% 292.08/187.86 inference(transitivity,[status(thm)],[1276, 1275])).
% 292.08/187.86 tff(1278,plain,
% 292.08/187.86 (not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))) = not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))),
% 292.08/187.86 inference(monotonicity,[status(thm)],[1277])).
% 292.08/187.86 tff(1279,plain,
% 292.08/187.86 (not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))) = not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))))),
% 292.08/187.87 inference(symmetry,[status(thm)],[1278])).
% 292.08/187.87 tff(1280,plain,
% 292.08/187.87 (or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))),
% 292.08/187.87 inference(monotonicity,[status(thm)],[1279, 1274])).
% 292.08/187.87 tff(1281,plain,
% 292.08/187.87 (implies(or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) = implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.87 inference(monotonicity,[status(thm)],[1280])).
% 292.08/187.87 tff(1282,plain,
% 292.08/187.87 (is_a_theorem(implies(or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) <=> is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.87 inference(monotonicity,[status(thm)],[1281])).
% 292.08/187.87 tff(1283,plain,
% 292.08/187.87 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) | is_a_theorem(implies(or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.87 inference(quant_inst,[status(thm)],[])).
% 292.08/187.87 tff(1284,plain,
% 292.08/187.87 (is_a_theorem(implies(or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.87 inference(unit_resolution,[status(thm)],[1283, 455])).
% 292.08/187.87 tff(1285,plain,
% 292.08/187.87 (is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.08/187.87 inference(modus_ponens,[status(thm)],[1284, 1282])).
% 292.08/187.87 tff(1286,plain,
% 292.08/187.87 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))) = or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))),
% 292.08/187.87 inference(quant_inst,[status(thm)],[])).
% 292.08/187.87 tff(1287,plain,
% 292.08/187.87 (implies(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))) = or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))),
% 292.08/187.87 inference(unit_resolution,[status(thm)],[1286, 20])).
% 292.08/187.87 tff(1288,plain,
% 292.08/187.87 (or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))) = implies(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))),
% 292.08/187.87 inference(symmetry,[status(thm)],[1287])).
% 292.08/187.87 tff(1289,plain,
% 292.08/187.87 (is_a_theorem(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))) <=> is_a_theorem(implies(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))),
% 292.08/187.87 inference(monotonicity,[status(thm)],[1288])).
% 292.08/187.87 tff(1290,plain,
% 292.08/187.87 (is_a_theorem(implies(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))) <=> is_a_theorem(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))),
% 292.08/187.87 inference(symmetry,[status(thm)],[1289])).
% 292.08/187.87 tff(1291,plain,
% 292.08/187.87 (implies(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))) = implies(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))))))),
% 292.08/187.87 inference(monotonicity,[status(thm)],[1088, 1090])).
% 292.08/187.87 tff(1292,plain,
% 292.08/187.87 (is_a_theorem(implies(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) <=> is_a_theorem(implies(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))),
% 292.08/187.87 inference(monotonicity,[status(thm)],[1291])).
% 292.08/187.87 tff(1293,plain,
% 292.08/187.87 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.87 inference(quant_inst,[status(thm)],[])).
% 292.08/187.87 tff(1294,plain,
% 292.08/187.87 (is_a_theorem(implies(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), or(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.08/187.87 inference(unit_resolution,[status(thm)],[1293, 399])).
% 292.08/187.87 tff(1295,plain,
% 292.08/187.87 (is_a_theorem(implies(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))),
% 292.08/187.87 inference(modus_ponens,[status(thm)],[1294, 1292])).
% 292.08/187.87 tff(1296,plain,
% 292.08/187.87 (is_a_theorem(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))),
% 292.08/187.87 inference(modus_ponens,[status(thm)],[1295, 1290])).
% 292.08/187.87 tff(1297,plain,
% 292.08/187.87 (((~![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(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))) | is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))) <=> ((~![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(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))) | is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.08/187.87 inference(rewrite,[status(thm)],[])).
% 292.08/187.87 tff(1298,plain,
% 292.08/187.87 ((is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))) <=> ((~is_a_theorem(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))) | is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.08/187.87 inference(rewrite,[status(thm)],[])).
% 292.08/187.87 tff(1299,plain,
% 292.08/187.87 (((~![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(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))) <=> ((~![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(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))) | is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))),
% 292.16/187.87 inference(monotonicity,[status(thm)],[1298])).
% 292.16/187.87 tff(1300,plain,
% 292.16/187.87 (((~![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(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))) <=> ((~![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(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))) | is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.16/187.88 inference(transitivity,[status(thm)],[1299, 1297])).
% 292.16/187.88 tff(1301,plain,
% 292.16/187.88 ((~![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(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.16/187.88 inference(quant_inst,[status(thm)],[])).
% 292.16/187.88 tff(1302,plain,
% 292.16/187.88 ((~![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(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))) | is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))),
% 292.16/187.88 inference(modus_ponens,[status(thm)],[1301, 1300])).
% 292.16/187.88 tff(1303,plain,
% 292.16/187.88 ((~is_a_theorem(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))))) | is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2))))), not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1))))))), not(and(not(and(or(Q!1, not(P!2)), not(or(not(P!2), Q!1)))), not(and(or(not(P!2), Q!1), not(or(Q!1, not(P!2)))))))), or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))),
% 292.16/187.88 inference(unit_resolution,[status(thm)],[1302, 495])).
% 292.16/187.88 tff(1304,plain,
% 292.16/187.88 (is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(P!2))))), not(and(not(not(not(not(P!2)))), not(not(not(Q!1))))))), or(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))), not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.16/187.88 inference(unit_resolution,[status(thm)],[1303, 1296, 1285])).
% 292.16/187.88 tff(1305,plain,
% 292.16/187.88 (is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))),
% 292.16/187.88 inference(modus_ponens,[status(thm)],[1304, 1271])).
% 292.16/187.88 tff(1306,plain,
% 292.16/187.88 (or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))) = implies(or(not(not(Q!1)), not(P!2)), or(not(P!2), not(not(Q!1))))),
% 292.16/187.88 inference(symmetry,[status(thm)],[971])).
% 292.16/187.88 tff(1307,plain,
% 292.16/187.88 (is_a_theorem(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1))))) <=> is_a_theorem(implies(or(not(not(Q!1)), not(P!2)), or(not(P!2), not(not(Q!1)))))),
% 292.16/187.88 inference(monotonicity,[status(thm)],[1306])).
% 292.16/187.88 tff(1308,plain,
% 292.16/187.88 (is_a_theorem(implies(or(not(not(Q!1)), not(P!2)), or(not(P!2), not(not(Q!1))))) <=> is_a_theorem(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))),
% 292.16/187.88 inference(symmetry,[status(thm)],[1307])).
% 292.16/187.88 tff(1309,plain,
% 292.16/187.88 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(not(Q!1)), not(P!2)), or(not(P!2), not(not(Q!1)))))),
% 292.16/187.88 inference(quant_inst,[status(thm)],[])).
% 292.16/187.88 tff(1310,plain,
% 292.16/187.88 (is_a_theorem(implies(or(not(not(Q!1)), not(P!2)), or(not(P!2), not(not(Q!1)))))),
% 292.16/187.88 inference(unit_resolution,[status(thm)],[1309, 399])).
% 292.16/187.88 tff(1311,plain,
% 292.16/187.88 (is_a_theorem(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))),
% 292.16/187.88 inference(modus_ponens,[status(thm)],[1310, 1308])).
% 292.16/187.88 tff(1312,plain,
% 292.16/187.88 (((~![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(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))) <=> ((~![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(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))),
% 292.16/187.88 inference(rewrite,[status(thm)],[])).
% 292.16/187.88 tff(1313,plain,
% 292.16/187.88 ((is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))) | (~is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))) <=> ((~is_a_theorem(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))),
% 292.16/187.88 inference(rewrite,[status(thm)],[])).
% 292.16/187.88 tff(1314,plain,
% 292.16/187.88 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))) | (~is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))) <=> ((~![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(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))))),
% 292.16/187.88 inference(monotonicity,[status(thm)],[1313])).
% 292.16/187.88 tff(1315,plain,
% 292.16/187.88 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))) | (~is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))) <=> ((~![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(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))),
% 292.16/187.88 inference(transitivity,[status(thm)],[1314, 1312])).
% 292.16/187.88 tff(1316,plain,
% 292.16/187.88 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))) | (~is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))))))),
% 292.16/187.88 inference(quant_inst,[status(thm)],[])).
% 292.16/187.88 tff(1317,plain,
% 292.16/187.88 ((~![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(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))))) | is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.16/187.88 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 292.16/187.88 tff(1318,plain,
% 292.16/187.88 (is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) | (~is_a_theorem(implies(or(not(or(not(not(Q!1)), not(P!2))), or(not(P!2), not(not(Q!1)))), not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))))),
% 292.16/187.88 inference(unit_resolution,[status(thm)],[1317, 495, 1311])).
% 292.16/187.88 tff(1319,plain,
% 292.16/187.88 (is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))),
% 292.16/187.88 inference(unit_resolution,[status(thm)],[1318, 1305])).
% 292.16/187.88 tff(1320,plain,
% 292.16/187.88 (((~![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(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))))))) <=> ((~![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(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))))))),
% 292.16/187.88 inference(rewrite,[status(thm)],[])).
% 292.16/187.88 tff(1321,plain,
% 292.16/187.88 ((~![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(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))))))),
% 292.16/187.88 inference(quant_inst,[status(thm)],[])).
% 292.16/187.88 tff(1322,plain,
% 292.16/187.88 ((~![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(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))))),
% 292.16/187.88 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 292.16/187.88 tff(1323,plain,
% 292.16/187.88 (is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))), not(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))), or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1322, 495])).
% 292.16/187.89 tff(1324,plain,
% 292.16/187.89 (is_a_theorem(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1323, 1319, 1247])).
% 292.16/187.89 tff(1325,plain,
% 292.16/187.89 (is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))),
% 292.16/187.89 inference(modus_ponens,[status(thm)],[1324, 1240])).
% 292.16/187.89 tff(1326,plain,
% 292.16/187.89 (implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2)))))) = implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.16/187.89 inference(monotonicity,[status(thm)],[1183])).
% 292.16/187.89 tff(1327,plain,
% 292.16/187.89 (is_a_theorem(implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2))))))) <=> is_a_theorem(implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.16/187.89 inference(monotonicity,[status(thm)],[1326])).
% 292.16/187.89 tff(1328,plain,
% 292.16/187.89 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1329,plain,
% 292.16/187.89 (is_a_theorem(implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(implies(P!2, Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1328, 399])).
% 292.16/187.89 tff(1330,plain,
% 292.16/187.89 (is_a_theorem(implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))),
% 292.16/187.89 inference(modus_ponens,[status(thm)],[1329, 1327])).
% 292.16/187.89 tff(1331,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1))) = not(and(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1332,plain,
% 292.16/187.89 (or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1))) = not(and(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1331, 63])).
% 292.16/187.89 tff(1333,plain,
% 292.16/187.89 (not(and(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))) = or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))),
% 292.16/187.89 inference(symmetry,[status(thm)],[1332])).
% 292.16/187.89 tff(1334,plain,
% 292.16/187.89 (and(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1)))) = and(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))),
% 292.16/187.89 inference(monotonicity,[status(thm)],[1125])).
% 292.16/187.89 tff(1335,plain,
% 292.16/187.89 (and(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))) = and(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1))))),
% 292.16/187.89 inference(symmetry,[status(thm)],[1334])).
% 292.16/187.89 tff(1336,plain,
% 292.16/187.89 (not(and(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))) = not(and(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1)))))),
% 292.16/187.89 inference(monotonicity,[status(thm)],[1335])).
% 292.16/187.89 tff(1337,plain,
% 292.16/187.89 (not(and(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1))))) = not(and(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))),
% 292.16/187.89 inference(symmetry,[status(thm)],[1336])).
% 292.16/187.89 tff(1338,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(or(Q!1, not(P!2))), not(implies(P!2, Q!1))) = not(and(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1))))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1339,plain,
% 292.16/187.89 (implies(not(or(Q!1, not(P!2))), not(implies(P!2, Q!1))) = not(and(not(or(Q!1, not(P!2))), not(not(implies(P!2, Q!1)))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1338, 41])).
% 292.16/187.89 tff(1340,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(Q!1, not(P!2))), not(implies(P!2, Q!1))) = or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1341,plain,
% 292.16/187.89 (implies(not(or(Q!1, not(P!2))), not(implies(P!2, Q!1))) = or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1)))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1340, 20])).
% 292.16/187.89 tff(1342,plain,
% 292.16/187.89 (or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))) = implies(not(or(Q!1, not(P!2))), not(implies(P!2, Q!1)))),
% 292.16/187.89 inference(symmetry,[status(thm)],[1341])).
% 292.16/187.89 tff(1343,plain,
% 292.16/187.89 (or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))) = or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))),
% 292.16/187.89 inference(transitivity,[status(thm)],[1342, 1339, 1337, 1333])).
% 292.16/187.89 tff(1344,plain,
% 292.16/187.89 (is_a_theorem(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1)))) <=> is_a_theorem(or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1))))),
% 292.16/187.89 inference(monotonicity,[status(thm)],[1343])).
% 292.16/187.89 tff(1345,plain,
% 292.16/187.89 (is_a_theorem(or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))) <=> is_a_theorem(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))))),
% 292.16/187.89 inference(symmetry,[status(thm)],[1344])).
% 292.16/187.89 tff(1346,plain,
% 292.16/187.89 (implies(or(not(implies(P!2, Q!1)), not(and(not(Q!1), not(not(P!2))))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))) = implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1))))),
% 292.16/187.89 inference(monotonicity,[status(thm)],[1221])).
% 292.16/187.89 tff(1347,plain,
% 292.16/187.89 (is_a_theorem(implies(or(not(implies(P!2, Q!1)), not(and(not(Q!1), not(not(P!2))))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1))))) <=> is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))))),
% 292.16/187.89 inference(monotonicity,[status(thm)],[1346])).
% 292.16/187.89 tff(1348,plain,
% 292.16/187.89 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(implies(P!2, Q!1)), not(and(not(Q!1), not(not(P!2))))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1349,plain,
% 292.16/187.89 (is_a_theorem(implies(or(not(implies(P!2, Q!1)), not(and(not(Q!1), not(not(P!2))))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1348, 399])).
% 292.16/187.89 tff(1350,plain,
% 292.16/187.89 (is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))))),
% 292.16/187.89 inference(modus_ponens,[status(thm)],[1349, 1347])).
% 292.16/187.89 tff(1351,plain,
% 292.16/187.89 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))))))),
% 292.16/187.89 inference(rewrite,[status(thm)],[])).
% 292.16/187.89 tff(1352,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1353,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1))))))),
% 292.16/187.89 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 292.16/187.89 tff(1354,plain,
% 292.16/187.89 (is_a_theorem(or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1)))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), or(Q!1, not(P!2))), or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1))))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1353, 495])).
% 292.16/187.89 tff(1355,plain,
% 292.16/187.89 (is_a_theorem(or(not(and(not(Q!1), not(not(P!2)))), not(implies(P!2, Q!1))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1354, 1110, 1350])).
% 292.16/187.89 tff(1356,plain,
% 292.16/187.89 (is_a_theorem(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))))),
% 292.16/187.89 inference(modus_ponens,[status(thm)],[1355, 1345])).
% 292.16/187.89 tff(1357,plain,
% 292.16/187.89 (((~![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(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) | (~is_a_theorem(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))))) | (~is_a_theorem(implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))) <=> ((~![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(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) | (~is_a_theorem(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))))) | (~is_a_theorem(implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.16/187.89 inference(rewrite,[status(thm)],[])).
% 292.16/187.89 tff(1358,plain,
% 292.16/187.89 ((~![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(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) | (~is_a_theorem(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))))) | (~is_a_theorem(implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1359,plain,
% 292.16/187.89 ((~![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(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) | (~is_a_theorem(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))))) | (~is_a_theorem(implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.16/187.89 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 292.16/187.89 tff(1360,plain,
% 292.16/187.89 (is_a_theorem(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))) | (~is_a_theorem(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))))) | (~is_a_theorem(implies(or(not(not(or(Q!1, not(P!2)))), not(implies(P!2, Q!1))), or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1359, 495])).
% 292.16/187.89 tff(1361,plain,
% 292.16/187.89 (is_a_theorem(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1360, 1356, 1330])).
% 292.16/187.89 tff(1362,plain,
% 292.16/187.89 (((~![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(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) | is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))))) <=> ((~![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(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) | is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))))),
% 292.16/187.89 inference(rewrite,[status(thm)],[])).
% 292.16/187.89 tff(1363,plain,
% 292.16/187.89 ((is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))))) <=> ((~is_a_theorem(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) | is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))))),
% 292.16/187.89 inference(rewrite,[status(thm)],[])).
% 292.16/187.89 tff(1364,plain,
% 292.16/187.89 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))))) <=> ((~![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(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) | is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))))))),
% 292.16/187.89 inference(monotonicity,[status(thm)],[1363])).
% 292.16/187.89 tff(1365,plain,
% 292.16/187.89 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))))) <=> ((~![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(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) | is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))))),
% 292.16/187.89 inference(transitivity,[status(thm)],[1364, 1362])).
% 292.16/187.89 tff(1366,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) | (~is_a_theorem(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1367,plain,
% 292.16/187.89 ((~![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(P!2), Q!1)), not(not(or(Q!1, not(P!2))))))) | is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))))),
% 292.16/187.89 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 292.16/187.89 tff(1368,plain,
% 292.16/187.89 (is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1)))))))) | (~is_a_theorem(implies(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2))))), not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1367, 495, 1361])).
% 292.16/187.89 tff(1369,plain,
% 292.16/187.89 (is_a_theorem(not(or(not(or(not(or(not(P!2), Q!1)), not(not(or(Q!1, not(P!2)))))), not(or(not(not(and(not(Q!1), not(not(P!2))))), not(not(implies(P!2, Q!1))))))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1368, 1325])).
% 292.16/187.89 tff(1370,plain,
% 292.16/187.89 (is_a_theorem(equiv(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))))),
% 292.16/187.89 inference(modus_ponens,[status(thm)],[1369, 1236])).
% 292.16/187.89 tff(1371,plain,
% 292.16/187.89 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))))) | (not(not(implies(P!2, Q!1))) = not(and(not(Q!1), not(not(P!2))))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))))) | (not(not(implies(P!2, Q!1))) = not(and(not(Q!1), not(not(P!2))))))),
% 292.16/187.89 inference(rewrite,[status(thm)],[])).
% 292.16/187.89 tff(1372,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))))) | (not(not(implies(P!2, Q!1))) = not(and(not(Q!1), not(not(P!2))))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1373,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))))) | (not(not(implies(P!2, Q!1))) = not(and(not(Q!1), not(not(P!2)))))),
% 292.16/187.89 inference(modus_ponens,[status(thm)],[1372, 1371])).
% 292.16/187.89 tff(1374,plain,
% 292.16/187.89 ((~is_a_theorem(equiv(not(not(implies(P!2, Q!1))), not(and(not(Q!1), not(not(P!2))))))) | (not(not(implies(P!2, Q!1))) = not(and(not(Q!1), not(not(P!2)))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1373, 564])).
% 292.16/187.89 tff(1375,plain,
% 292.16/187.89 (not(not(implies(P!2, Q!1))) = not(and(not(Q!1), not(not(P!2))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1374, 1370])).
% 292.16/187.89 tff(1376,plain,
% 292.16/187.89 (not(and(not(Q!1), not(not(P!2)))) = not(not(implies(P!2, Q!1)))),
% 292.16/187.89 inference(symmetry,[status(thm)],[1375])).
% 292.16/187.89 tff(1377,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(not(Q!1)), not(P!2)) = not(and(not(not(not(Q!1))), not(not(P!2)))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1378,plain,
% 292.16/187.89 (or(not(not(Q!1)), not(P!2)) = not(and(not(not(not(Q!1))), not(not(P!2))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1377, 63])).
% 292.16/187.89 tff(1379,plain,
% 292.16/187.89 (not(and(not(not(not(Q!1))), not(not(P!2)))) = or(not(not(Q!1)), not(P!2))),
% 292.16/187.89 inference(symmetry,[status(thm)],[1378])).
% 292.16/187.89 tff(1380,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(not(Q!1))), not(P!2)) = not(and(not(not(not(Q!1))), not(not(P!2)))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1381,plain,
% 292.16/187.89 (implies(not(not(not(Q!1))), not(P!2)) = not(and(not(not(not(Q!1))), not(not(P!2))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1380, 41])).
% 292.16/187.89 tff(1382,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(not(Q!1))), not(P!2)) = or(not(not(not(not(Q!1)))), not(P!2)))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1383,plain,
% 292.16/187.89 (implies(not(not(not(Q!1))), not(P!2)) = or(not(not(not(not(Q!1)))), not(P!2))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1382, 20])).
% 292.16/187.89 tff(1384,plain,
% 292.16/187.89 (or(not(not(not(not(Q!1)))), not(P!2)) = implies(not(not(not(Q!1))), not(P!2))),
% 292.16/187.89 inference(symmetry,[status(thm)],[1383])).
% 292.16/187.89 tff(1385,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(not(not(not(Q!1)))), not(P!2)) = not(and(not(not(not(not(not(Q!1))))), not(not(P!2)))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1386,plain,
% 292.16/187.89 (or(not(not(not(not(Q!1)))), not(P!2)) = not(and(not(not(not(not(not(Q!1))))), not(not(P!2))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1385, 63])).
% 292.16/187.89 tff(1387,plain,
% 292.16/187.89 (not(and(not(not(not(not(not(Q!1))))), not(not(P!2)))) = or(not(not(not(not(Q!1)))), not(P!2))),
% 292.16/187.89 inference(symmetry,[status(thm)],[1386])).
% 292.16/187.89 tff(1388,plain,
% 292.16/187.89 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(not(not(not(Q!1))))), not(P!2)) = not(and(not(not(not(not(not(Q!1))))), not(not(P!2)))))),
% 292.16/187.89 inference(quant_inst,[status(thm)],[])).
% 292.16/187.89 tff(1389,plain,
% 292.16/187.89 (implies(not(not(not(not(not(Q!1))))), not(P!2)) = not(and(not(not(not(not(not(Q!1))))), not(not(P!2))))),
% 292.16/187.89 inference(unit_resolution,[status(thm)],[1388, 41])).
% 292.16/187.89 tff(1390,plain,
% 292.16/187.89 (implies(not(not(not(not(not(Q!1))))), not(P!2)) = or(not(P!2), not(not(Q!1)))),
% 292.16/187.89 inference(transitivity,[status(thm)],[1389, 1387, 1384, 1381, 1379, 979, 976, 1376, 1209, 1180])).
% 292.16/187.89 tff(1391,plain,
% 292.16/187.89 (implies(implies(not(not(not(not(not(Q!1))))), not(P!2)), implies(or(not(R!0), not(not(not(not(not(Q!1)))))), or(not(R!0), not(P!2)))) = implies(or(not(P!2), not(not(Q!1))), not(and(not(and(Q!1, R!0)), not(or(not(R!0), not(P!2))))))),
% 292.16/187.89 inference(monotonicity,[status(thm)],[1390, 906])).
% 292.16/187.89 tff(1392,plain,
% 292.16/187.89 (implies(implies(not(not(not(not(not(Q!1))))), not(P!2)), implies(or(not(R!0), not(not(not(not(not(Q!1)))))), or(not(R!0), not(P!2)))) = not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 292.16/187.89 inference(transitivity,[status(thm)],[1391, 596, 594, 592, 590, 587, 572, 570])).
% 292.16/187.89 tff(1393,plain,
% 292.16/187.89 (is_a_theorem(implies(implies(not(not(not(not(not(Q!1))))), not(P!2)), implies(or(not(R!0), not(not(not(not(not(Q!1)))))), or(not(R!0), not(P!2))))) <=> is_a_theorem(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 292.16/187.89 inference(monotonicity,[status(thm)],[1392])).
% 292.16/187.89 tff(1394,plain,
% 292.16/187.89 (is_a_theorem(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))) <=> is_a_theorem(implies(implies(not(not(not(not(not(Q!1))))), not(P!2)), implies(or(not(R!0), not(not(not(not(not(Q!1)))))), or(not(R!0), not(P!2)))))),
% 292.16/187.89 inference(symmetry,[status(thm)],[1393])).
% 292.16/187.89 tff(1395,plain,
% 292.16/187.89 ((~is_a_theorem(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))) <=> (~is_a_theorem(implies(implies(not(not(not(not(not(Q!1))))), not(P!2)), implies(or(not(R!0), not(not(not(not(not(Q!1)))))), or(not(R!0), not(P!2))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1394])).
% 292.16/187.90 tff(1396,plain,
% 292.16/187.90 (or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))) = not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))),
% 292.16/187.90 inference(transitivity,[status(thm)],[111, 183, 180, 178])).
% 292.16/187.90 tff(1397,plain,
% 292.16/187.90 (is_a_theorem(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2))))))) <=> is_a_theorem(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1396])).
% 292.16/187.90 tff(1398,plain,
% 292.16/187.90 ((~is_a_theorem(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))))) <=> (~is_a_theorem(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2))))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1397])).
% 292.16/187.90 tff(1399,plain,
% 292.16/187.90 (and(not(not(or(not(P!2), not(not(Q!1))))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))) = and(or(not(P!2), Q!1), and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[105, 149])).
% 292.16/187.90 tff(1400,plain,
% 292.16/187.90 (and(not(not(or(not(P!2), not(not(Q!1))))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))) = not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))),
% 292.16/187.90 inference(transitivity,[status(thm)],[1399, 146])).
% 292.16/187.90 tff(1401,plain,
% 292.16/187.90 (not(and(not(not(or(not(P!2), not(not(Q!1))))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))) = not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1400])).
% 292.16/187.90 tff(1402,plain,
% 292.16/187.90 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = not(and(not(not(or(not(P!2), not(not(Q!1))))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 292.16/187.90 inference(quant_inst,[status(thm)],[])).
% 292.16/187.90 tff(1403,plain,
% 292.16/187.90 (or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = not(and(not(not(or(not(P!2), not(not(Q!1))))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 292.16/187.90 inference(unit_resolution,[status(thm)],[1402, 63])).
% 292.16/187.90 tff(1404,plain,
% 292.16/187.90 (or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))) = not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 292.16/187.90 inference(transitivity,[status(thm)],[1403, 1401, 161])).
% 292.16/187.90 tff(1405,plain,
% 292.16/187.90 (implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))) = implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1404])).
% 292.16/187.90 tff(1406,plain,
% 292.16/187.90 (implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) = implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[1405])).
% 292.16/187.90 tff(1407,plain,
% 292.16/187.90 (is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))) <=> is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1406])).
% 292.16/187.90 tff(1408,plain,
% 292.16/187.90 (is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))) <=> is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[1407])).
% 292.16/187.90 tff(1409,plain,
% 292.16/187.90 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) | is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 292.16/187.90 inference(quant_inst,[status(thm)],[])).
% 292.16/187.90 tff(1410,plain,
% 292.16/187.90 (is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 292.16/187.90 inference(unit_resolution,[status(thm)],[1409, 455])).
% 292.16/187.90 tff(1411,plain,
% 292.16/187.90 (is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1410, 1408])).
% 292.16/187.90 tff(1412,plain,
% 292.16/187.90 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))), not(or(not(P!2), not(not(Q!1))))) = not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1))))))))),
% 292.16/187.90 inference(quant_inst,[status(thm)],[])).
% 292.16/187.90 tff(1413,plain,
% 292.16/187.90 (or(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))), not(or(not(P!2), not(not(Q!1))))) = not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))),
% 292.16/187.90 inference(unit_resolution,[status(thm)],[1412, 63])).
% 292.16/187.90 tff(1414,plain,
% 292.16/187.90 (not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1))))))) = or(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))), not(or(not(P!2), not(not(Q!1)))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[1413])).
% 292.16/187.90 tff(1415,plain,
% 292.16/187.90 (not(and(not(not(or(not(P!2), not(not(Q!1))))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))) = or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[1403])).
% 292.16/187.90 tff(1416,plain,
% 292.16/187.90 (not(not(or(not(or(not(P!2), Q!1)), not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))))) = not(and(not(not(or(not(P!2), not(not(Q!1))))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[1401])).
% 292.16/187.90 tff(1417,plain,
% 292.16/187.90 (not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))) = or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))),
% 292.16/187.90 inference(transitivity,[status(thm)],[162, 1416, 1415])).
% 292.16/187.90 tff(1418,plain,
% 292.16/187.90 (implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))) = implies(or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), or(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))), not(or(not(P!2), not(not(Q!1))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1417, 1414])).
% 292.16/187.90 tff(1419,plain,
% 292.16/187.90 (implies(or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), or(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))), not(or(not(P!2), not(not(Q!1)))))) = implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1))))))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[1418])).
% 292.16/187.90 tff(1420,plain,
% 292.16/187.90 (is_a_theorem(implies(or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), or(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))), not(or(not(P!2), not(not(Q!1))))))) <=> is_a_theorem(implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1419])).
% 292.16/187.90 tff(1421,plain,
% 292.16/187.90 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), or(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))), not(or(not(P!2), not(not(Q!1)))))))),
% 292.16/187.90 inference(quant_inst,[status(thm)],[])).
% 292.16/187.90 tff(1422,plain,
% 292.16/187.90 (is_a_theorem(implies(or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), or(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))), not(or(not(P!2), not(not(Q!1)))))))),
% 292.16/187.90 inference(unit_resolution,[status(thm)],[1421, 399])).
% 292.16/187.90 tff(1423,plain,
% 292.16/187.90 (is_a_theorem(implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1422, 1420])).
% 292.16/187.90 tff(1424,plain,
% 292.16/187.90 (not(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))) = not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2)))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[149])).
% 292.16/187.90 tff(1425,plain,
% 292.16/187.90 (not(and(not(and(Q!1, R!0)), not(not(and(R!0, P!2))))) = not(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[1424])).
% 292.16/187.90 tff(1426,plain,
% 292.16/187.90 (or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))) = not(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))),
% 292.16/187.90 inference(transitivity,[status(thm)],[507, 224, 1425])).
% 292.16/187.90 tff(1427,plain,
% 292.16/187.90 (or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))) = or(not(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))), not(or(not(P!2), not(not(Q!1)))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1426])).
% 292.16/187.90 tff(1428,plain,
% 292.16/187.90 (or(not(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))), not(or(not(P!2), not(not(Q!1))))) = or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1)))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[1427])).
% 292.16/187.90 tff(1429,plain,
% 292.16/187.90 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(or(not(P!2), not(not(Q!1))))) = or(not(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))), not(or(not(P!2), not(not(Q!1))))))),
% 292.16/187.90 inference(quant_inst,[status(thm)],[])).
% 292.16/187.90 tff(1430,plain,
% 292.16/187.90 (implies(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(or(not(P!2), not(not(Q!1))))) = or(not(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))), not(or(not(P!2), not(not(Q!1)))))),
% 292.16/187.90 inference(unit_resolution,[status(thm)],[1429, 20])).
% 292.16/187.90 tff(1431,plain,
% 292.16/187.90 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(or(not(P!2), not(not(Q!1))))) = not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1))))))))),
% 292.16/187.90 inference(quant_inst,[status(thm)],[])).
% 292.16/187.90 tff(1432,plain,
% 292.16/187.90 (implies(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(or(not(P!2), not(not(Q!1))))) = not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))),
% 292.16/187.90 inference(unit_resolution,[status(thm)],[1431, 41])).
% 292.16/187.90 tff(1433,plain,
% 292.16/187.90 (not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1))))))) = implies(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(or(not(P!2), not(not(Q!1)))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[1432])).
% 292.16/187.90 tff(1434,plain,
% 292.16/187.90 (not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1))))))) = or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1)))))),
% 292.16/187.90 inference(transitivity,[status(thm)],[1433, 1430, 1428])).
% 292.16/187.90 tff(1435,plain,
% 292.16/187.90 (is_a_theorem(not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))) <=> is_a_theorem(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1434])).
% 292.16/187.90 tff(1436,plain,
% 292.16/187.90 (is_a_theorem(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1)))))) <=> is_a_theorem(not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1))))))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[1435])).
% 292.16/187.90 tff(1437,plain,
% 292.16/187.90 ((~is_a_theorem(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))))) <=> (~is_a_theorem(not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1436])).
% 292.16/187.90 tff(1438,plain,
% 292.16/187.90 (not(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))) = not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[507])).
% 292.16/187.90 tff(1439,plain,
% 292.16/187.90 (and(not(and(P!2, not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))))) = and(implies(P!2, Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[81, 1438])).
% 292.16/187.90 tff(1440,plain,
% 292.16/187.90 (not(and(not(and(P!2, not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))))) = not(and(implies(P!2, Q!1), not(implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1439])).
% 292.16/187.90 tff(1441,plain,
% 292.16/187.90 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(P!2, not(Q!1)), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))) = not(and(not(and(P!2, not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))))))),
% 292.16/187.90 inference(quant_inst,[status(thm)],[])).
% 292.16/187.90 tff(1442,plain,
% 292.16/187.90 (or(and(P!2, not(Q!1)), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))) = not(and(not(and(P!2, not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))))))),
% 292.16/187.90 inference(unit_resolution,[status(thm)],[1441, 63])).
% 292.16/187.90 tff(1443,plain,
% 292.16/187.90 (or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))) = or(and(P!2, not(Q!1)), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[103])).
% 292.16/187.90 tff(1444,plain,
% 292.16/187.90 (or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))) = or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))),
% 292.16/187.90 inference(transitivity,[status(thm)],[1443, 1442, 1440, 272, 269])).
% 292.16/187.90 tff(1445,plain,
% 292.16/187.90 (implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))))) = implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1444])).
% 292.16/187.90 tff(1446,plain,
% 292.16/187.90 (is_a_theorem(implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2)))))) <=> is_a_theorem(implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1445])).
% 292.16/187.90 tff(1447,plain,
% 292.16/187.90 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))))))),
% 292.16/187.90 inference(quant_inst,[status(thm)],[])).
% 292.16/187.90 tff(1448,plain,
% 292.16/187.90 (is_a_theorem(implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(or(not(P!2), not(not(Q!1)))), or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))))))),
% 292.16/187.90 inference(unit_resolution,[status(thm)],[1447, 399])).
% 292.16/187.90 tff(1449,plain,
% 292.16/187.90 (is_a_theorem(implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1448, 1446])).
% 292.16/187.90 tff(1450,plain,
% 292.16/187.90 (or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))) = implies(implies(P!2, Q!1), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[269])).
% 292.16/187.90 tff(1451,plain,
% 292.16/187.90 (is_a_theorem(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) <=> is_a_theorem(implies(implies(P!2, Q!1), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1450])).
% 292.16/187.90 tff(1452,plain,
% 292.16/187.90 (is_a_theorem(implies(implies(P!2, Q!1), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) <=> is_a_theorem(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 292.16/187.90 inference(symmetry,[status(thm)],[1451])).
% 292.16/187.90 tff(1453,plain,
% 292.16/187.90 ((~is_a_theorem(implies(implies(P!2, Q!1), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))) <=> (~is_a_theorem(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1452])).
% 292.16/187.90 tff(1454,plain,
% 292.16/187.90 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))) <=> (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P))))))),
% 292.16/187.90 inference(rewrite,[status(thm)],[])).
% 292.16/187.90 tff(1455,plain,
% 292.16/187.90 (($false <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))) <=> (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P))))))),
% 292.16/187.90 inference(rewrite,[status(thm)],[])).
% 292.16/187.90 tff(1456,axiom,(~kn3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rosser_kn3')).
% 292.16/187.90 tff(1457,plain,
% 292.16/187.90 (kn3 <=> $false),
% 292.16/187.90 inference(iff_false,[status(thm)],[1456])).
% 292.16/187.90 tff(1458,plain,
% 292.16/187.90 ((kn3 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))) <=> ($false <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P))))))),
% 292.16/187.90 inference(monotonicity,[status(thm)],[1457])).
% 292.16/187.90 tff(1459,plain,
% 292.16/187.90 ((kn3 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))) <=> (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P))))))),
% 292.16/187.90 inference(transitivity,[status(thm)],[1458, 1455])).
% 292.16/187.90 tff(1460,plain,
% 292.16/187.90 ((kn3 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))) <=> (kn3 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P))))))),
% 292.16/187.90 inference(rewrite,[status(thm)],[])).
% 292.16/187.90 tff(1461,axiom,(kn3 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','kn3')).
% 292.16/187.90 tff(1462,plain,
% 292.16/187.90 (kn3 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 292.16/187.90 tff(1463,plain,
% 292.16/187.90 (kn3 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1462, 1460])).
% 292.16/187.90 tff(1464,plain,
% 292.16/187.90 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1463, 1459])).
% 292.16/187.90 tff(1465,plain,
% 292.16/187.90 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1464, 1454])).
% 292.16/187.90 tff(1466,plain,
% 292.16/187.90 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1465, 1454])).
% 292.16/187.90 tff(1467,plain,
% 292.16/187.90 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1466, 1454])).
% 292.16/187.90 tff(1468,plain,
% 292.16/187.90 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1467, 1454])).
% 292.16/187.90 tff(1469,plain,
% 292.16/187.90 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1468, 1454])).
% 292.16/187.90 tff(1470,plain,
% 292.16/187.90 (~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(P, Q), implies(not(and(Q, R)), not(and(R, P)))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1469, 1454])).
% 292.16/187.90 tff(1471,plain,(
% 292.16/187.90 ~is_a_theorem(implies(implies(P!2, Q!1), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 292.16/187.90 inference(skolemize,[status(sab)],[1470])).
% 292.16/187.90 tff(1472,plain,
% 292.16/187.90 (~is_a_theorem(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1471, 1453])).
% 292.16/187.90 tff(1473,plain,
% 292.16/187.90 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) | (~is_a_theorem(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))))) | (~is_a_theorem(implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) | (~is_a_theorem(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))))) | (~is_a_theorem(implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 292.16/187.90 inference(rewrite,[status(thm)],[])).
% 292.16/187.90 tff(1474,plain,
% 292.16/187.90 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) | (~is_a_theorem(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))))) | (~is_a_theorem(implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))))))),
% 292.16/187.90 inference(quant_inst,[status(thm)],[])).
% 292.16/187.90 tff(1475,plain,
% 292.16/187.90 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2))))) | (~is_a_theorem(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))))) | (~is_a_theorem(implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 292.16/187.90 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 292.16/187.90 tff(1476,plain,
% 292.16/187.90 ((~is_a_theorem(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))))) | (~is_a_theorem(implies(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))), or(not(implies(P!2, Q!1)), implies(not(and(Q!1, R!0)), not(and(R!0, P!2)))))))),
% 292.16/187.91 inference(unit_resolution,[status(thm)],[1475, 495, 1472])).
% 292.16/187.91 tff(1477,plain,
% 292.16/187.91 (~is_a_theorem(or(or(not(not(and(Q!1, R!0))), not(and(R!0, P!2))), not(or(not(P!2), not(not(Q!1))))))),
% 292.16/187.91 inference(unit_resolution,[status(thm)],[1476, 1449])).
% 292.16/187.91 tff(1478,plain,
% 292.16/187.91 (~is_a_theorem(not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1))))))))),
% 292.16/187.91 inference(modus_ponens,[status(thm)],[1477, 1437])).
% 292.16/187.91 tff(1479,plain,
% 292.16/187.91 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))) | (~is_a_theorem(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))) | (~is_a_theorem(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))))))),
% 292.16/187.91 inference(rewrite,[status(thm)],[])).
% 292.16/187.91 tff(1480,plain,
% 292.16/187.91 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))) | (~is_a_theorem(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))))))),
% 292.16/187.91 inference(quant_inst,[status(thm)],[])).
% 292.16/187.91 tff(1481,plain,
% 292.16/187.91 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))) | (~is_a_theorem(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1))))))))))),
% 292.16/187.91 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 292.16/187.91 tff(1482,plain,
% 292.16/187.91 (is_a_theorem(not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1)))))))) | (~is_a_theorem(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))) | (~is_a_theorem(implies(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))), not(and(not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))), not(not(or(not(P!2), not(not(Q!1))))))))))),
% 292.16/187.91 inference(unit_resolution,[status(thm)],[1481, 495])).
% 292.16/187.91 tff(1483,plain,
% 292.16/187.91 (~is_a_theorem(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))),
% 292.16/187.91 inference(unit_resolution,[status(thm)],[1482, 1478, 1423])).
% 292.16/187.91 tff(1484,plain,
% 292.16/187.91 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) | (~is_a_theorem(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))))) | (~is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) | (~is_a_theorem(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))))) | (~is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))))),
% 292.16/187.91 inference(rewrite,[status(thm)],[])).
% 292.16/187.91 tff(1485,plain,
% 292.16/187.91 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) | (~is_a_theorem(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))))) | (~is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))))))),
% 292.16/187.91 inference(quant_inst,[status(thm)],[])).
% 292.16/187.91 tff(1486,plain,
% 292.16/187.91 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) | (~is_a_theorem(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))))) | (~is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))))),
% 292.16/187.91 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 292.16/187.91 tff(1487,plain,
% 292.16/187.91 (is_a_theorem(not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2))))))))) | (~is_a_theorem(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))))) | (~is_a_theorem(implies(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))), not(and(not(and(not(not(P!2)), not(Q!1))), not(or(not(not(and(Q!1, R!0))), not(not(not(and(R!0, P!2)))))))))))),
% 292.16/187.91 inference(unit_resolution,[status(thm)],[1486, 495])).
% 292.16/187.91 tff(1488,plain,
% 292.16/187.91 (~is_a_theorem(or(not(not(and(Q!1, R!0))), or(not(or(not(P!2), not(not(Q!1)))), not(not(not(and(R!0, P!2)))))))),
% 292.16/187.91 inference(unit_resolution,[status(thm)],[1487, 1483, 1411])).
% 292.16/187.91 tff(1489,plain,
% 292.16/187.91 (~is_a_theorem(not(not(or(not(not(and(Q!1, R!0))), or(not(implies(P!2, Q!1)), not(and(R!0, P!2)))))))),
% 292.16/187.91 inference(modus_ponens,[status(thm)],[1488, 1398])).
% 292.16/187.91 tff(1490,plain,
% 292.16/187.91 (~is_a_theorem(implies(implies(not(not(not(not(not(Q!1))))), not(P!2)), implies(or(not(R!0), not(not(not(not(not(Q!1)))))), or(not(R!0), not(P!2)))))),
% 292.16/187.91 inference(modus_ponens,[status(thm)],[1489, 1395])).
% 292.16/187.91 tff(1491,plain,
% 292.16/187.91 (^[P: $i, Q: $i, R: $i] : refl(is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))) <=> is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))))),
% 292.16/187.91 inference(bind,[status(th)],[])).
% 292.16/187.91 tff(1492,plain,
% 292.16/187.91 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 292.16/187.91 inference(quant_intro,[status(thm)],[1491])).
% 292.16/187.91 tff(1493,plain,
% 292.16/187.91 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 292.38/188.17 inference(rewrite,[status(thm)],[])).
% 292.38/188.17 tff(1494,plain,
% 292.38/188.17 (($true <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 292.38/188.17 inference(rewrite,[status(thm)],[])).
% 292.38/188.17 tff(1495,axiom,(r5), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_r5')).
% 292.38/188.17 tff(1496,plain,
% 292.38/188.17 (r5 <=> $true),
% 292.38/188.17 inference(iff_true,[status(thm)],[1495])).
% 292.38/188.17 tff(1497,plain,
% 292.38/188.17 ((r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))) <=> ($true <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))))),
% 292.38/188.17 inference(monotonicity,[status(thm)],[1496])).
% 292.38/188.17 tff(1498,plain,
% 292.38/188.17 ((r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 292.38/188.17 inference(transitivity,[status(thm)],[1497, 1494])).
% 292.38/188.17 tff(1499,plain,
% 292.38/188.17 ((r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))) <=> (r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))))),
% 292.38/188.17 inference(rewrite,[status(thm)],[])).
% 292.38/188.17 tff(1500,axiom,(r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','r5')).
% 292.38/188.17 tff(1501,plain,
% 292.38/188.17 (r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 292.38/188.17 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 292.38/188.17 tff(1502,plain,
% 292.38/188.17 (r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 292.38/188.17 inference(modus_ponens,[status(thm)],[1501, 1499])).
% 292.38/188.17 tff(1503,plain,
% 292.38/188.17 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 292.38/188.17 inference(modus_ponens,[status(thm)],[1502, 1498])).
% 292.38/188.17 tff(1504,plain,
% 292.38/188.17 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 292.38/188.17 inference(modus_ponens,[status(thm)],[1503, 1493])).
% 292.38/188.17 tff(1505,plain,(
% 292.38/188.17 ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 292.38/188.17 inference(skolemize,[status(sab)],[1504])).
% 292.38/188.17 tff(1506,plain,
% 292.38/188.17 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 292.38/188.17 inference(modus_ponens,[status(thm)],[1505, 1492])).
% 292.38/188.17 tff(1507,plain,
% 292.38/188.17 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))) | is_a_theorem(implies(implies(not(not(not(not(not(Q!1))))), not(P!2)), implies(or(not(R!0), not(not(not(not(not(Q!1)))))), or(not(R!0), not(P!2)))))),
% 292.38/188.17 inference(quant_inst,[status(thm)],[])).
% 292.38/188.17 tff(1508,plain,
% 292.38/188.17 (is_a_theorem(implies(implies(not(not(not(not(not(Q!1))))), not(P!2)), implies(or(not(R!0), not(not(not(not(not(Q!1)))))), or(not(R!0), not(P!2)))))),
% 292.38/188.17 inference(unit_resolution,[status(thm)],[1507, 1506])).
% 292.38/188.17 tff(1509,plain,
% 292.38/188.17 ($false),
% 292.38/188.17 inference(unit_resolution,[status(thm)],[1508, 1490])).
% 292.38/188.17 % SZS output end Proof
%------------------------------------------------------------------------------