TSTP Solution File: LCL495+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL495+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 04:56:30 EDT 2022
% Result : Timeout 299.37s 189.56s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL495+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 22:02:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 299.37/189.56 % SZS status Theorem
% 299.37/189.56 % SZS output start Proof
% 299.37/189.56 tff(is_a_theorem_type, type, (
% 299.37/189.56 is_a_theorem: $i > $o)).
% 299.37/189.56 tff(or_type, type, (
% 299.37/189.56 or: ( $i * $i ) > $i)).
% 299.37/189.56 tff(not_type, type, (
% 299.37/189.56 not: $i > $i)).
% 299.37/189.56 tff(tptp_fun_X_1_type, type, (
% 299.37/189.56 tptp_fun_X_1: $i)).
% 299.37/189.56 tff(tptp_fun_Y_0_type, type, (
% 299.37/189.56 tptp_fun_Y_0: $i)).
% 299.37/189.56 tff(and_type, type, (
% 299.37/189.56 and: ( $i * $i ) > $i)).
% 299.37/189.56 tff(implies_type, type, (
% 299.37/189.56 implies: ( $i * $i ) > $i)).
% 299.37/189.56 tff(equiv_type, type, (
% 299.37/189.56 equiv: ( $i * $i ) > $i)).
% 299.37/189.56 tff(op_implies_or_type, type, (
% 299.37/189.56 op_implies_or: $o)).
% 299.37/189.56 tff(op_implies_and_type, type, (
% 299.37/189.56 op_implies_and: $o)).
% 299.37/189.56 tff(op_or_type, type, (
% 299.37/189.56 op_or: $o)).
% 299.37/189.56 tff(op_equiv_type, type, (
% 299.37/189.56 op_equiv: $o)).
% 299.37/189.56 tff(op_and_type, type, (
% 299.37/189.56 op_and: $o)).
% 299.37/189.56 tff(r3_type, type, (
% 299.37/189.56 r3: $o)).
% 299.37/189.56 tff(r4_type, type, (
% 299.37/189.56 r4: $o)).
% 299.37/189.56 tff(modus_ponens_type, type, (
% 299.37/189.56 modus_ponens: $o)).
% 299.37/189.56 tff(substitution_of_equivalents_type, type, (
% 299.37/189.56 substitution_of_equivalents: $o)).
% 299.37/189.56 tff(equivalence_3_type, type, (
% 299.37/189.56 equivalence_3: $o)).
% 299.37/189.56 tff(r5_type, type, (
% 299.37/189.56 r5: $o)).
% 299.37/189.56 tff(r2_type, type, (
% 299.37/189.56 r2: $o)).
% 299.37/189.56 tff(1,plain,
% 299.37/189.56 (^[X: $i, Y: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 299.37/189.56 inference(bind,[status(th)],[])).
% 299.37/189.56 tff(2,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 299.37/189.56 inference(quant_intro,[status(thm)],[1])).
% 299.37/189.56 tff(3,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(4,plain,
% 299.37/189.56 (($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(5,plain,
% 299.37/189.56 ((~$true) <=> $false),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(6,axiom,(op_implies_or), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_op_implies_or')).
% 299.37/189.56 tff(7,plain,
% 299.37/189.56 (op_implies_or <=> $true),
% 299.37/189.56 inference(iff_true,[status(thm)],[6])).
% 299.37/189.56 tff(8,plain,
% 299.37/189.56 ((~op_implies_or) <=> (~$true)),
% 299.37/189.56 inference(monotonicity,[status(thm)],[7])).
% 299.37/189.56 tff(9,plain,
% 299.37/189.56 ((~op_implies_or) <=> $false),
% 299.37/189.56 inference(transitivity,[status(thm)],[8, 5])).
% 299.37/189.56 tff(10,plain,
% 299.37/189.56 (((~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)))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[9])).
% 299.37/189.56 tff(11,plain,
% 299.37/189.56 (((~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))),
% 299.37/189.56 inference(transitivity,[status(thm)],[10, 4])).
% 299.37/189.56 tff(12,plain,
% 299.37/189.56 (((~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)))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(13,plain,
% 299.37/189.56 ((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)))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(14,axiom,(op_implies_or => ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_implies_or')).
% 299.37/189.56 tff(15,plain,
% 299.37/189.56 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[14, 13])).
% 299.37/189.56 tff(16,plain,
% 299.37/189.56 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[15, 12])).
% 299.37/189.56 tff(17,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[16, 11])).
% 299.37/189.56 tff(18,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[17, 3])).
% 299.37/189.56 tff(19,plain,(
% 299.37/189.56 ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 299.37/189.56 inference(skolemize,[status(sab)],[18])).
% 299.37/189.56 tff(20,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[19, 2])).
% 299.37/189.56 tff(21,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(implies(X!1, Y!0))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(22,plain,
% 299.37/189.56 (implies(not(not(implies(X!1, Y!0))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[21, 20])).
% 299.37/189.56 tff(23,plain,
% 299.37/189.56 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 299.37/189.56 inference(bind,[status(th)],[])).
% 299.37/189.56 tff(24,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 299.37/189.56 inference(quant_intro,[status(thm)],[23])).
% 299.37/189.56 tff(25,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(26,plain,
% 299.37/189.56 (($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))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(27,axiom,(op_implies_and), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hilbert_op_implies_and')).
% 299.37/189.56 tff(28,plain,
% 299.37/189.56 (op_implies_and <=> $true),
% 299.37/189.56 inference(iff_true,[status(thm)],[27])).
% 299.37/189.56 tff(29,plain,
% 299.37/189.56 ((~op_implies_and) <=> (~$true)),
% 299.37/189.56 inference(monotonicity,[status(thm)],[28])).
% 299.37/189.56 tff(30,plain,
% 299.37/189.56 ((~op_implies_and) <=> $false),
% 299.37/189.56 inference(transitivity,[status(thm)],[29, 5])).
% 299.37/189.56 tff(31,plain,
% 299.37/189.56 (((~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)))))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[30])).
% 299.37/189.56 tff(32,plain,
% 299.37/189.56 (((~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))))),
% 299.37/189.56 inference(transitivity,[status(thm)],[31, 26])).
% 299.37/189.56 tff(33,plain,
% 299.37/189.56 (((~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)))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(34,plain,
% 299.37/189.56 ((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)))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(35,axiom,(op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_implies_and')).
% 299.37/189.56 tff(36,plain,
% 299.37/189.56 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[35, 34])).
% 299.37/189.56 tff(37,plain,
% 299.37/189.56 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[36, 33])).
% 299.37/189.56 tff(38,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[37, 32])).
% 299.37/189.56 tff(39,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[38, 25])).
% 299.37/189.56 tff(40,plain,(
% 299.37/189.56 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 299.37/189.56 inference(skolemize,[status(sab)],[39])).
% 299.37/189.56 tff(41,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[40, 24])).
% 299.37/189.56 tff(42,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(implies(X!1, Y!0))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = not(and(not(not(implies(X!1, Y!0))), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(43,plain,
% 299.37/189.56 (implies(not(not(implies(X!1, Y!0))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = not(and(not(not(implies(X!1, Y!0))), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[42, 41])).
% 299.37/189.56 tff(44,plain,
% 299.37/189.56 (not(and(not(not(implies(X!1, Y!0))), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))) = implies(not(not(implies(X!1, Y!0))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.37/189.56 inference(symmetry,[status(thm)],[43])).
% 299.37/189.56 tff(45,plain,
% 299.37/189.56 (^[X: $i, Y: $i] : refl((or(X, Y) = not(and(not(X), not(Y)))) <=> (or(X, Y) = not(and(not(X), not(Y)))))),
% 299.37/189.56 inference(bind,[status(th)],[])).
% 299.37/189.56 tff(46,plain,
% 299.37/189.56 (![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))))),
% 299.37/189.56 inference(quant_intro,[status(thm)],[45])).
% 299.37/189.56 tff(47,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(48,plain,
% 299.37/189.56 (($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))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(49,axiom,(op_or), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hilbert_op_or')).
% 299.37/189.56 tff(50,plain,
% 299.37/189.56 (op_or <=> $true),
% 299.37/189.56 inference(iff_true,[status(thm)],[49])).
% 299.37/189.56 tff(51,plain,
% 299.37/189.56 ((~op_or) <=> (~$true)),
% 299.37/189.56 inference(monotonicity,[status(thm)],[50])).
% 299.37/189.56 tff(52,plain,
% 299.37/189.56 ((~op_or) <=> $false),
% 299.37/189.56 inference(transitivity,[status(thm)],[51, 5])).
% 299.37/189.56 tff(53,plain,
% 299.37/189.56 (((~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)))))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[52])).
% 299.37/189.56 tff(54,plain,
% 299.37/189.56 (((~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))))),
% 299.37/189.56 inference(transitivity,[status(thm)],[53, 48])).
% 299.37/189.56 tff(55,plain,
% 299.37/189.56 (((~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)))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(56,plain,
% 299.37/189.56 ((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)))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(57,axiom,(op_or => ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_or')).
% 299.37/189.56 tff(58,plain,
% 299.37/189.56 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[57, 56])).
% 299.37/189.56 tff(59,plain,
% 299.37/189.56 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[58, 55])).
% 299.37/189.56 tff(60,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[59, 54])).
% 299.37/189.56 tff(61,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[60, 47])).
% 299.37/189.56 tff(62,plain,(
% 299.37/189.56 ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 299.37/189.56 inference(skolemize,[status(sab)],[61])).
% 299.37/189.56 tff(63,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[62, 46])).
% 299.37/189.56 tff(64,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = not(and(not(not(implies(X!1, Y!0))), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(65,plain,
% 299.37/189.56 (or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = not(and(not(not(implies(X!1, Y!0))), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[64, 63])).
% 299.37/189.56 tff(66,plain,
% 299.37/189.56 (or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.37/189.56 inference(transitivity,[status(thm)],[65, 44, 22])).
% 299.37/189.56 tff(67,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(Y!0, X!1) = or(not(Y!0), X!1))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(68,plain,
% 299.37/189.56 (implies(Y!0, X!1) = or(not(Y!0), X!1)),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[67, 20])).
% 299.37/189.56 tff(69,plain,
% 299.37/189.56 (or(not(Y!0), X!1) = implies(Y!0, X!1)),
% 299.37/189.56 inference(symmetry,[status(thm)],[68])).
% 299.37/189.56 tff(70,plain,
% 299.37/189.56 (not(or(not(Y!0), X!1)) = not(implies(Y!0, X!1))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[69])).
% 299.37/189.56 tff(71,plain,
% 299.37/189.56 (not(implies(Y!0, X!1)) = not(or(not(Y!0), X!1))),
% 299.37/189.56 inference(symmetry,[status(thm)],[70])).
% 299.37/189.56 tff(72,plain,
% 299.37/189.56 (or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(Y!0), X!1)), or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[71, 66])).
% 299.37/189.56 tff(73,plain,
% 299.37/189.56 (or(not(or(not(Y!0), X!1)), or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.37/189.56 inference(symmetry,[status(thm)],[72])).
% 299.37/189.56 tff(74,plain,
% 299.37/189.56 (^[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))))),
% 299.37/189.56 inference(bind,[status(th)],[])).
% 299.37/189.56 tff(75,plain,
% 299.37/189.56 (![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)))),
% 299.37/189.56 inference(quant_intro,[status(thm)],[74])).
% 299.37/189.56 tff(76,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(77,plain,
% 299.37/189.56 (($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)))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(78,axiom,(op_equiv), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_op_equiv')).
% 299.37/189.56 tff(79,plain,
% 299.37/189.56 (op_equiv <=> $true),
% 299.37/189.56 inference(iff_true,[status(thm)],[78])).
% 299.37/189.56 tff(80,plain,
% 299.37/189.56 ((~op_equiv) <=> (~$true)),
% 299.37/189.56 inference(monotonicity,[status(thm)],[79])).
% 299.37/189.56 tff(81,plain,
% 299.37/189.56 ((~op_equiv) <=> $false),
% 299.37/189.56 inference(transitivity,[status(thm)],[80, 5])).
% 299.37/189.56 tff(82,plain,
% 299.37/189.56 (((~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))))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[81])).
% 299.37/189.56 tff(83,plain,
% 299.37/189.56 (((~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)))),
% 299.37/189.56 inference(transitivity,[status(thm)],[82, 77])).
% 299.37/189.56 tff(84,plain,
% 299.37/189.56 (((~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))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(85,plain,
% 299.37/189.56 ((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))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(86,axiom,(op_equiv => ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_equiv')).
% 299.37/189.56 tff(87,plain,
% 299.37/189.56 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[86, 85])).
% 299.37/189.56 tff(88,plain,
% 299.37/189.56 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[87, 84])).
% 299.37/189.56 tff(89,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[88, 83])).
% 299.37/189.56 tff(90,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[89, 76])).
% 299.37/189.56 tff(91,plain,(
% 299.37/189.56 ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 299.37/189.56 inference(skolemize,[status(sab)],[90])).
% 299.37/189.56 tff(92,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[91, 75])).
% 299.37/189.56 tff(93,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(X!1, Y!0) = and(implies(X!1, Y!0), implies(Y!0, X!1)))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(94,plain,
% 299.37/189.56 (equiv(X!1, Y!0) = and(implies(X!1, Y!0), implies(Y!0, X!1))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[93, 92])).
% 299.37/189.56 tff(95,plain,
% 299.37/189.56 (and(implies(X!1, Y!0), implies(Y!0, X!1)) = equiv(X!1, Y!0)),
% 299.37/189.56 inference(symmetry,[status(thm)],[94])).
% 299.37/189.56 tff(96,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(Y!0, X!1) = not(and(Y!0, not(X!1))))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(97,plain,
% 299.37/189.56 (implies(Y!0, X!1) = not(and(Y!0, not(X!1)))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[96, 41])).
% 299.37/189.56 tff(98,plain,
% 299.37/189.56 (not(and(Y!0, not(X!1))) = implies(Y!0, X!1)),
% 299.37/189.56 inference(symmetry,[status(thm)],[97])).
% 299.37/189.56 tff(99,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(X!1, Y!0) = not(and(X!1, not(Y!0))))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(100,plain,
% 299.37/189.56 (implies(X!1, Y!0) = not(and(X!1, not(Y!0)))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[99, 41])).
% 299.37/189.56 tff(101,plain,
% 299.37/189.56 (not(and(X!1, not(Y!0))) = implies(X!1, Y!0)),
% 299.37/189.56 inference(symmetry,[status(thm)],[100])).
% 299.37/189.56 tff(102,plain,
% 299.37/189.56 (and(not(and(X!1, not(Y!0))), not(and(Y!0, not(X!1)))) = and(implies(X!1, Y!0), implies(Y!0, X!1))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[101, 98])).
% 299.37/189.56 tff(103,plain,
% 299.37/189.56 (and(not(and(X!1, not(Y!0))), not(and(Y!0, not(X!1)))) = equiv(X!1, Y!0)),
% 299.37/189.56 inference(transitivity,[status(thm)],[102, 95])).
% 299.37/189.56 tff(104,plain,
% 299.37/189.56 (not(and(not(and(X!1, not(Y!0))), not(and(Y!0, not(X!1))))) = not(equiv(X!1, Y!0))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[103])).
% 299.37/189.56 tff(105,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(X!1, not(Y!0)), and(Y!0, not(X!1))) = not(and(not(and(X!1, not(Y!0))), not(and(Y!0, not(X!1))))))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(106,plain,
% 299.37/189.56 (or(and(X!1, not(Y!0)), and(Y!0, not(X!1))) = not(and(not(and(X!1, not(Y!0))), not(and(Y!0, not(X!1)))))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[105, 63])).
% 299.37/189.56 tff(107,plain,
% 299.37/189.56 (^[X: $i, Y: $i] : refl((and(X, Y) = not(or(not(X), not(Y)))) <=> (and(X, Y) = not(or(not(X), not(Y)))))),
% 299.37/189.56 inference(bind,[status(th)],[])).
% 299.37/189.56 tff(108,plain,
% 299.37/189.56 (![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))))),
% 299.37/189.56 inference(quant_intro,[status(thm)],[107])).
% 299.37/189.56 tff(109,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(110,plain,
% 299.37/189.56 (($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))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(111,axiom,(op_and), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_op_and')).
% 299.37/189.56 tff(112,plain,
% 299.37/189.56 (op_and <=> $true),
% 299.37/189.56 inference(iff_true,[status(thm)],[111])).
% 299.37/189.56 tff(113,plain,
% 299.37/189.56 ((~op_and) <=> (~$true)),
% 299.37/189.56 inference(monotonicity,[status(thm)],[112])).
% 299.37/189.56 tff(114,plain,
% 299.37/189.56 ((~op_and) <=> $false),
% 299.37/189.56 inference(transitivity,[status(thm)],[113, 5])).
% 299.37/189.56 tff(115,plain,
% 299.37/189.56 (((~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)))))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[114])).
% 299.37/189.56 tff(116,plain,
% 299.37/189.56 (((~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))))),
% 299.37/189.56 inference(transitivity,[status(thm)],[115, 110])).
% 299.37/189.56 tff(117,plain,
% 299.37/189.56 (((~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)))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(118,plain,
% 299.37/189.56 ((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)))))),
% 299.37/189.56 inference(rewrite,[status(thm)],[])).
% 299.37/189.56 tff(119,axiom,(op_and => ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_and')).
% 299.37/189.56 tff(120,plain,
% 299.37/189.56 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[119, 118])).
% 299.37/189.56 tff(121,plain,
% 299.37/189.56 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[120, 117])).
% 299.37/189.56 tff(122,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[121, 116])).
% 299.37/189.56 tff(123,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[122, 109])).
% 299.37/189.56 tff(124,plain,(
% 299.37/189.56 ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 299.37/189.56 inference(skolemize,[status(sab)],[123])).
% 299.37/189.56 tff(125,plain,
% 299.37/189.56 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 299.37/189.56 inference(modus_ponens,[status(thm)],[124, 108])).
% 299.37/189.56 tff(126,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(Y!0, not(X!1)) = not(or(not(Y!0), not(not(X!1)))))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(127,plain,
% 299.37/189.56 (and(Y!0, not(X!1)) = not(or(not(Y!0), not(not(X!1))))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[126, 125])).
% 299.37/189.56 tff(128,plain,
% 299.37/189.56 (not(or(not(Y!0), not(not(X!1)))) = and(Y!0, not(X!1))),
% 299.37/189.56 inference(symmetry,[status(thm)],[127])).
% 299.37/189.56 tff(129,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(X!1, not(Y!0)) = not(or(not(X!1), not(not(Y!0)))))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(130,plain,
% 299.37/189.56 (and(X!1, not(Y!0)) = not(or(not(X!1), not(not(Y!0))))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[129, 125])).
% 299.37/189.56 tff(131,plain,
% 299.37/189.56 (not(or(not(X!1), not(not(Y!0)))) = and(X!1, not(Y!0))),
% 299.37/189.56 inference(symmetry,[status(thm)],[130])).
% 299.37/189.56 tff(132,plain,
% 299.37/189.56 (or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))) = or(and(X!1, not(Y!0)), and(Y!0, not(X!1)))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[131, 128])).
% 299.37/189.56 tff(133,plain,
% 299.37/189.56 (or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))) = not(equiv(X!1, Y!0))),
% 299.37/189.56 inference(transitivity,[status(thm)],[132, 106, 104])).
% 299.37/189.56 tff(134,plain,
% 299.37/189.56 (not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))) = not(not(equiv(X!1, Y!0)))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[133])).
% 299.37/189.56 tff(135,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(X!1, Y!0) = or(not(X!1), Y!0))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(136,plain,
% 299.37/189.56 (implies(X!1, Y!0) = or(not(X!1), Y!0)),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[135, 20])).
% 299.37/189.56 tff(137,plain,
% 299.37/189.56 (or(not(X!1), Y!0) = implies(X!1, Y!0)),
% 299.37/189.56 inference(symmetry,[status(thm)],[136])).
% 299.37/189.56 tff(138,plain,
% 299.37/189.56 (not(or(not(X!1), Y!0)) = not(implies(X!1, Y!0))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[137])).
% 299.37/189.56 tff(139,plain,
% 299.37/189.56 (not(implies(X!1, Y!0)) = not(or(not(X!1), Y!0))),
% 299.37/189.56 inference(symmetry,[status(thm)],[138])).
% 299.37/189.56 tff(140,plain,
% 299.37/189.56 (or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = or(not(or(not(X!1), Y!0)), not(not(equiv(X!1, Y!0))))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[139, 134])).
% 299.37/189.56 tff(141,plain,
% 299.37/189.56 (or(not(or(not(X!1), Y!0)), not(not(equiv(X!1, Y!0)))) = or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.37/189.56 inference(symmetry,[status(thm)],[140])).
% 299.37/189.56 tff(142,plain,
% 299.37/189.56 (not(not(equiv(X!1, Y!0))) = not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))),
% 299.37/189.56 inference(symmetry,[status(thm)],[134])).
% 299.37/189.56 tff(143,plain,
% 299.37/189.56 (or(not(or(not(X!1), Y!0)), not(not(equiv(X!1, Y!0)))) = or(not(or(not(X!1), Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[142])).
% 299.37/189.56 tff(144,plain,
% 299.37/189.56 (or(not(or(not(X!1), Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = or(not(or(not(X!1), Y!0)), not(not(equiv(X!1, Y!0))))),
% 299.37/189.56 inference(symmetry,[status(thm)],[143])).
% 299.37/189.56 tff(145,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(X!1), Y!0), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = or(not(or(not(X!1), Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(146,plain,
% 299.37/189.56 (implies(or(not(X!1), Y!0), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = or(not(or(not(X!1), Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[145, 20])).
% 299.37/189.56 tff(147,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(X!1), Y!0), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = not(and(or(not(X!1), Y!0), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(148,plain,
% 299.37/189.56 (implies(or(not(X!1), Y!0), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = not(and(or(not(X!1), Y!0), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[147, 41])).
% 299.37/189.56 tff(149,plain,
% 299.37/189.56 (not(and(or(not(X!1), Y!0), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))) = implies(or(not(X!1), Y!0), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.37/189.56 inference(symmetry,[status(thm)],[148])).
% 299.37/189.56 tff(150,plain,
% 299.37/189.56 (not(not(or(not(X!1), not(not(Y!0))))) = not(and(X!1, not(Y!0)))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[131])).
% 299.37/189.56 tff(151,plain,
% 299.37/189.56 (not(and(X!1, not(Y!0))) = not(not(or(not(X!1), not(not(Y!0)))))),
% 299.37/189.56 inference(symmetry,[status(thm)],[150])).
% 299.37/189.56 tff(152,plain,
% 299.37/189.56 (or(not(X!1), Y!0) = not(not(or(not(X!1), not(not(Y!0)))))),
% 299.37/189.56 inference(transitivity,[status(thm)],[137, 100, 151])).
% 299.37/189.56 tff(153,plain,
% 299.37/189.56 (and(or(not(X!1), Y!0), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = and(not(not(or(not(X!1), not(not(Y!0))))), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[152])).
% 299.37/189.56 tff(154,plain,
% 299.37/189.56 (not(and(or(not(X!1), Y!0), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.56 inference(monotonicity,[status(thm)],[153])).
% 299.37/189.56 tff(155,plain,
% 299.37/189.56 (not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))) = not(and(or(not(X!1), Y!0), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.56 inference(symmetry,[status(thm)],[154])).
% 299.37/189.56 tff(156,plain,
% 299.37/189.56 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.37/189.56 inference(quant_inst,[status(thm)],[])).
% 299.37/189.56 tff(157,plain,
% 299.37/189.56 (or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.56 inference(unit_resolution,[status(thm)],[156, 63])).
% 299.37/189.56 tff(158,plain,
% 299.37/189.57 (or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.37/189.57 inference(transitivity,[status(thm)],[157, 155, 149, 146, 144, 141, 65, 44, 22])).
% 299.37/189.57 tff(159,plain,
% 299.37/189.57 (or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(Y!0), X!1)), or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[71, 158])).
% 299.37/189.57 tff(160,plain,
% 299.37/189.57 (or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.37/189.57 inference(transitivity,[status(thm)],[159, 73])).
% 299.37/189.57 tff(161,plain,
% 299.37/189.57 (equiv(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = equiv(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[160])).
% 299.37/189.57 tff(162,plain,
% 299.37/189.57 (equiv(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = equiv(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[161])).
% 299.37/189.57 tff(163,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = and(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(164,plain,
% 299.37/189.57 (equiv(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = and(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[163, 92])).
% 299.37/189.57 tff(165,plain,
% 299.37/189.57 (and(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))) = equiv(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[164])).
% 299.37/189.57 tff(166,plain,
% 299.37/189.57 (or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[71, 134])).
% 299.37/189.57 tff(167,plain,
% 299.37/189.57 (or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(X!1), Y!0)), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[139, 166])).
% 299.37/189.57 tff(168,plain,
% 299.37/189.57 (or(not(or(not(X!1), Y!0)), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))) = or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[167])).
% 299.37/189.57 tff(169,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(X!1), Y!0), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))) = or(not(or(not(X!1), Y!0)), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(170,plain,
% 299.37/189.57 (implies(or(not(X!1), Y!0), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))) = or(not(or(not(X!1), Y!0)), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[169, 20])).
% 299.37/189.57 tff(171,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(X!1), Y!0), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))) = not(and(or(not(X!1), Y!0), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(172,plain,
% 299.37/189.57 (implies(or(not(X!1), Y!0), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))) = not(and(or(not(X!1), Y!0), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[171, 41])).
% 299.37/189.57 tff(173,plain,
% 299.37/189.57 (not(and(or(not(X!1), Y!0), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))) = implies(or(not(X!1), Y!0), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[172])).
% 299.37/189.57 tff(174,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(X!1), Y!0), and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))) = not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(175,plain,
% 299.37/189.57 (and(or(not(X!1), Y!0), and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))) = not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[174, 125])).
% 299.37/189.57 tff(176,plain,
% 299.37/189.57 (and(implies(Y!0, X!1), not(equiv(X!1, Y!0))) = and(or(not(Y!0), X!1), not(equiv(X!1, Y!0)))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[68])).
% 299.37/189.57 tff(177,plain,
% 299.37/189.57 (and(or(not(Y!0), X!1), not(equiv(X!1, Y!0))) = and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))),
% 299.37/189.57 inference(symmetry,[status(thm)],[176])).
% 299.37/189.57 tff(178,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(Y!0), X!1), not(equiv(X!1, Y!0))) = not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(179,plain,
% 299.37/189.57 (and(or(not(Y!0), X!1), not(equiv(X!1, Y!0))) = not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[178, 125])).
% 299.37/189.57 tff(180,plain,
% 299.37/189.57 (not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))) = and(or(not(Y!0), X!1), not(equiv(X!1, Y!0)))),
% 299.37/189.57 inference(symmetry,[status(thm)],[179])).
% 299.37/189.57 tff(181,plain,
% 299.37/189.57 (not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))) = and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))),
% 299.37/189.57 inference(transitivity,[status(thm)],[180, 177])).
% 299.37/189.57 tff(182,plain,
% 299.37/189.57 (and(or(not(X!1), Y!0), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))) = and(or(not(X!1), Y!0), and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[181])).
% 299.37/189.57 tff(183,plain,
% 299.37/189.57 (and(or(not(X!1), Y!0), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))) = not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))),
% 299.37/189.57 inference(transitivity,[status(thm)],[182, 175])).
% 299.37/189.57 tff(184,plain,
% 299.37/189.57 (not(and(or(not(X!1), Y!0), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))) = not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[183])).
% 299.37/189.57 tff(185,plain,
% 299.37/189.57 (not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))) = not(and(or(not(X!1), Y!0), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[184])).
% 299.37/189.57 tff(186,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(X!1), Y!0) = not(and(not(not(X!1)), not(Y!0))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(187,plain,
% 299.37/189.57 (or(not(X!1), Y!0) = not(and(not(not(X!1)), not(Y!0)))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[186, 63])).
% 299.37/189.57 tff(188,plain,
% 299.37/189.57 (not(and(not(not(X!1)), not(Y!0))) = or(not(X!1), Y!0)),
% 299.37/189.57 inference(symmetry,[status(thm)],[187])).
% 299.37/189.57 tff(189,plain,
% 299.37/189.57 (and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))) = and(or(not(X!1), Y!0), and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[188, 181])).
% 299.37/189.57 tff(190,plain,
% 299.37/189.57 (and(or(not(X!1), Y!0), and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))) = and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[189])).
% 299.37/189.57 tff(191,plain,
% 299.37/189.57 (not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))) = and(or(not(X!1), Y!0), and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[175])).
% 299.37/189.57 tff(192,plain,
% 299.37/189.57 (not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))) = and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))),
% 299.37/189.57 inference(transitivity,[status(thm)],[191, 190])).
% 299.37/189.57 tff(193,plain,
% 299.37/189.57 (not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))) = not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[192])).
% 299.37/189.57 tff(194,plain,
% 299.37/189.57 (not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))) = not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[193])).
% 299.37/189.57 tff(195,plain,
% 299.37/189.57 (not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))) = or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.37/189.57 inference(transitivity,[status(thm)],[194, 185, 173, 170, 168])).
% 299.37/189.57 tff(196,plain,
% 299.37/189.57 (implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))) = implies(or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[195])).
% 299.37/189.57 tff(197,plain,
% 299.37/189.57 (implies(or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))) = implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[196])).
% 299.37/189.57 tff(198,plain,
% 299.37/189.57 (not(and(implies(X!1, Y!0), implies(Y!0, X!1))) = not(equiv(X!1, Y!0))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[95])).
% 299.37/189.57 tff(199,plain,
% 299.37/189.57 (and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))) = and(not(not(implies(X!1, Y!0))), not(equiv(X!1, Y!0)))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[198])).
% 299.37/189.57 tff(200,plain,
% 299.37/189.57 (and(not(not(implies(X!1, Y!0))), not(equiv(X!1, Y!0))) = and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[199])).
% 299.37/189.57 tff(201,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(implies(X!1, Y!0))), not(equiv(X!1, Y!0))) = not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(202,plain,
% 299.37/189.57 (and(not(not(implies(X!1, Y!0))), not(equiv(X!1, Y!0))) = not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[201, 125])).
% 299.37/189.57 tff(203,plain,
% 299.37/189.57 (not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))) = and(not(not(implies(X!1, Y!0))), not(equiv(X!1, Y!0)))),
% 299.37/189.57 inference(symmetry,[status(thm)],[202])).
% 299.37/189.57 tff(204,plain,
% 299.37/189.57 (not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))) = and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))),
% 299.37/189.57 inference(transitivity,[status(thm)],[203, 200])).
% 299.37/189.57 tff(205,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(Y!0), not(not(X!1))) = not(and(not(not(Y!0)), not(not(not(X!1))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(206,plain,
% 299.37/189.57 (or(not(Y!0), not(not(X!1))) = not(and(not(not(Y!0)), not(not(not(X!1)))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[205, 63])).
% 299.37/189.57 tff(207,plain,
% 299.37/189.57 (not(and(not(not(Y!0)), not(not(not(X!1))))) = or(not(Y!0), not(not(X!1)))),
% 299.37/189.57 inference(symmetry,[status(thm)],[206])).
% 299.37/189.57 tff(208,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(Y!0)), not(not(X!1))) = not(and(not(not(Y!0)), not(not(not(X!1))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(209,plain,
% 299.37/189.57 (implies(not(not(Y!0)), not(not(X!1))) = not(and(not(not(Y!0)), not(not(not(X!1)))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[208, 41])).
% 299.37/189.57 tff(210,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(not(Y!0)), not(not(X!1))) = or(not(not(not(Y!0))), not(not(X!1))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(211,plain,
% 299.37/189.57 (implies(not(not(Y!0)), not(not(X!1))) = or(not(not(not(Y!0))), not(not(X!1)))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[210, 20])).
% 299.37/189.57 tff(212,plain,
% 299.37/189.57 (or(not(not(not(Y!0))), not(not(X!1))) = implies(not(not(Y!0)), not(not(X!1)))),
% 299.37/189.57 inference(symmetry,[status(thm)],[211])).
% 299.37/189.57 tff(213,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(not(not(Y!0))), not(not(X!1))) = not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(214,plain,
% 299.37/189.57 (or(not(not(not(Y!0))), not(not(X!1))) = not(and(not(not(not(not(Y!0)))), not(not(not(X!1)))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[213, 63])).
% 299.37/189.57 tff(215,plain,
% 299.37/189.57 (not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))) = or(not(not(not(Y!0))), not(not(X!1)))),
% 299.37/189.57 inference(symmetry,[status(thm)],[214])).
% 299.37/189.57 tff(216,plain,
% 299.37/189.57 (not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))) = or(not(Y!0), not(not(X!1)))),
% 299.37/189.57 inference(transitivity,[status(thm)],[215, 212, 209, 207])).
% 299.37/189.57 tff(217,plain,
% 299.37/189.57 (and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))) = and(or(not(Y!0), not(not(X!1))), and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[216, 204])).
% 299.37/189.57 tff(218,plain,
% 299.37/189.57 (and(or(not(Y!0), not(not(X!1))), and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))) = and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[217])).
% 299.37/189.57 tff(219,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(Y!0), not(not(X!1))), and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))) = not(or(not(or(not(Y!0), not(not(X!1)))), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(220,plain,
% 299.37/189.57 (and(or(not(Y!0), not(not(X!1))), and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))) = not(or(not(or(not(Y!0), not(not(X!1)))), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[219, 125])).
% 299.37/189.57 tff(221,plain,
% 299.37/189.57 (not(or(not(or(not(Y!0), not(not(X!1)))), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = and(or(not(Y!0), not(not(X!1))), and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[220])).
% 299.37/189.57 tff(222,plain,
% 299.37/189.57 (or(not(or(not(Y!0), X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))) = or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[70])).
% 299.37/189.57 tff(223,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(Y!0), X!1), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))) = or(not(or(not(Y!0), X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(224,plain,
% 299.37/189.57 (implies(or(not(Y!0), X!1), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))) = or(not(or(not(Y!0), X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[223, 20])).
% 299.37/189.57 tff(225,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))) = not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(226,plain,
% 299.37/189.57 (or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))) = not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[225, 63])).
% 299.37/189.57 tff(227,plain,
% 299.37/189.57 (not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))) = or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))),
% 299.37/189.57 inference(symmetry,[status(thm)],[226])).
% 299.37/189.57 tff(228,plain,
% 299.37/189.57 (implies(or(not(Y!0), X!1), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = implies(or(not(Y!0), X!1), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[227])).
% 299.37/189.57 tff(229,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(Y!0), X!1), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = not(and(or(not(Y!0), X!1), not(not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(230,plain,
% 299.37/189.57 (implies(or(not(Y!0), X!1), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = not(and(or(not(Y!0), X!1), not(not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[229, 41])).
% 299.37/189.57 tff(231,plain,
% 299.37/189.57 (not(and(or(not(Y!0), X!1), not(not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = implies(or(not(Y!0), X!1), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[230])).
% 299.37/189.57 tff(232,plain,
% 299.37/189.57 (not(not(or(not(Y!0), not(not(X!1))))) = not(and(Y!0, not(X!1)))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[128])).
% 299.37/189.57 tff(233,plain,
% 299.37/189.57 (not(and(Y!0, not(X!1))) = not(not(or(not(Y!0), not(not(X!1)))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[232])).
% 299.37/189.57 tff(234,plain,
% 299.37/189.57 (or(not(Y!0), X!1) = not(not(or(not(Y!0), not(not(X!1)))))),
% 299.37/189.57 inference(transitivity,[status(thm)],[69, 97, 233])).
% 299.37/189.57 tff(235,plain,
% 299.37/189.57 (and(or(not(Y!0), X!1), not(not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = and(not(not(or(not(Y!0), not(not(X!1))))), not(not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[234])).
% 299.37/189.57 tff(236,plain,
% 299.37/189.57 (and(not(not(or(not(Y!0), not(not(X!1))))), not(not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = and(or(not(Y!0), X!1), not(not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[235])).
% 299.37/189.57 tff(237,plain,
% 299.37/189.57 (not(and(not(not(or(not(Y!0), not(not(X!1))))), not(not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = not(and(or(not(Y!0), X!1), not(not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[236])).
% 299.37/189.57 tff(238,plain,
% 299.37/189.57 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(Y!0), not(not(X!1)))), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = not(and(not(not(or(not(Y!0), not(not(X!1))))), not(not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.37/189.57 inference(quant_inst,[status(thm)],[])).
% 299.37/189.57 tff(239,plain,
% 299.37/189.57 (or(not(or(not(Y!0), not(not(X!1)))), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = not(and(not(not(or(not(Y!0), not(not(X!1))))), not(not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.37/189.57 inference(unit_resolution,[status(thm)],[238, 63])).
% 299.37/189.57 tff(240,plain,
% 299.37/189.57 (or(not(or(not(Y!0), not(not(X!1)))), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))),
% 299.37/189.57 inference(transitivity,[status(thm)],[239, 237, 231, 228, 224, 222])).
% 299.37/189.57 tff(241,plain,
% 299.37/189.57 (not(or(not(or(not(Y!0), not(not(X!1)))), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.37/189.57 inference(monotonicity,[status(thm)],[240])).
% 299.37/189.57 tff(242,plain,
% 299.37/189.57 (not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))) = not(or(not(or(not(Y!0), not(not(X!1)))), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.37/189.57 inference(symmetry,[status(thm)],[241])).
% 299.37/189.57 tff(243,plain,
% 299.37/189.57 (not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))) = and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))),
% 299.37/189.57 inference(transitivity,[status(thm)],[242, 221, 218])).
% 299.37/189.57 tff(244,plain,
% 299.37/189.57 (not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[243])).
% 299.37/189.58 tff(245,plain,
% 299.37/189.58 (or(not(or(not(Y!0), X!1)), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[70, 227])).
% 299.37/189.58 tff(246,plain,
% 299.37/189.58 (not(or(not(or(not(Y!0), X!1)), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[245])).
% 299.37/189.58 tff(247,plain,
% 299.37/189.58 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(Y!0), X!1), and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))) = not(or(not(or(not(Y!0), X!1)), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.37/189.58 inference(quant_inst,[status(thm)],[])).
% 299.37/189.58 tff(248,plain,
% 299.37/189.58 (and(or(not(Y!0), X!1), and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))) = not(or(not(or(not(Y!0), X!1)), not(and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.37/189.58 inference(unit_resolution,[status(thm)],[247, 125])).
% 299.37/189.58 tff(249,plain,
% 299.37/189.58 (and(or(not(Y!0), X!1), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))) = and(or(not(Y!0), X!1), and(not(not(implies(X!1, Y!0))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[204])).
% 299.37/189.58 tff(250,plain,
% 299.37/189.58 (and(or(not(Y!0), X!1), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))) = not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.37/189.58 inference(transitivity,[status(thm)],[249, 248, 246])).
% 299.37/189.58 tff(251,plain,
% 299.37/189.58 (not(and(or(not(Y!0), X!1), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))) = not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[250])).
% 299.37/189.58 tff(252,plain,
% 299.37/189.58 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(Y!0), X!1), or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))) = not(and(or(not(Y!0), X!1), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(quant_inst,[status(thm)],[])).
% 299.37/189.58 tff(253,plain,
% 299.37/189.58 (implies(or(not(Y!0), X!1), or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))) = not(and(or(not(Y!0), X!1), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))),
% 299.37/189.58 inference(unit_resolution,[status(thm)],[252, 41])).
% 299.37/189.58 tff(254,plain,
% 299.37/189.58 (or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))) = or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[142])).
% 299.37/189.58 tff(255,plain,
% 299.37/189.58 (or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) = or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[254])).
% 299.37/189.58 tff(256,plain,
% 299.37/189.58 (implies(or(not(Y!0), X!1), or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = implies(or(not(Y!0), X!1), or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[255])).
% 299.37/189.58 tff(257,plain,
% 299.37/189.58 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(Y!0), X!1), or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(Y!0), X!1)), or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.58 inference(quant_inst,[status(thm)],[])).
% 299.37/189.58 tff(258,plain,
% 299.37/189.58 (implies(or(not(Y!0), X!1), or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(Y!0), X!1)), or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.37/189.58 inference(unit_resolution,[status(thm)],[257, 20])).
% 299.37/189.58 tff(259,plain,
% 299.37/189.58 (or(not(or(not(Y!0), X!1)), or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = implies(or(not(Y!0), X!1), or(not(not(not(implies(X!1, Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[258])).
% 299.37/189.58 tff(260,plain,
% 299.37/189.58 (or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))),
% 299.37/189.58 inference(transitivity,[status(thm)],[72, 259, 256, 253, 251, 244])).
% 299.37/189.58 tff(261,plain,
% 299.37/189.58 (or(not(or(not(X!1), Y!0)), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))) = implies(or(not(X!1), Y!0), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[170])).
% 299.37/189.58 tff(262,plain,
% 299.37/189.58 (or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))),
% 299.37/189.58 inference(transitivity,[status(thm)],[167, 261, 172, 184, 193])).
% 299.37/189.58 tff(263,plain,
% 299.37/189.58 (implies(or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))) = implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[262, 260])).
% 299.37/189.58 tff(264,plain,
% 299.37/189.58 (implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = implies(or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[263])).
% 299.37/189.58 tff(265,plain,
% 299.37/189.58 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))),
% 299.37/189.58 inference(quant_inst,[status(thm)],[])).
% 299.37/189.58 tff(266,plain,
% 299.37/189.58 (implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(unit_resolution,[status(thm)],[265, 20])).
% 299.37/189.58 tff(267,plain,
% 299.37/189.58 (or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[266])).
% 299.37/189.58 tff(268,plain,
% 299.37/189.58 (or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[244])).
% 299.37/189.58 tff(269,plain,
% 299.37/189.58 (or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.58 inference(transitivity,[status(thm)],[268, 267, 264, 197])).
% 299.37/189.58 tff(270,plain,
% 299.37/189.58 (implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[195])).
% 299.37/189.58 tff(271,plain,
% 299.37/189.58 (implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))) = implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[270])).
% 299.37/189.58 tff(272,plain,
% 299.37/189.58 (implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))) = implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[260, 262])).
% 299.37/189.58 tff(273,plain,
% 299.37/189.58 (implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[272])).
% 299.37/189.58 tff(274,plain,
% 299.37/189.58 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = not(and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))))),
% 299.37/189.58 inference(quant_inst,[status(thm)],[])).
% 299.37/189.58 tff(275,plain,
% 299.37/189.58 (implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = not(and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))))),
% 299.37/189.58 inference(unit_resolution,[status(thm)],[274, 41])).
% 299.37/189.58 tff(276,plain,
% 299.37/189.58 (not(and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) = implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[275])).
% 299.37/189.58 tff(277,plain,
% 299.37/189.58 (not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))) = not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[244])).
% 299.37/189.58 tff(278,plain,
% 299.37/189.58 (and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))) = and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[277])).
% 299.37/189.58 tff(279,plain,
% 299.37/189.58 (not(and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) = not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[278])).
% 299.37/189.58 tff(280,plain,
% 299.37/189.58 (not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) = not(and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[279])).
% 299.37/189.58 tff(281,plain,
% 299.37/189.58 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))))),
% 299.37/189.58 inference(quant_inst,[status(thm)],[])).
% 299.37/189.58 tff(282,plain,
% 299.37/189.58 (or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))))),
% 299.37/189.58 inference(unit_resolution,[status(thm)],[281, 63])).
% 299.37/189.58 tff(283,plain,
% 299.37/189.58 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))) = not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.37/189.58 inference(quant_inst,[status(thm)],[])).
% 299.37/189.58 tff(284,plain,
% 299.37/189.58 (or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))) = not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.37/189.58 inference(unit_resolution,[status(thm)],[283, 63])).
% 299.37/189.58 tff(285,plain,
% 299.37/189.58 (not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[284])).
% 299.37/189.58 tff(286,plain,
% 299.37/189.58 (not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[285])).
% 299.37/189.58 tff(287,plain,
% 299.37/189.58 (not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))) = not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[286])).
% 299.37/189.58 tff(288,plain,
% 299.37/189.58 (or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[287, 194])).
% 299.37/189.58 tff(289,plain,
% 299.37/189.58 (or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))) = or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[288])).
% 299.37/189.58 tff(290,plain,
% 299.37/189.58 (or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))) = or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(monotonicity,[status(thm)],[193])).
% 299.37/189.58 tff(291,plain,
% 299.37/189.58 (or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))),
% 299.37/189.58 inference(symmetry,[status(thm)],[290])).
% 299.37/189.58 tff(292,plain,
% 299.37/189.58 (or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.59 inference(transitivity,[status(thm)],[291, 289, 282, 280, 276, 273, 271])).
% 299.37/189.59 tff(293,plain,
% 299.37/189.59 (and(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.37/189.59 inference(monotonicity,[status(thm)],[292, 269])).
% 299.37/189.59 tff(294,plain,
% 299.37/189.59 (not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) = or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.59 inference(symmetry,[status(thm)],[282])).
% 299.37/189.59 tff(295,plain,
% 299.37/189.59 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))),
% 299.37/189.59 inference(quant_inst,[status(thm)],[])).
% 299.37/189.59 tff(296,plain,
% 299.37/189.59 (implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.59 inference(unit_resolution,[status(thm)],[295, 20])).
% 299.37/189.59 tff(297,plain,
% 299.37/189.59 (or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.59 inference(symmetry,[status(thm)],[296])).
% 299.37/189.59 tff(298,plain,
% 299.37/189.59 (not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.37/189.59 inference(monotonicity,[status(thm)],[277])).
% 299.37/189.59 tff(299,plain,
% 299.37/189.59 (not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.59 inference(symmetry,[status(thm)],[298])).
% 299.37/189.59 tff(300,plain,
% 299.37/189.59 (or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))) = or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.59 inference(monotonicity,[status(thm)],[299, 193])).
% 299.37/189.59 tff(301,plain,
% 299.37/189.59 (or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))) = or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.37/189.59 inference(transitivity,[status(thm)],[300, 297, 275, 279, 294, 288, 290])).
% 299.37/189.59 tff(302,plain,
% 299.37/189.59 (and(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))), or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.37/189.59 inference(monotonicity,[status(thm)],[301])).
% 299.37/189.59 tff(303,plain,
% 299.37/189.59 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))), or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = not(or(not(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))),
% 299.37/189.59 inference(quant_inst,[status(thm)],[])).
% 299.37/189.59 tff(304,plain,
% 299.37/189.59 (and(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))), or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = not(or(not(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.37/189.59 inference(unit_resolution,[status(thm)],[303, 125])).
% 299.37/189.59 tff(305,plain,
% 299.37/189.59 (not(or(not(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))) = and(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))), or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.37/189.59 inference(symmetry,[status(thm)],[304])).
% 299.37/189.59 tff(306,plain,
% 299.37/189.59 (and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.37/189.59 inference(monotonicity,[status(thm)],[193, 286])).
% 299.37/189.59 tff(307,plain,
% 299.37/189.59 (and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.37/189.59 inference(symmetry,[status(thm)],[306])).
% 299.37/189.59 tff(308,plain,
% 299.37/189.59 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.37/189.59 inference(quant_inst,[status(thm)],[])).
% 299.37/189.59 tff(309,plain,
% 299.37/189.59 (and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.37/189.59 inference(unit_resolution,[status(thm)],[308, 125])).
% 299.37/189.59 tff(310,plain,
% 299.37/189.59 (not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.37/189.59 inference(symmetry,[status(thm)],[309])).
% 299.37/189.59 tff(311,plain,
% 299.37/189.59 (not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.37/189.59 inference(transitivity,[status(thm)],[310, 307])).
% 299.37/189.59 tff(312,plain,
% 299.37/189.59 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(implies(Y!0, X!1), equiv(X!1, Y!0)) = not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))),
% 299.37/189.59 inference(quant_inst,[status(thm)],[])).
% 299.37/189.59 tff(313,plain,
% 299.37/189.59 (implies(implies(Y!0, X!1), equiv(X!1, Y!0)) = not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))),
% 299.37/189.59 inference(unit_resolution,[status(thm)],[312, 41])).
% 299.37/189.59 tff(314,plain,
% 299.37/189.59 (not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))) = implies(implies(Y!0, X!1), equiv(X!1, Y!0))),
% 299.37/189.59 inference(symmetry,[status(thm)],[313])).
% 299.37/189.59 tff(315,plain,
% 299.37/189.59 (or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))) = or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))),
% 299.37/189.59 inference(monotonicity,[status(thm)],[138, 314])).
% 299.37/189.59 tff(316,plain,
% 299.37/189.59 (not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))) = not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.37/189.59 inference(monotonicity,[status(thm)],[315])).
% 299.37/189.59 tff(317,plain,
% 299.37/189.59 (not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))),
% 299.37/189.59 inference(symmetry,[status(thm)],[316])).
% 299.37/189.59 tff(318,plain,
% 299.37/189.59 (and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))),
% 299.37/189.59 inference(monotonicity,[status(thm)],[317])).
% 299.37/189.59 tff(319,plain,
% 299.37/189.59 (and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))) = and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.37/189.59 inference(symmetry,[status(thm)],[318])).
% 299.37/189.59 tff(320,plain,
% 299.37/189.59 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))) = not(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))))),
% 299.37/189.59 inference(quant_inst,[status(thm)],[])).
% 299.37/189.59 tff(321,plain,
% 299.37/189.59 (and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))) = not(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))))),
% 299.37/189.59 inference(unit_resolution,[status(thm)],[320, 125])).
% 299.37/189.59 tff(322,plain,
% 299.37/189.59 (not(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))) = and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))),
% 299.37/189.59 inference(symmetry,[status(thm)],[321])).
% 299.37/189.59 tff(323,plain,
% 299.37/189.59 (not(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))) = and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.37/189.59 inference(transitivity,[status(thm)],[322, 319])).
% 299.37/189.59 tff(324,plain,
% 299.37/189.59 (or(not(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.37/189.59 inference(monotonicity,[status(thm)],[323, 311])).
% 299.37/189.59 tff(325,plain,
% 299.37/189.59 (or(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(not(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.37/189.59 inference(symmetry,[status(thm)],[324])).
% 299.37/189.59 tff(326,plain,
% 299.37/189.59 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))),
% 299.37/189.59 inference(quant_inst,[status(thm)],[])).
% 299.37/189.59 tff(327,plain,
% 299.37/189.59 (or(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))),
% 299.37/189.59 inference(unit_resolution,[status(thm)],[326, 63])).
% 299.37/189.60 tff(328,plain,
% 299.37/189.60 (not(and(not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) = or(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.37/189.60 inference(symmetry,[status(thm)],[327])).
% 299.37/189.60 tff(329,plain,
% 299.37/189.60 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))) = not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.37/189.60 inference(quant_inst,[status(thm)],[])).
% 299.37/189.60 tff(330,plain,
% 299.37/189.60 (implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))) = not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.37/189.60 inference(unit_resolution,[status(thm)],[329, 41])).
% 299.37/189.60 tff(331,plain,
% 299.37/189.60 (not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.37/189.60 inference(symmetry,[status(thm)],[330])).
% 299.37/189.60 tff(332,plain,
% 299.37/189.60 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.37/189.60 inference(quant_inst,[status(thm)],[])).
% 299.37/189.60 tff(333,plain,
% 299.37/189.60 (implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.37/189.60 inference(unit_resolution,[status(thm)],[332, 41])).
% 299.37/189.60 tff(334,plain,
% 299.37/189.60 (not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.37/189.60 inference(symmetry,[status(thm)],[333])).
% 299.37/189.60 tff(335,plain,
% 299.37/189.60 (and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.41/189.60 inference(monotonicity,[status(thm)],[334, 331])).
% 299.41/189.60 tff(336,plain,
% 299.41/189.60 (and(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.60 inference(symmetry,[status(thm)],[335])).
% 299.41/189.60 tff(337,plain,
% 299.41/189.60 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))) = or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.41/189.60 inference(quant_inst,[status(thm)],[])).
% 299.41/189.60 tff(338,plain,
% 299.41/189.60 (implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))) = or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.41/189.60 inference(unit_resolution,[status(thm)],[337, 20])).
% 299.41/189.60 tff(339,plain,
% 299.41/189.60 (or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))) = implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.41/189.60 inference(symmetry,[status(thm)],[338])).
% 299.41/189.60 tff(340,plain,
% 299.41/189.60 (or(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.41/189.60 inference(monotonicity,[status(thm)],[316, 285])).
% 299.41/189.60 tff(341,plain,
% 299.41/189.60 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.41/189.60 inference(quant_inst,[status(thm)],[])).
% 299.41/189.60 tff(342,plain,
% 299.41/189.60 (or(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.60 inference(unit_resolution,[status(thm)],[341, 63])).
% 299.41/189.60 tff(343,plain,
% 299.41/189.60 (not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.60 inference(symmetry,[status(thm)],[342])).
% 299.41/189.60 tff(344,plain,
% 299.41/189.60 (not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.41/189.60 inference(transitivity,[status(thm)],[343, 340, 339])).
% 299.41/189.60 tff(345,plain,
% 299.41/189.60 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.41/189.60 inference(quant_inst,[status(thm)],[])).
% 299.41/189.60 tff(346,plain,
% 299.41/189.60 (implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.41/189.60 inference(unit_resolution,[status(thm)],[345, 20])).
% 299.41/189.60 tff(347,plain,
% 299.41/189.60 (or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.41/189.60 inference(symmetry,[status(thm)],[346])).
% 299.41/189.60 tff(348,plain,
% 299.41/189.60 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.41/189.60 inference(quant_inst,[status(thm)],[])).
% 299.41/189.60 tff(349,plain,
% 299.41/189.60 (or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.41/189.60 inference(unit_resolution,[status(thm)],[348, 63])).
% 299.41/189.60 tff(350,plain,
% 299.41/189.60 (not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.41/189.60 inference(symmetry,[status(thm)],[349])).
% 299.41/189.60 tff(351,plain,
% 299.41/189.60 (not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.41/189.60 inference(transitivity,[status(thm)],[350, 347])).
% 299.41/189.60 tff(352,plain,
% 299.41/189.60 (and(not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))) = and(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.41/189.60 inference(monotonicity,[status(thm)],[351, 344])).
% 299.41/189.60 tff(353,plain,
% 299.41/189.60 (and(not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))) = and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.60 inference(transitivity,[status(thm)],[352, 336])).
% 299.41/189.60 tff(354,plain,
% 299.41/189.60 (not(and(not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) = not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.60 inference(monotonicity,[status(thm)],[353])).
% 299.41/189.60 tff(355,plain,
% 299.41/189.60 (not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))),
% 299.41/189.60 inference(symmetry,[status(thm)],[354])).
% 299.41/189.60 tff(356,plain,
% 299.41/189.60 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.41/189.60 inference(quant_inst,[status(thm)],[])).
% 299.41/189.60 tff(357,plain,
% 299.41/189.60 (or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.60 inference(unit_resolution,[status(thm)],[356, 63])).
% 299.41/189.60 tff(358,plain,
% 299.41/189.60 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.60 inference(quant_inst,[status(thm)],[])).
% 299.41/189.60 tff(359,plain,
% 299.41/189.60 (and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.60 inference(unit_resolution,[status(thm)],[358, 125])).
% 299.41/189.60 tff(360,plain,
% 299.41/189.60 (not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.41/189.60 inference(symmetry,[status(thm)],[359])).
% 299.41/189.60 tff(361,plain,
% 299.41/189.60 (and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))) = and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.41/189.60 inference(monotonicity,[status(thm)],[285, 316])).
% 299.41/189.60 tff(362,plain,
% 299.41/189.60 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))) = not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))))),
% 299.41/189.60 inference(quant_inst,[status(thm)],[])).
% 299.41/189.60 tff(363,plain,
% 299.41/189.60 (and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))) = not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))))),
% 299.41/189.60 inference(unit_resolution,[status(thm)],[362, 125])).
% 299.41/189.61 tff(364,plain,
% 299.41/189.61 (not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))) = and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))),
% 299.41/189.61 inference(symmetry,[status(thm)],[363])).
% 299.41/189.61 tff(365,plain,
% 299.41/189.61 (not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))) = and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.41/189.61 inference(transitivity,[status(thm)],[364, 361])).
% 299.41/189.61 tff(366,plain,
% 299.41/189.61 (or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.61 inference(monotonicity,[status(thm)],[365, 360])).
% 299.41/189.61 tff(367,plain,
% 299.41/189.61 (or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(not(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.61 inference(transitivity,[status(thm)],[366, 357, 355, 328, 325])).
% 299.41/189.61 tff(368,plain,
% 299.41/189.61 (not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))) = not(or(not(or(not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.41/189.61 inference(monotonicity,[status(thm)],[367])).
% 299.41/189.61 tff(369,plain,
% 299.41/189.61 (or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.61 inference(symmetry,[status(thm)],[366])).
% 299.41/189.61 tff(370,plain,
% 299.41/189.61 (not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.61 inference(symmetry,[status(thm)],[357])).
% 299.41/189.61 tff(371,plain,
% 299.41/189.61 (and(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.41/189.61 inference(monotonicity,[status(thm)],[347, 331])).
% 299.41/189.61 tff(372,plain,
% 299.41/189.61 (and(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.61 inference(transitivity,[status(thm)],[371, 336])).
% 299.41/189.61 tff(373,plain,
% 299.41/189.61 (not(and(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.61 inference(monotonicity,[status(thm)],[372])).
% 299.41/189.61 tff(374,plain,
% 299.41/189.61 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(and(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.41/189.61 inference(quant_inst,[status(thm)],[])).
% 299.41/189.61 tff(375,plain,
% 299.41/189.61 (implies(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(and(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.61 inference(unit_resolution,[status(thm)],[374, 41])).
% 299.41/189.61 tff(376,plain,
% 299.41/189.61 (implies(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = implies(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.61 inference(monotonicity,[status(thm)],[360])).
% 299.41/189.61 tff(377,plain,
% 299.41/189.61 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(not(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.41/189.61 inference(quant_inst,[status(thm)],[])).
% 299.41/189.61 tff(378,plain,
% 299.41/189.61 (implies(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(not(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.61 inference(unit_resolution,[status(thm)],[377, 20])).
% 299.41/189.61 tff(379,plain,
% 299.41/189.61 (or(not(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = implies(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.61 inference(symmetry,[status(thm)],[378])).
% 299.41/189.61 tff(380,plain,
% 299.41/189.61 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(implies(X!1, Y!0), implies(implies(Y!0, X!1), equiv(X!1, Y!0))) = or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.41/189.61 inference(quant_inst,[status(thm)],[])).
% 299.41/189.61 tff(381,plain,
% 299.41/189.61 (implies(implies(X!1, Y!0), implies(implies(Y!0, X!1), equiv(X!1, Y!0))) = or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))),
% 299.41/189.61 inference(unit_resolution,[status(thm)],[380, 20])).
% 299.41/189.61 tff(382,plain,
% 299.41/189.61 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(implies(X!1, Y!0), implies(implies(Y!0, X!1), equiv(X!1, Y!0))) = not(and(implies(X!1, Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.41/189.61 inference(quant_inst,[status(thm)],[])).
% 299.41/189.61 tff(383,plain,
% 299.41/189.61 (implies(implies(X!1, Y!0), implies(implies(Y!0, X!1), equiv(X!1, Y!0))) = not(and(implies(X!1, Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.41/189.61 inference(unit_resolution,[status(thm)],[382, 41])).
% 299.41/189.61 tff(384,plain,
% 299.41/189.61 (not(and(implies(X!1, Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = implies(implies(X!1, Y!0), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))),
% 299.41/189.61 inference(symmetry,[status(thm)],[383])).
% 299.41/189.61 tff(385,plain,
% 299.41/189.61 (and(implies(X!1, Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = and(or(not(X!1), Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.41/189.61 inference(monotonicity,[status(thm)],[136])).
% 299.41/189.61 tff(386,plain,
% 299.41/189.61 (and(or(not(X!1), Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = and(implies(X!1, Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.41/189.61 inference(symmetry,[status(thm)],[385])).
% 299.41/189.61 tff(387,plain,
% 299.41/189.61 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(X!1), Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.41/189.61 inference(quant_inst,[status(thm)],[])).
% 299.41/189.61 tff(388,plain,
% 299.41/189.61 (and(or(not(X!1), Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.41/189.61 inference(unit_resolution,[status(thm)],[387, 125])).
% 299.41/189.61 tff(389,plain,
% 299.41/189.61 (not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = and(or(not(X!1), Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.41/189.61 inference(symmetry,[status(thm)],[388])).
% 299.41/189.61 tff(390,plain,
% 299.41/189.61 (not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = and(implies(X!1, Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.41/189.61 inference(transitivity,[status(thm)],[389, 386])).
% 299.41/189.61 tff(391,plain,
% 299.41/189.61 (not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = not(and(implies(X!1, Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.41/189.61 inference(monotonicity,[status(thm)],[390])).
% 299.41/189.61 tff(392,plain,
% 299.41/189.61 (not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))),
% 299.41/189.61 inference(transitivity,[status(thm)],[391, 384, 381])).
% 299.41/189.61 tff(393,plain,
% 299.41/189.61 (or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) = or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.41/189.61 inference(monotonicity,[status(thm)],[286, 392])).
% 299.41/189.61 tff(394,plain,
% 299.41/189.61 (or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.41/189.61 inference(symmetry,[status(thm)],[393])).
% 299.41/189.61 tff(395,plain,
% 299.41/189.61 (not(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.41/189.61 inference(monotonicity,[status(thm)],[394])).
% 299.41/189.61 tff(396,plain,
% 299.41/189.61 (not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) = not(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.41/189.61 inference(symmetry,[status(thm)],[395])).
% 299.41/189.61 tff(397,plain,
% 299.41/189.61 (or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(not(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.61 inference(monotonicity,[status(thm)],[396])).
% 299.41/189.61 tff(398,plain,
% 299.41/189.61 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(not(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))),
% 299.41/189.61 inference(quant_inst,[status(thm)],[])).
% 299.41/189.61 tff(399,plain,
% 299.41/189.61 (or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(not(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))),
% 299.41/189.62 inference(unit_resolution,[status(thm)],[398, 63])).
% 299.41/189.62 tff(400,plain,
% 299.41/189.62 (not(and(not(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) = or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.62 inference(symmetry,[status(thm)],[399])).
% 299.41/189.62 tff(401,plain,
% 299.41/189.62 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = or(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.62 inference(quant_inst,[status(thm)],[])).
% 299.41/189.62 tff(402,plain,
% 299.41/189.62 (implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = or(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.62 inference(unit_resolution,[status(thm)],[401, 20])).
% 299.41/189.62 tff(403,plain,
% 299.41/189.62 (or(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.62 inference(symmetry,[status(thm)],[402])).
% 299.41/189.62 tff(404,plain,
% 299.41/189.62 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(and(not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.41/189.62 inference(quant_inst,[status(thm)],[])).
% 299.41/189.62 tff(405,plain,
% 299.41/189.62 (or(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(and(not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.62 inference(unit_resolution,[status(thm)],[404, 63])).
% 299.41/189.62 tff(406,plain,
% 299.41/189.62 (not(and(not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.62 inference(symmetry,[status(thm)],[405])).
% 299.41/189.62 tff(407,plain,
% 299.41/189.62 (and(not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.41/189.62 inference(monotonicity,[status(thm)],[392, 286])).
% 299.41/189.62 tff(408,plain,
% 299.41/189.62 (not(and(not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.62 inference(monotonicity,[status(thm)],[407])).
% 299.41/189.62 tff(409,plain,
% 299.41/189.62 (not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(and(not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.62 inference(symmetry,[status(thm)],[408])).
% 299.41/189.62 tff(410,plain,
% 299.41/189.62 (not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.62 inference(monotonicity,[status(thm)],[360])).
% 299.41/189.62 tff(411,plain,
% 299.41/189.62 (not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.62 inference(transitivity,[status(thm)],[410, 409, 406, 403])).
% 299.41/189.62 tff(412,plain,
% 299.41/189.62 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.41/189.62 inference(quant_inst,[status(thm)],[])).
% 299.41/189.62 tff(413,plain,
% 299.41/189.62 (implies(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.41/189.62 inference(unit_resolution,[status(thm)],[412, 41])).
% 299.41/189.62 tff(414,plain,
% 299.41/189.62 (not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) = implies(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.41/189.62 inference(symmetry,[status(thm)],[413])).
% 299.41/189.62 tff(415,plain,
% 299.41/189.62 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.41/189.62 inference(quant_inst,[status(thm)],[])).
% 299.41/189.62 tff(416,plain,
% 299.41/189.62 (and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.41/189.62 inference(unit_resolution,[status(thm)],[415, 125])).
% 299.41/189.62 tff(417,plain,
% 299.41/189.62 (not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) = and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.41/189.62 inference(symmetry,[status(thm)],[416])).
% 299.41/189.62 tff(418,plain,
% 299.41/189.62 (not(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))) = not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.41/189.62 inference(monotonicity,[status(thm)],[417])).
% 299.41/189.62 tff(419,plain,
% 299.41/189.62 (not(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))) = implies(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.41/189.62 inference(transitivity,[status(thm)],[418, 414])).
% 299.41/189.62 tff(420,plain,
% 299.41/189.62 (and(not(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))) = and(implies(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.62 inference(monotonicity,[status(thm)],[419, 411])).
% 299.41/189.62 tff(421,plain,
% 299.41/189.62 (and(implies(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(not(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.41/189.62 inference(symmetry,[status(thm)],[420])).
% 299.41/189.62 tff(422,plain,
% 299.41/189.62 (and(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))) = and(implies(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.62 inference(monotonicity,[status(thm)],[414, 411])).
% 299.41/189.62 tff(423,plain,
% 299.41/189.62 (and(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))) = and(not(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.41/189.62 inference(transitivity,[status(thm)],[422, 421])).
% 299.41/189.62 tff(424,plain,
% 299.41/189.62 (not(and(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) = not(and(not(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))),
% 299.41/189.62 inference(monotonicity,[status(thm)],[423])).
% 299.41/189.62 tff(425,plain,
% 299.41/189.62 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))),
% 299.41/189.62 inference(quant_inst,[status(thm)],[])).
% 299.41/189.62 tff(426,plain,
% 299.41/189.62 (implies(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))),
% 299.41/189.63 inference(unit_resolution,[status(thm)],[425, 41])).
% 299.41/189.63 tff(427,plain,
% 299.41/189.63 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(not(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.41/189.63 inference(quant_inst,[status(thm)],[])).
% 299.41/189.63 tff(428,plain,
% 299.41/189.63 (implies(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(not(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.63 inference(unit_resolution,[status(thm)],[427, 20])).
% 299.41/189.63 tff(429,plain,
% 299.41/189.63 (or(not(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = implies(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.63 inference(symmetry,[status(thm)],[428])).
% 299.41/189.63 tff(430,plain,
% 299.41/189.63 (or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = or(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.63 inference(monotonicity,[status(thm)],[317])).
% 299.41/189.63 tff(431,plain,
% 299.41/189.63 (or(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.63 inference(symmetry,[status(thm)],[430])).
% 299.41/189.63 tff(432,plain,
% 299.41/189.63 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.41/189.63 inference(quant_inst,[status(thm)],[])).
% 299.41/189.63 tff(433,plain,
% 299.41/189.63 (or(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.63 inference(unit_resolution,[status(thm)],[432, 63])).
% 299.41/189.63 tff(434,plain,
% 299.41/189.63 (not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.63 inference(symmetry,[status(thm)],[433])).
% 299.41/189.63 tff(435,plain,
% 299.41/189.63 (and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))) = and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.63 inference(monotonicity,[status(thm)],[194, 298])).
% 299.41/189.63 tff(436,plain,
% 299.41/189.63 (and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))),
% 299.41/189.63 inference(symmetry,[status(thm)],[435])).
% 299.41/189.63 tff(437,plain,
% 299.41/189.63 (not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))),
% 299.41/189.63 inference(monotonicity,[status(thm)],[436])).
% 299.41/189.63 tff(438,plain,
% 299.41/189.63 (not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))) = not(and(not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))), not(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.63 inference(symmetry,[status(thm)],[437])).
% 299.41/189.63 tff(439,plain,
% 299.41/189.63 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))))),
% 299.41/189.63 inference(quant_inst,[status(thm)],[])).
% 299.41/189.63 tff(440,plain,
% 299.41/189.63 (implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))),
% 299.41/189.63 inference(unit_resolution,[status(thm)],[439, 41])).
% 299.41/189.63 tff(441,plain,
% 299.41/189.63 (or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.63 inference(transitivity,[status(thm)],[268, 267, 440, 438, 434, 431])).
% 299.41/189.63 tff(442,plain,
% 299.41/189.63 (not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.63 inference(monotonicity,[status(thm)],[441])).
% 299.41/189.63 tff(443,plain,
% 299.41/189.63 (or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.63 inference(symmetry,[status(thm)],[268])).
% 299.41/189.63 tff(444,plain,
% 299.41/189.63 (not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))) = implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.41/189.63 inference(symmetry,[status(thm)],[440])).
% 299.41/189.63 tff(445,plain,
% 299.41/189.63 (not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))) = or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.63 inference(transitivity,[status(thm)],[444, 266, 443])).
% 299.41/189.63 tff(446,plain,
% 299.41/189.63 (not(not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))) = not(or(not(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.63 inference(monotonicity,[status(thm)],[445])).
% 299.41/189.63 tff(447,plain,
% 299.41/189.63 (not(not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))) = not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.63 inference(transitivity,[status(thm)],[446, 442])).
% 299.41/189.63 tff(448,plain,
% 299.41/189.63 (or(not(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))))) = or(not(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.63 inference(monotonicity,[status(thm)],[447])).
% 299.41/189.63 tff(449,plain,
% 299.41/189.63 (or(not(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))))) = or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.41/189.63 inference(transitivity,[status(thm)],[448, 429, 426, 424, 400, 397, 379, 376, 375, 373, 370, 369])).
% 299.41/189.63 tff(450,plain,
% 299.41/189.63 (not(or(not(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))))) = not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.41/189.63 inference(monotonicity,[status(thm)],[449])).
% 299.41/189.63 tff(451,plain,
% 299.41/189.63 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))) = not(or(not(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))))))),
% 299.41/189.63 inference(quant_inst,[status(thm)],[])).
% 299.41/189.63 tff(452,plain,
% 299.41/189.63 (and(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))) = not(or(not(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), not(not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))))))),
% 299.41/189.63 inference(unit_resolution,[status(thm)],[451, 125])).
% 299.41/189.63 tff(453,plain,
% 299.41/189.63 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.41/189.63 inference(quant_inst,[status(thm)],[])).
% 299.41/189.63 tff(454,plain,
% 299.41/189.63 (implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.63 inference(unit_resolution,[status(thm)],[453, 20])).
% 299.41/189.63 tff(455,plain,
% 299.41/189.63 (implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.41/189.63 inference(monotonicity,[status(thm)],[277])).
% 299.41/189.63 tff(456,plain,
% 299.41/189.63 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))))),
% 299.41/189.63 inference(quant_inst,[status(thm)],[])).
% 299.41/189.63 tff(457,plain,
% 299.41/189.63 (implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))),
% 299.41/189.63 inference(unit_resolution,[status(thm)],[456, 41])).
% 299.41/189.63 tff(458,plain,
% 299.41/189.63 (not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))) = implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.41/189.63 inference(symmetry,[status(thm)],[457])).
% 299.41/189.63 tff(459,plain,
% 299.41/189.63 (and(not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))) = and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))),
% 299.41/189.63 inference(monotonicity,[status(thm)],[392])).
% 299.41/189.63 tff(460,plain,
% 299.41/189.63 (not(and(not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))) = not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))),
% 299.41/189.63 inference(monotonicity,[status(thm)],[459])).
% 299.41/189.63 tff(461,plain,
% 299.41/189.63 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = not(and(not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))))),
% 299.41/189.63 inference(quant_inst,[status(thm)],[])).
% 299.41/189.63 tff(462,plain,
% 299.41/189.63 (or(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = not(and(not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))),
% 299.41/189.63 inference(unit_resolution,[status(thm)],[461, 63])).
% 299.41/189.63 tff(463,plain,
% 299.41/189.63 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = or(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))),
% 299.41/189.63 inference(quant_inst,[status(thm)],[])).
% 299.41/189.63 tff(464,plain,
% 299.41/189.63 (implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = or(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.45/189.64 inference(unit_resolution,[status(thm)],[463, 20])).
% 299.45/189.64 tff(465,plain,
% 299.45/189.64 (implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) = not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))),
% 299.45/189.64 inference(transitivity,[status(thm)],[464, 462, 460, 458, 455, 454, 430, 433, 437])).
% 299.45/189.64 tff(466,plain,
% 299.45/189.64 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.64 inference(quant_inst,[status(thm)],[])).
% 299.45/189.64 tff(467,plain,
% 299.45/189.64 (implies(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(and(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.45/189.64 inference(unit_resolution,[status(thm)],[466, 41])).
% 299.45/189.64 tff(468,plain,
% 299.45/189.64 (implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = implies(not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.45/189.64 inference(monotonicity,[status(thm)],[277])).
% 299.45/189.64 tff(469,plain,
% 299.45/189.64 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.45/189.64 inference(quant_inst,[status(thm)],[])).
% 299.45/189.64 tff(470,plain,
% 299.45/189.64 (implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.45/189.64 inference(unit_resolution,[status(thm)],[469, 20])).
% 299.45/189.64 tff(471,plain,
% 299.45/189.64 (or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.45/189.64 inference(symmetry,[status(thm)],[470])).
% 299.45/189.64 tff(472,plain,
% 299.45/189.64 (or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) = or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.45/189.64 inference(monotonicity,[status(thm)],[392])).
% 299.45/189.64 tff(473,plain,
% 299.45/189.64 (or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) = or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.45/189.64 inference(transitivity,[status(thm)],[472, 471, 468, 467, 350])).
% 299.45/189.64 tff(474,plain,
% 299.45/189.64 (not(or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) = not(or(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.45/189.64 inference(monotonicity,[status(thm)],[473])).
% 299.45/189.64 tff(475,plain,
% 299.45/189.64 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = not(or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.45/189.64 inference(quant_inst,[status(thm)],[])).
% 299.45/189.64 tff(476,plain,
% 299.45/189.64 (and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = not(or(not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))), not(not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.64 inference(unit_resolution,[status(thm)],[475, 125])).
% 299.45/189.64 tff(477,plain,
% 299.45/189.64 (and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.64 inference(transitivity,[status(thm)],[476, 474, 395, 417])).
% 299.45/189.64 tff(478,plain,
% 299.45/189.64 (not(and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) = not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.64 inference(monotonicity,[status(thm)],[477])).
% 299.45/189.64 tff(479,plain,
% 299.45/189.64 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.64 inference(quant_inst,[status(thm)],[])).
% 299.45/189.64 tff(480,plain,
% 299.45/189.64 (implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.64 inference(unit_resolution,[status(thm)],[479, 41])).
% 299.45/189.64 tff(481,plain,
% 299.45/189.64 (implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.64 inference(transitivity,[status(thm)],[480, 478])).
% 299.45/189.64 tff(482,plain,
% 299.45/189.64 (and(implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))) = and(not(and(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), not(and(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))))),
% 299.45/189.64 inference(monotonicity,[status(thm)],[481, 465])).
% 299.45/189.64 tff(483,plain,
% 299.45/189.64 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = and(implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))))),
% 299.45/189.64 inference(quant_inst,[status(thm)],[])).
% 299.45/189.64 tff(484,plain,
% 299.45/189.64 (equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = and(implies(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), implies(or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))),
% 299.45/189.64 inference(unit_resolution,[status(thm)],[483, 92])).
% 299.45/189.64 tff(485,plain,
% 299.45/189.64 (equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = equiv(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.45/189.64 inference(transitivity,[status(thm)],[484, 482, 452, 450, 368, 305, 302, 293, 165, 162])).
% 299.45/189.64 tff(486,plain,
% 299.45/189.64 (is_a_theorem(equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) <=> is_a_theorem(equiv(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))),
% 299.45/189.64 inference(monotonicity,[status(thm)],[485])).
% 299.45/189.64 tff(487,plain,
% 299.45/189.64 (is_a_theorem(equiv(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))) <=> is_a_theorem(equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.64 inference(symmetry,[status(thm)],[486])).
% 299.45/189.64 tff(488,plain,
% 299.45/189.64 (not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))) = equiv(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.45/189.64 inference(transitivity,[status(thm)],[368, 305, 302, 293, 165, 162])).
% 299.45/189.64 tff(489,plain,
% 299.45/189.64 (is_a_theorem(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) <=> is_a_theorem(equiv(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))),
% 299.45/189.64 inference(monotonicity,[status(thm)],[488])).
% 299.45/189.64 tff(490,plain,
% 299.45/189.64 (is_a_theorem(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) <=> is_a_theorem(equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.64 inference(transitivity,[status(thm)],[489, 487])).
% 299.45/189.64 tff(491,plain,
% 299.45/189.64 (not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))) = not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))))),
% 299.45/189.64 inference(monotonicity,[status(thm)],[291])).
% 299.45/189.64 tff(492,plain,
% 299.45/189.64 (not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))) = and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.45/189.64 inference(transitivity,[status(thm)],[491, 364, 361])).
% 299.45/189.64 tff(493,plain,
% 299.45/189.64 (or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) = or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))),
% 299.45/189.64 inference(monotonicity,[status(thm)],[492])).
% 299.45/189.64 tff(494,plain,
% 299.45/189.64 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) = or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))),
% 299.45/189.64 inference(quant_inst,[status(thm)],[])).
% 299.45/189.64 tff(495,plain,
% 299.45/189.64 (implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) = or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))),
% 299.45/189.65 inference(unit_resolution,[status(thm)],[494, 20])).
% 299.45/189.65 tff(496,plain,
% 299.45/189.65 (implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) = or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))),
% 299.45/189.65 inference(transitivity,[status(thm)],[495, 493])).
% 299.45/189.65 tff(497,plain,
% 299.45/189.65 (is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))) <=> is_a_theorem(or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))),
% 299.45/189.65 inference(monotonicity,[status(thm)],[496])).
% 299.45/189.65 tff(498,plain,
% 299.45/189.65 (is_a_theorem(or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))) <=> is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))),
% 299.45/189.65 inference(symmetry,[status(thm)],[497])).
% 299.45/189.65 tff(499,plain,
% 299.45/189.65 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.65 inference(quant_inst,[status(thm)],[])).
% 299.45/189.65 tff(500,plain,
% 299.45/189.65 (or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.65 inference(unit_resolution,[status(thm)],[499, 63])).
% 299.45/189.65 tff(501,plain,
% 299.45/189.65 (implies(or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))) = implies(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))),
% 299.45/189.65 inference(monotonicity,[status(thm)],[500])).
% 299.45/189.65 tff(502,plain,
% 299.45/189.65 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))) <=> is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))))),
% 299.45/189.65 inference(monotonicity,[status(thm)],[501])).
% 299.45/189.65 tff(503,plain,
% 299.45/189.65 (^[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))))),
% 299.45/189.65 inference(bind,[status(th)],[])).
% 299.45/189.65 tff(504,plain,
% 299.45/189.65 (![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)))),
% 299.45/189.65 inference(quant_intro,[status(thm)],[503])).
% 299.45/189.65 tff(505,plain,
% 299.45/189.65 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 299.45/189.65 inference(rewrite,[status(thm)],[])).
% 299.45/189.65 tff(506,plain,
% 299.45/189.65 (($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)))),
% 299.45/189.65 inference(rewrite,[status(thm)],[])).
% 299.45/189.65 tff(507,axiom,(r3), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r3')).
% 299.45/189.65 tff(508,plain,
% 299.45/189.65 (r3 <=> $true),
% 299.45/189.65 inference(iff_true,[status(thm)],[507])).
% 299.45/189.65 tff(509,plain,
% 299.45/189.65 ((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))))),
% 299.45/189.65 inference(monotonicity,[status(thm)],[508])).
% 299.45/189.65 tff(510,plain,
% 299.45/189.65 ((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)))),
% 299.45/189.65 inference(transitivity,[status(thm)],[509, 506])).
% 299.45/189.65 tff(511,plain,
% 299.45/189.65 ((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))))),
% 299.45/189.65 inference(rewrite,[status(thm)],[])).
% 299.45/189.65 tff(512,axiom,(r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','r3')).
% 299.45/189.65 tff(513,plain,
% 299.45/189.65 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 299.45/189.65 inference(modus_ponens,[status(thm)],[512, 511])).
% 299.45/189.65 tff(514,plain,
% 299.45/189.65 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 299.45/189.65 inference(modus_ponens,[status(thm)],[513, 511])).
% 299.45/189.65 tff(515,plain,
% 299.45/189.65 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 299.45/189.65 inference(modus_ponens,[status(thm)],[514, 510])).
% 299.45/189.65 tff(516,plain,
% 299.45/189.65 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 299.45/189.65 inference(modus_ponens,[status(thm)],[515, 505])).
% 299.45/189.65 tff(517,plain,(
% 299.45/189.65 ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 299.45/189.65 inference(skolemize,[status(sab)],[516])).
% 299.45/189.65 tff(518,plain,
% 299.45/189.65 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 299.45/189.65 inference(modus_ponens,[status(thm)],[517, 504])).
% 299.45/189.65 tff(519,plain,
% 299.45/189.65 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))))),
% 299.45/189.65 inference(quant_inst,[status(thm)],[])).
% 299.45/189.65 tff(520,plain,
% 299.45/189.65 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))))),
% 299.45/189.65 inference(unit_resolution,[status(thm)],[519, 518])).
% 299.45/189.65 tff(521,plain,
% 299.45/189.65 (is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))))),
% 299.45/189.65 inference(modus_ponens,[status(thm)],[520, 502])).
% 299.45/189.65 tff(522,plain,
% 299.45/189.65 (or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) = or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.45/189.65 inference(monotonicity,[status(thm)],[285])).
% 299.45/189.65 tff(523,plain,
% 299.45/189.65 (or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))) = or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.45/189.65 inference(symmetry,[status(thm)],[522])).
% 299.45/189.65 tff(524,plain,
% 299.45/189.65 (not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))) = not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))),
% 299.45/189.66 inference(monotonicity,[status(thm)],[523])).
% 299.45/189.66 tff(525,plain,
% 299.45/189.66 (not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))) = not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.45/189.66 inference(symmetry,[status(thm)],[524])).
% 299.45/189.66 tff(526,plain,
% 299.45/189.66 (or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.66 inference(monotonicity,[status(thm)],[525])).
% 299.45/189.66 tff(527,plain,
% 299.45/189.66 (or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.66 inference(symmetry,[status(thm)],[526])).
% 299.45/189.66 tff(528,plain,
% 299.45/189.66 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.66 inference(quant_inst,[status(thm)],[])).
% 299.45/189.66 tff(529,plain,
% 299.45/189.66 (implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.66 inference(unit_resolution,[status(thm)],[528, 20])).
% 299.45/189.66 tff(530,plain,
% 299.45/189.66 (implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.66 inference(monotonicity,[status(thm)],[500])).
% 299.45/189.66 tff(531,plain,
% 299.45/189.66 (implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) = implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.66 inference(symmetry,[status(thm)],[530])).
% 299.45/189.66 tff(532,plain,
% 299.45/189.66 (implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) = or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.66 inference(transitivity,[status(thm)],[531, 529, 527])).
% 299.45/189.66 tff(533,plain,
% 299.45/189.66 (is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))) <=> is_a_theorem(or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.66 inference(monotonicity,[status(thm)],[532])).
% 299.45/189.66 tff(534,plain,
% 299.45/189.66 (is_a_theorem(or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) <=> is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.45/189.66 inference(symmetry,[status(thm)],[533])).
% 299.45/189.66 tff(535,plain,
% 299.45/189.66 (and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = and(implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.45/189.67 inference(monotonicity,[status(thm)],[331, 334])).
% 299.45/189.67 tff(536,plain,
% 299.45/189.67 (and(implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.67 inference(symmetry,[status(thm)],[535])).
% 299.45/189.67 tff(537,plain,
% 299.45/189.67 (and(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = and(implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.45/189.67 inference(monotonicity,[status(thm)],[339, 334])).
% 299.45/189.67 tff(538,plain,
% 299.45/189.67 (and(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.67 inference(transitivity,[status(thm)],[537, 536])).
% 299.45/189.67 tff(539,plain,
% 299.45/189.67 (not(and(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) = not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.67 inference(monotonicity,[status(thm)],[538])).
% 299.45/189.67 tff(540,plain,
% 299.45/189.67 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.67 inference(quant_inst,[status(thm)],[])).
% 299.45/189.67 tff(541,plain,
% 299.45/189.67 (implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.67 inference(unit_resolution,[status(thm)],[540, 41])).
% 299.45/189.67 tff(542,plain,
% 299.45/189.67 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.67 inference(quant_inst,[status(thm)],[])).
% 299.45/189.67 tff(543,plain,
% 299.45/189.67 (implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.45/189.67 inference(unit_resolution,[status(thm)],[542, 20])).
% 299.45/189.67 tff(544,plain,
% 299.45/189.67 (or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.45/189.67 inference(symmetry,[status(thm)],[543])).
% 299.45/189.67 tff(545,plain,
% 299.45/189.67 (or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.45/189.67 inference(monotonicity,[status(thm)],[525])).
% 299.45/189.67 tff(546,plain,
% 299.45/189.67 (or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.67 inference(transitivity,[status(thm)],[545, 544, 541, 539])).
% 299.45/189.67 tff(547,plain,
% 299.45/189.67 (not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.45/189.67 inference(transitivity,[status(thm)],[370, 369])).
% 299.45/189.67 tff(548,plain,
% 299.45/189.67 (not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))) = not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.45/189.67 inference(monotonicity,[status(thm)],[547])).
% 299.45/189.67 tff(549,plain,
% 299.45/189.67 (not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))) = not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))),
% 299.45/189.67 inference(symmetry,[status(thm)],[548])).
% 299.45/189.67 tff(550,plain,
% 299.45/189.67 (or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.67 inference(monotonicity,[status(thm)],[549, 546])).
% 299.45/189.67 tff(551,plain,
% 299.45/189.67 (or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) = or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.67 inference(symmetry,[status(thm)],[550])).
% 299.45/189.67 tff(552,plain,
% 299.45/189.67 (implies(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) = implies(or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.67 inference(monotonicity,[status(thm)],[551])).
% 299.45/189.67 tff(553,plain,
% 299.45/189.67 (implies(or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) = implies(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.68 inference(symmetry,[status(thm)],[552])).
% 299.45/189.68 tff(554,plain,
% 299.45/189.68 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) <=> is_a_theorem(implies(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.68 inference(monotonicity,[status(thm)],[553])).
% 299.45/189.68 tff(555,plain,
% 299.45/189.68 (^[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)))))),
% 299.45/189.68 inference(bind,[status(th)],[])).
% 299.45/189.68 tff(556,plain,
% 299.45/189.68 (![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))))),
% 299.45/189.68 inference(quant_intro,[status(thm)],[555])).
% 299.45/189.68 tff(557,plain,
% 299.45/189.68 (![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: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 299.45/189.68 inference(rewrite,[status(thm)],[])).
% 299.45/189.68 tff(558,plain,
% 299.45/189.68 (($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))))),
% 299.45/189.68 inference(rewrite,[status(thm)],[])).
% 299.45/189.68 tff(559,axiom,(r4), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r4')).
% 299.45/189.68 tff(560,plain,
% 299.45/189.68 (r4 <=> $true),
% 299.45/189.68 inference(iff_true,[status(thm)],[559])).
% 299.45/189.68 tff(561,plain,
% 299.45/189.68 ((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)))))),
% 299.45/189.68 inference(monotonicity,[status(thm)],[560])).
% 299.45/189.68 tff(562,plain,
% 299.45/189.68 ((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))))),
% 299.45/189.68 inference(transitivity,[status(thm)],[561, 558])).
% 299.45/189.68 tff(563,plain,
% 299.45/189.68 ((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)))))),
% 299.45/189.68 inference(rewrite,[status(thm)],[])).
% 299.45/189.68 tff(564,axiom,(r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','r4')).
% 299.45/189.68 tff(565,plain,
% 299.45/189.68 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 299.45/189.68 inference(modus_ponens,[status(thm)],[564, 563])).
% 299.45/189.68 tff(566,plain,
% 299.45/189.68 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 299.45/189.68 inference(modus_ponens,[status(thm)],[565, 563])).
% 299.45/189.68 tff(567,plain,
% 299.45/189.68 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 299.45/189.68 inference(modus_ponens,[status(thm)],[566, 562])).
% 299.45/189.68 tff(568,plain,
% 299.45/189.68 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 299.45/189.68 inference(modus_ponens,[status(thm)],[567, 557])).
% 299.45/189.68 tff(569,plain,(
% 299.45/189.68 ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 299.45/189.68 inference(skolemize,[status(sab)],[568])).
% 299.45/189.68 tff(570,plain,
% 299.45/189.68 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 299.45/189.68 inference(modus_ponens,[status(thm)],[569, 556])).
% 299.45/189.68 tff(571,plain,
% 299.45/189.68 ((~![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(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.68 inference(quant_inst,[status(thm)],[])).
% 299.45/189.68 tff(572,plain,
% 299.45/189.68 (is_a_theorem(implies(or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.68 inference(unit_resolution,[status(thm)],[571, 570])).
% 299.45/189.68 tff(573,plain,
% 299.45/189.68 (is_a_theorem(implies(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.68 inference(modus_ponens,[status(thm)],[572, 554])).
% 299.45/189.68 tff(574,plain,
% 299.45/189.68 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) = or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.45/189.68 inference(quant_inst,[status(thm)],[])).
% 299.45/189.68 tff(575,plain,
% 299.45/189.68 (implies(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) = or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.68 inference(unit_resolution,[status(thm)],[574, 20])).
% 299.45/189.68 tff(576,plain,
% 299.45/189.68 (or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) = implies(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.68 inference(symmetry,[status(thm)],[575])).
% 299.45/189.68 tff(577,plain,
% 299.45/189.68 (is_a_theorem(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))) <=> is_a_theorem(implies(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.45/189.68 inference(monotonicity,[status(thm)],[576])).
% 299.45/189.68 tff(578,plain,
% 299.45/189.68 (is_a_theorem(implies(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))) <=> is_a_theorem(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.45/189.69 inference(symmetry,[status(thm)],[577])).
% 299.45/189.69 tff(579,plain,
% 299.45/189.69 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.69 inference(quant_inst,[status(thm)],[])).
% 299.45/189.69 tff(580,plain,
% 299.45/189.69 (or(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.69 inference(unit_resolution,[status(thm)],[579, 63])).
% 299.45/189.69 tff(581,plain,
% 299.45/189.69 (or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = or(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.45/189.69 inference(monotonicity,[status(thm)],[360])).
% 299.45/189.69 tff(582,plain,
% 299.45/189.69 (or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.69 inference(transitivity,[status(thm)],[581, 580])).
% 299.45/189.69 tff(583,plain,
% 299.45/189.69 (or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))),
% 299.45/189.69 inference(monotonicity,[status(thm)],[360])).
% 299.45/189.69 tff(584,plain,
% 299.45/189.69 (or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))) = not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))),
% 299.45/189.69 inference(transitivity,[status(thm)],[583, 357])).
% 299.45/189.69 tff(585,plain,
% 299.45/189.69 (implies(or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = implies(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.69 inference(monotonicity,[status(thm)],[584, 582])).
% 299.45/189.69 tff(586,plain,
% 299.45/189.69 (is_a_theorem(implies(or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) <=> is_a_theorem(implies(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.45/189.69 inference(monotonicity,[status(thm)],[585])).
% 299.45/189.69 tff(587,plain,
% 299.45/189.69 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.69 inference(quant_inst,[status(thm)],[])).
% 299.45/189.69 tff(588,plain,
% 299.45/189.69 (is_a_theorem(implies(or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.69 inference(unit_resolution,[status(thm)],[587, 518])).
% 299.45/189.69 tff(589,plain,
% 299.45/189.69 (is_a_theorem(implies(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.45/189.69 inference(modus_ponens,[status(thm)],[588, 586])).
% 299.45/189.69 tff(590,plain,
% 299.45/189.69 (is_a_theorem(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.45/189.69 inference(modus_ponens,[status(thm)],[589, 578])).
% 299.45/189.69 tff(591,plain,
% 299.45/189.69 (^[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)))))),
% 299.45/189.69 inference(bind,[status(th)],[])).
% 299.45/189.69 tff(592,plain,
% 299.45/189.69 (![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))))),
% 299.45/189.69 inference(quant_intro,[status(thm)],[591])).
% 299.45/189.69 tff(593,plain,
% 299.45/189.69 (^[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))))))),
% 299.45/189.69 inference(bind,[status(th)],[])).
% 299.45/189.69 tff(594,plain,
% 299.45/189.69 (![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))))),
% 299.45/189.69 inference(quant_intro,[status(thm)],[593])).
% 299.45/189.69 tff(595,plain,
% 299.45/189.69 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 299.45/189.69 inference(rewrite,[status(thm)],[])).
% 299.45/189.69 tff(596,plain,
% 299.45/189.69 (($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)))))),
% 299.45/189.69 inference(rewrite,[status(thm)],[])).
% 299.45/189.69 tff(597,axiom,(modus_ponens), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_modus_ponens')).
% 299.45/189.69 tff(598,plain,
% 299.45/189.69 (modus_ponens <=> $true),
% 299.45/189.69 inference(iff_true,[status(thm)],[597])).
% 299.45/189.69 tff(599,plain,
% 299.45/189.69 ((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))))))),
% 299.45/189.69 inference(monotonicity,[status(thm)],[598])).
% 299.45/189.69 tff(600,plain,
% 299.45/189.69 ((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)))))),
% 299.45/189.69 inference(transitivity,[status(thm)],[599, 596])).
% 299.45/189.69 tff(601,plain,
% 299.45/189.69 ((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))))))),
% 299.45/189.69 inference(rewrite,[status(thm)],[])).
% 299.45/189.69 tff(602,plain,
% 299.45/189.69 ((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))))))),
% 299.45/189.69 inference(rewrite,[status(thm)],[])).
% 299.45/189.69 tff(603,axiom,(modus_ponens <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(implies(X, Y))) => is_a_theorem(Y))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','modus_ponens')).
% 299.45/189.69 tff(604,plain,
% 299.45/189.69 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 299.45/189.69 inference(modus_ponens,[status(thm)],[603, 602])).
% 299.45/189.69 tff(605,plain,
% 299.45/189.69 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 299.45/189.69 inference(modus_ponens,[status(thm)],[604, 601])).
% 299.45/189.69 tff(606,plain,
% 299.45/189.69 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 299.45/189.69 inference(modus_ponens,[status(thm)],[605, 600])).
% 299.45/189.69 tff(607,plain,
% 299.45/189.69 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 299.45/189.69 inference(modus_ponens,[status(thm)],[606, 595])).
% 299.45/189.69 tff(608,plain,(
% 299.45/189.69 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 299.45/189.69 inference(skolemize,[status(sab)],[607])).
% 299.45/189.69 tff(609,plain,
% 299.45/189.69 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 299.45/189.69 inference(modus_ponens,[status(thm)],[608, 594])).
% 299.45/189.69 tff(610,plain,
% 299.45/189.69 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 299.45/189.69 inference(modus_ponens,[status(thm)],[609, 592])).
% 299.45/189.69 tff(611,plain,
% 299.45/189.69 (((~![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(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))))),
% 299.45/189.70 inference(rewrite,[status(thm)],[])).
% 299.45/189.70 tff(612,plain,
% 299.45/189.70 ((~![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(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))))),
% 299.45/189.70 inference(quant_inst,[status(thm)],[])).
% 299.45/189.70 tff(613,plain,
% 299.45/189.70 ((~![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(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.45/189.70 inference(modus_ponens,[status(thm)],[612, 611])).
% 299.45/189.70 tff(614,plain,
% 299.45/189.70 (is_a_theorem(or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), not(and(not(and(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))), or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.45/189.70 inference(unit_resolution,[status(thm)],[613, 610])).
% 299.45/189.70 tff(615,plain,
% 299.45/189.70 (is_a_theorem(or(not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))), or(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))), and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.70 inference(unit_resolution,[status(thm)],[614, 590, 573])).
% 299.45/189.70 tff(616,plain,
% 299.45/189.70 (is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))),
% 299.45/189.70 inference(modus_ponens,[status(thm)],[615, 534])).
% 299.45/189.70 tff(617,plain,
% 299.45/189.70 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(implies(Y!0, X!1), equiv(X!1, Y!0)) = or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.45/189.70 inference(quant_inst,[status(thm)],[])).
% 299.45/189.70 tff(618,plain,
% 299.45/189.70 (implies(implies(Y!0, X!1), equiv(X!1, Y!0)) = or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))),
% 299.45/189.70 inference(unit_resolution,[status(thm)],[617, 20])).
% 299.45/189.70 tff(619,plain,
% 299.45/189.70 (or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)) = implies(implies(Y!0, X!1), equiv(X!1, Y!0))),
% 299.45/189.70 inference(symmetry,[status(thm)],[618])).
% 299.45/189.70 tff(620,plain,
% 299.45/189.70 (or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1))) = or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))),
% 299.45/189.70 inference(monotonicity,[status(thm)],[95])).
% 299.45/189.70 tff(621,plain,
% 299.45/189.70 (or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1))) = implies(implies(Y!0, X!1), equiv(X!1, Y!0))),
% 299.45/189.70 inference(transitivity,[status(thm)],[620, 619])).
% 299.45/189.70 tff(622,plain,
% 299.45/189.70 (or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1)))) = or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))),
% 299.45/189.70 inference(monotonicity,[status(thm)],[621])).
% 299.45/189.70 tff(623,plain,
% 299.45/189.70 (or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))) = or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1))))),
% 299.45/189.70 inference(symmetry,[status(thm)],[622])).
% 299.45/189.70 tff(624,plain,
% 299.45/189.70 (implies(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))) = implies(or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.45/189.70 inference(monotonicity,[status(thm)],[623])).
% 299.45/189.70 tff(625,plain,
% 299.45/189.70 (or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))) = implies(or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.45/189.70 inference(transitivity,[status(thm)],[339, 624])).
% 299.45/189.70 tff(626,plain,
% 299.45/189.70 (is_a_theorem(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))) <=> is_a_theorem(implies(or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.45/189.70 inference(monotonicity,[status(thm)],[625])).
% 299.45/189.70 tff(627,plain,
% 299.45/189.70 (is_a_theorem(implies(or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))) <=> is_a_theorem(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.45/189.70 inference(symmetry,[status(thm)],[626])).
% 299.45/189.70 tff(628,plain,
% 299.45/189.70 ((~![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(X!1, Y!0)), or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.45/189.70 inference(quant_inst,[status(thm)],[])).
% 299.45/189.70 tff(629,plain,
% 299.45/189.70 (is_a_theorem(implies(or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.45/189.70 inference(unit_resolution,[status(thm)],[628, 570])).
% 299.45/189.70 tff(630,plain,
% 299.45/189.70 (is_a_theorem(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.45/189.70 inference(modus_ponens,[status(thm)],[629, 627])).
% 299.45/189.70 tff(631,plain,
% 299.45/189.70 (((~![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(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))))),
% 299.45/189.71 inference(rewrite,[status(thm)],[])).
% 299.45/189.71 tff(632,plain,
% 299.45/189.71 ((is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) | (~is_a_theorem(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) | (~is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))))) <=> ((~is_a_theorem(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))))),
% 299.45/189.71 inference(rewrite,[status(thm)],[])).
% 299.45/189.71 tff(633,plain,
% 299.45/189.71 (((~![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(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) | (~is_a_theorem(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) | (~is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))))))),
% 299.45/189.71 inference(monotonicity,[status(thm)],[632])).
% 299.45/189.71 tff(634,plain,
% 299.45/189.71 (((~![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(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) | (~is_a_theorem(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) | (~is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))))),
% 299.45/189.71 inference(transitivity,[status(thm)],[633, 631])).
% 299.45/189.71 tff(635,plain,
% 299.45/189.71 ((~![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(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) | (~is_a_theorem(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) | (~is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))))))),
% 299.45/189.71 inference(quant_inst,[status(thm)],[])).
% 299.45/189.71 tff(636,plain,
% 299.45/189.71 ((~![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(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))) | is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))))),
% 299.45/189.72 inference(modus_ponens,[status(thm)],[635, 634])).
% 299.45/189.72 tff(637,plain,
% 299.45/189.72 (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))))),
% 299.45/189.72 inference(unit_resolution,[status(thm)],[636, 610, 630])).
% 299.45/189.72 tff(638,plain,
% 299.45/189.72 (is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))),
% 299.45/189.72 inference(unit_resolution,[status(thm)],[637, 616])).
% 299.45/189.72 tff(639,plain,
% 299.45/189.72 (((~![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(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))))))),
% 299.45/189.72 inference(rewrite,[status(thm)],[])).
% 299.45/189.72 tff(640,plain,
% 299.45/189.72 ((~![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(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))))))),
% 299.45/189.72 inference(quant_inst,[status(thm)],[])).
% 299.45/189.72 tff(641,plain,
% 299.45/189.72 ((~![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(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))))),
% 299.45/189.72 inference(modus_ponens,[status(thm)],[640, 639])).
% 299.45/189.72 tff(642,plain,
% 299.45/189.72 (is_a_theorem(or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))) | (~is_a_theorem(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(not(and(not(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))), not(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))), or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))))),
% 299.45/189.72 inference(unit_resolution,[status(thm)],[641, 610])).
% 299.45/189.72 tff(643,plain,
% 299.45/189.72 (is_a_theorem(or(and(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))), not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))),
% 299.45/189.72 inference(unit_resolution,[status(thm)],[642, 638, 521])).
% 299.45/189.72 tff(644,plain,
% 299.45/189.72 (is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))),
% 299.45/189.72 inference(modus_ponens,[status(thm)],[643, 498])).
% 299.45/189.72 tff(645,plain,
% 299.45/189.72 (implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.45/189.72 inference(transitivity,[status(thm)],[270, 272, 275, 279, 294, 288, 290])).
% 299.45/189.72 tff(646,plain,
% 299.45/189.72 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))) <=> is_a_theorem(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))),
% 299.45/189.72 inference(monotonicity,[status(thm)],[645])).
% 299.45/189.72 tff(647,plain,
% 299.45/189.72 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))) <=> is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))),
% 299.45/189.72 inference(monotonicity,[status(thm)],[271])).
% 299.45/189.72 tff(648,plain,
% 299.45/189.72 ((~![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(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.45/189.73 inference(quant_inst,[status(thm)],[])).
% 299.45/189.73 tff(649,plain,
% 299.45/189.73 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(implies(X!1, Y!0)), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.45/189.73 inference(unit_resolution,[status(thm)],[648, 570])).
% 299.45/189.73 tff(650,plain,
% 299.45/189.73 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))),
% 299.45/189.73 inference(modus_ponens,[status(thm)],[649, 647])).
% 299.45/189.73 tff(651,plain,
% 299.45/189.73 (is_a_theorem(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))),
% 299.45/189.73 inference(modus_ponens,[status(thm)],[650, 646])).
% 299.45/189.73 tff(652,plain,
% 299.45/189.73 (((~![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(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) | is_a_theorem(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) | is_a_theorem(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))))),
% 299.45/189.73 inference(rewrite,[status(thm)],[])).
% 299.45/189.73 tff(653,plain,
% 299.45/189.73 ((is_a_theorem(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) | (~is_a_theorem(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))))) <=> ((~is_a_theorem(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) | is_a_theorem(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))))),
% 299.45/189.73 inference(rewrite,[status(thm)],[])).
% 299.45/189.73 tff(654,plain,
% 299.45/189.73 (((~![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(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) | (~is_a_theorem(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) | is_a_theorem(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))))))),
% 299.45/189.73 inference(monotonicity,[status(thm)],[653])).
% 299.45/189.73 tff(655,plain,
% 299.45/189.73 (((~![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(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) | (~is_a_theorem(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) | is_a_theorem(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))))),
% 299.45/189.73 inference(transitivity,[status(thm)],[654, 652])).
% 299.45/189.73 tff(656,plain,
% 299.45/189.73 ((~![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(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) | (~is_a_theorem(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))))))),
% 299.45/189.73 inference(quant_inst,[status(thm)],[])).
% 299.45/189.73 tff(657,plain,
% 299.45/189.73 ((~![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(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))) | is_a_theorem(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))))),
% 299.45/189.73 inference(modus_ponens,[status(thm)],[656, 655])).
% 299.45/189.73 tff(658,plain,
% 299.45/189.73 (is_a_theorem(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))), not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))))),
% 299.45/189.73 inference(unit_resolution,[status(thm)],[657, 610, 651])).
% 299.45/189.73 tff(659,plain,
% 299.45/189.73 (is_a_theorem(not(or(not(or(not(not(and(not(not(implies(Y!0, X!1))), not(or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1))))))), not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))))), not(or(not(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(or(not(implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), and(implies(X!1, Y!0), implies(Y!0, X!1)))))))))))),
% 299.45/189.73 inference(unit_resolution,[status(thm)],[658, 644])).
% 299.45/189.73 tff(660,plain,
% 299.45/189.73 (is_a_theorem(equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.73 inference(modus_ponens,[status(thm)],[659, 490])).
% 299.45/189.73 tff(661,plain,
% 299.45/189.73 (^[X: $i, Y: $i] : refl(((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 299.45/189.73 inference(bind,[status(th)],[])).
% 299.45/189.73 tff(662,plain,
% 299.45/189.73 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 299.45/189.73 inference(quant_intro,[status(thm)],[661])).
% 299.45/189.73 tff(663,plain,
% 299.45/189.73 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 299.45/189.73 inference(rewrite,[status(thm)],[])).
% 299.45/189.73 tff(664,plain,
% 299.45/189.73 (($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))),
% 299.45/189.73 inference(rewrite,[status(thm)],[])).
% 299.45/189.73 tff(665,axiom,(substitution_of_equivalents), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','substitution_of_equivalents')).
% 299.45/189.73 tff(666,plain,
% 299.45/189.73 (substitution_of_equivalents <=> $true),
% 299.45/189.73 inference(iff_true,[status(thm)],[665])).
% 299.45/189.73 tff(667,plain,
% 299.45/189.73 ((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)))),
% 299.45/189.73 inference(monotonicity,[status(thm)],[666])).
% 299.45/189.73 tff(668,plain,
% 299.45/189.73 ((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))),
% 299.45/189.73 inference(transitivity,[status(thm)],[667, 664])).
% 299.45/189.73 tff(669,plain,
% 299.45/189.73 ((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)))),
% 299.45/189.73 inference(rewrite,[status(thm)],[])).
% 299.45/189.73 tff(670,plain,
% 299.45/189.73 ((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)))),
% 299.45/189.73 inference(rewrite,[status(thm)],[])).
% 299.45/189.73 tff(671,axiom,(substitution_of_equivalents <=> ![X: $i, Y: $i] : (is_a_theorem(equiv(X, Y)) => (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','substitution_of_equivalents')).
% 299.45/189.73 tff(672,plain,
% 299.45/189.73 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 299.45/189.73 inference(modus_ponens,[status(thm)],[671, 670])).
% 299.45/189.73 tff(673,plain,
% 299.45/189.73 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 299.45/189.73 inference(modus_ponens,[status(thm)],[672, 669])).
% 299.45/189.73 tff(674,plain,
% 299.45/189.74 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 299.45/189.74 inference(modus_ponens,[status(thm)],[673, 668])).
% 299.45/189.74 tff(675,plain,
% 299.45/189.74 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 299.45/189.74 inference(modus_ponens,[status(thm)],[674, 663])).
% 299.45/189.74 tff(676,plain,(
% 299.45/189.74 ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 299.45/189.74 inference(skolemize,[status(sab)],[675])).
% 299.45/189.74 tff(677,plain,
% 299.45/189.74 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 299.45/189.74 inference(modus_ponens,[status(thm)],[676, 662])).
% 299.45/189.74 tff(678,plain,
% 299.45/189.74 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) | (not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))) = or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) | (not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))) = or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.74 inference(rewrite,[status(thm)],[])).
% 299.45/189.74 tff(679,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) | (not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))) = or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(680,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) | (not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))) = or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.45/189.74 inference(modus_ponens,[status(thm)],[679, 678])).
% 299.45/189.74 tff(681,plain,
% 299.45/189.74 ((~is_a_theorem(equiv(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))), or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) | (not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))) = or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[680, 677])).
% 299.45/189.74 tff(682,plain,
% 299.45/189.74 (not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))) = or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[681, 660])).
% 299.45/189.74 tff(683,plain,
% 299.45/189.74 (or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[682])).
% 299.45/189.74 tff(684,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(X!1), Y!0), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(685,plain,
% 299.45/189.74 (implies(or(not(X!1), Y!0), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = or(not(or(not(X!1), Y!0)), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[684, 20])).
% 299.45/189.74 tff(686,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(X!1), Y!0), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = not(and(or(not(X!1), Y!0), not(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(687,plain,
% 299.45/189.74 (implies(or(not(X!1), Y!0), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = not(and(or(not(X!1), Y!0), not(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[686, 41])).
% 299.45/189.74 tff(688,plain,
% 299.45/189.74 (not(and(or(not(X!1), Y!0), not(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))) = implies(or(not(X!1), Y!0), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[687])).
% 299.45/189.74 tff(689,plain,
% 299.45/189.74 (or(not(implies(X!1, Y!0)), not(implies(Y!0, X!1))) = or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[139, 71])).
% 299.45/189.74 tff(690,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(implies(X!1, Y!0)), not(implies(Y!0, X!1))) = not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(691,plain,
% 299.45/189.74 (or(not(implies(X!1, Y!0)), not(implies(Y!0, X!1))) = not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[690, 63])).
% 299.45/189.74 tff(692,plain,
% 299.45/189.74 (not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))) = or(not(implies(X!1, Y!0)), not(implies(Y!0, X!1)))),
% 299.45/189.74 inference(symmetry,[status(thm)],[691])).
% 299.45/189.74 tff(693,plain,
% 299.45/189.74 (not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))) = or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))),
% 299.45/189.74 inference(transitivity,[status(thm)],[692, 689])).
% 299.45/189.74 tff(694,plain,
% 299.45/189.74 (and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))) = and(or(not(Y!0), not(not(X!1))), or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[207, 693])).
% 299.45/189.74 tff(695,plain,
% 299.45/189.74 (and(or(not(Y!0), not(not(X!1))), or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))) = and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[694])).
% 299.45/189.74 tff(696,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(Y!0), not(not(X!1))), or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))) = not(or(not(or(not(Y!0), not(not(X!1)))), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(697,plain,
% 299.45/189.74 (and(or(not(Y!0), not(not(X!1))), or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))) = not(or(not(or(not(Y!0), not(not(X!1)))), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[696, 125])).
% 299.45/189.74 tff(698,plain,
% 299.45/189.74 (not(or(not(or(not(Y!0), not(not(X!1)))), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))))) = and(or(not(Y!0), not(not(X!1))), or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[697])).
% 299.45/189.74 tff(699,plain,
% 299.45/189.74 (and(not(and(Y!0, not(X!1))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))) = and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[98, 198])).
% 299.45/189.74 tff(700,plain,
% 299.45/189.74 (not(and(not(and(Y!0, not(X!1))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))) = not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[699])).
% 299.45/189.74 tff(701,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(Y!0, not(X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1))) = not(and(not(and(Y!0, not(X!1))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(702,plain,
% 299.45/189.74 (or(and(Y!0, not(X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1))) = not(and(not(and(Y!0, not(X!1))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[701, 63])).
% 299.45/189.74 tff(703,plain,
% 299.45/189.74 (and(or(not(X!1), Y!0), or(not(Y!0), X!1)) = and(implies(X!1, Y!0), implies(Y!0, X!1))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[137, 69])).
% 299.45/189.74 tff(704,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(X!1), Y!0), or(not(Y!0), X!1)) = not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(705,plain,
% 299.45/189.74 (and(or(not(X!1), Y!0), or(not(Y!0), X!1)) = not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[704, 125])).
% 299.45/189.74 tff(706,plain,
% 299.45/189.74 (not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))) = and(or(not(X!1), Y!0), or(not(Y!0), X!1))),
% 299.45/189.74 inference(symmetry,[status(thm)],[705])).
% 299.45/189.74 tff(707,plain,
% 299.45/189.74 (not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))) = and(implies(X!1, Y!0), implies(Y!0, X!1))),
% 299.45/189.74 inference(transitivity,[status(thm)],[706, 703])).
% 299.45/189.74 tff(708,plain,
% 299.45/189.74 (or(not(or(not(Y!0), not(not(X!1)))), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))) = or(and(Y!0, not(X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1)))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[128, 707])).
% 299.45/189.74 tff(709,plain,
% 299.45/189.74 (or(not(or(not(Y!0), not(not(X!1)))), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))) = implies(implies(Y!0, X!1), equiv(X!1, Y!0))),
% 299.45/189.74 inference(transitivity,[status(thm)],[708, 702, 700, 314])).
% 299.45/189.74 tff(710,plain,
% 299.45/189.74 (not(or(not(or(not(Y!0), not(not(X!1)))), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))))) = not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[709])).
% 299.45/189.74 tff(711,plain,
% 299.45/189.74 (not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))) = not(or(not(or(not(Y!0), not(not(X!1)))), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[710])).
% 299.45/189.74 tff(712,plain,
% 299.45/189.74 (not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))) = and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))),
% 299.45/189.74 inference(transitivity,[status(thm)],[711, 698, 695])).
% 299.45/189.74 tff(713,plain,
% 299.45/189.74 (not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[712])).
% 299.45/189.74 tff(714,plain,
% 299.45/189.74 (not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))) = not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[713])).
% 299.45/189.74 tff(715,plain,
% 299.45/189.74 (not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = not(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[714])).
% 299.45/189.74 tff(716,plain,
% 299.45/189.74 (not(not(or(not(X!1), not(not(Y!0))))) = or(not(X!1), Y!0)),
% 299.45/189.74 inference(transitivity,[status(thm)],[150, 101, 136])).
% 299.45/189.74 tff(717,plain,
% 299.45/189.74 (and(not(not(or(not(X!1), not(not(Y!0))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))) = and(or(not(X!1), Y!0), not(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[716, 715])).
% 299.45/189.74 tff(718,plain,
% 299.45/189.74 (not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) = not(and(or(not(X!1), Y!0), not(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[717])).
% 299.45/189.74 tff(719,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(X!1), not(not(Y!0)))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(720,plain,
% 299.45/189.74 (or(not(or(not(X!1), not(not(Y!0)))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[719, 63])).
% 299.45/189.74 tff(721,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(X!1), not(not(Y!0))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = or(not(or(not(X!1), not(not(Y!0)))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(722,plain,
% 299.45/189.74 (implies(or(not(X!1), not(not(Y!0))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = or(not(or(not(X!1), not(not(Y!0)))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[721, 20])).
% 299.45/189.74 tff(723,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(X!1), not(not(Y!0))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = not(and(or(not(X!1), not(not(Y!0))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(724,plain,
% 299.45/189.74 (implies(or(not(X!1), not(not(Y!0))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = not(and(or(not(X!1), not(not(Y!0))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[723, 41])).
% 299.45/189.74 tff(725,plain,
% 299.45/189.74 (not(and(or(not(X!1), not(not(Y!0))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) = implies(or(not(X!1), not(not(Y!0))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[724])).
% 299.45/189.74 tff(726,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(X!1)), not(not(not(Y!0)))) = not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(727,plain,
% 299.45/189.74 (and(not(not(X!1)), not(not(not(Y!0)))) = not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[726, 125])).
% 299.45/189.74 tff(728,plain,
% 299.45/189.74 (not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))) = and(not(not(X!1)), not(not(not(Y!0))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[727])).
% 299.45/189.74 tff(729,plain,
% 299.45/189.74 (not(not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))) = not(and(not(not(X!1)), not(not(not(Y!0)))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[728])).
% 299.45/189.74 tff(730,plain,
% 299.45/189.74 (not(and(not(not(X!1)), not(not(not(Y!0))))) = not(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[729])).
% 299.45/189.74 tff(731,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(X!1), not(not(Y!0))) = not(and(not(not(X!1)), not(not(not(Y!0))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(732,plain,
% 299.45/189.74 (or(not(X!1), not(not(Y!0))) = not(and(not(not(X!1)), not(not(not(Y!0)))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[731, 63])).
% 299.45/189.74 tff(733,plain,
% 299.45/189.74 (or(not(X!1), not(not(Y!0))) = not(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))))),
% 299.45/189.74 inference(transitivity,[status(thm)],[732, 730])).
% 299.45/189.74 tff(734,plain,
% 299.45/189.74 (and(or(not(X!1), not(not(Y!0))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))) = and(not(not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[733])).
% 299.45/189.74 tff(735,plain,
% 299.45/189.74 (and(not(not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))) = and(or(not(X!1), not(not(Y!0))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[734])).
% 299.45/189.74 tff(736,plain,
% 299.45/189.74 (not(and(not(not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) = not(and(or(not(X!1), not(not(Y!0))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[735])).
% 299.45/189.74 tff(737,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = not(and(not(not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(738,plain,
% 299.45/189.74 (or(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = not(and(not(not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[737, 63])).
% 299.45/189.74 tff(739,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(not(not(Y!0)), not(not(not(X!1)))), and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))) = not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(740,plain,
% 299.45/189.74 (or(and(not(not(Y!0)), not(not(not(X!1)))), and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))) = not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[739, 63])).
% 299.45/189.74 tff(741,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))) = not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(742,plain,
% 299.45/189.74 (and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))) = not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1))))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[741, 125])).
% 299.45/189.74 tff(743,plain,
% 299.45/189.74 (not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))) = and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[742])).
% 299.45/189.74 tff(744,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(Y!0)), not(not(not(X!1)))) = not(or(not(not(not(Y!0))), not(not(not(not(X!1)))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(745,plain,
% 299.45/189.74 (and(not(not(Y!0)), not(not(not(X!1)))) = not(or(not(not(not(Y!0))), not(not(not(not(X!1))))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[744, 125])).
% 299.45/189.74 tff(746,plain,
% 299.45/189.74 (not(or(not(not(not(Y!0))), not(not(not(not(X!1)))))) = and(not(not(Y!0)), not(not(not(X!1))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[745])).
% 299.45/189.74 tff(747,plain,
% 299.45/189.74 (or(not(or(not(not(not(Y!0))), not(not(not(not(X!1)))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1))))))) = or(and(not(not(Y!0)), not(not(not(X!1)))), and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[746, 743])).
% 299.45/189.74 tff(748,plain,
% 299.45/189.74 (or(not(or(not(not(not(Y!0))), not(not(not(not(X!1)))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1))))))) = not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))),
% 299.45/189.74 inference(transitivity,[status(thm)],[747, 740])).
% 299.45/189.74 tff(749,plain,
% 299.45/189.74 (or(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))), or(not(or(not(not(not(Y!0))), not(not(not(not(X!1)))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))))) = or(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[748])).
% 299.45/189.74 tff(750,plain,
% 299.45/189.74 (or(and(not(not(Y!0)), not(not(not(X!1)))), and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))) = or(not(or(not(not(not(Y!0))), not(not(not(not(X!1)))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[747])).
% 299.45/189.74 tff(751,plain,
% 299.45/189.74 (not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))) = or(and(not(not(Y!0)), not(not(not(X!1)))), and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[740])).
% 299.45/189.74 tff(752,plain,
% 299.45/189.74 (not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))) = not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[693])).
% 299.45/189.74 tff(753,plain,
% 299.45/189.74 (not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))) = not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[752])).
% 299.45/189.74 tff(754,plain,
% 299.45/189.74 (and(implies(X!1, Y!0), implies(Y!0, X!1)) = and(or(not(X!1), Y!0), or(not(Y!0), X!1))),
% 299.45/189.74 inference(symmetry,[status(thm)],[703])).
% 299.45/189.74 tff(755,plain,
% 299.45/189.74 (and(implies(X!1, Y!0), implies(Y!0, X!1)) = not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))),
% 299.45/189.74 inference(transitivity,[status(thm)],[754, 705, 753])).
% 299.45/189.74 tff(756,plain,
% 299.45/189.74 (or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))) = or(not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1)))))),
% 299.45/189.74 inference(monotonicity,[status(thm)],[755])).
% 299.45/189.74 tff(757,plain,
% 299.45/189.74 (or(not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1))))) = or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))),
% 299.45/189.74 inference(symmetry,[status(thm)],[756])).
% 299.45/189.74 tff(758,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1))))) = or(not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1))))))),
% 299.45/189.74 inference(quant_inst,[status(thm)],[])).
% 299.45/189.74 tff(759,plain,
% 299.45/189.74 (implies(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1))))) = or(not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1)))))),
% 299.45/189.74 inference(unit_resolution,[status(thm)],[758, 20])).
% 299.45/189.74 tff(760,plain,
% 299.45/189.74 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1))))) = not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.45/189.75 inference(quant_inst,[status(thm)],[])).
% 299.45/189.75 tff(761,plain,
% 299.45/189.75 (implies(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1))))) = not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))),
% 299.45/189.75 inference(unit_resolution,[status(thm)],[760, 41])).
% 299.45/189.75 tff(762,plain,
% 299.45/189.75 (not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))) = implies(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))),
% 299.45/189.75 inference(symmetry,[status(thm)],[761])).
% 299.45/189.75 tff(763,plain,
% 299.45/189.75 (not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))) = or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))),
% 299.45/189.75 inference(transitivity,[status(thm)],[762, 759, 757])).
% 299.45/189.75 tff(764,plain,
% 299.45/189.75 (equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = equiv(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.45/189.75 inference(monotonicity,[status(thm)],[763])).
% 299.45/189.75 tff(765,plain,
% 299.45/189.75 (equiv(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.45/189.75 inference(symmetry,[status(thm)],[764])).
% 299.45/189.75 tff(766,plain,
% 299.45/189.75 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.45/189.75 inference(quant_inst,[status(thm)],[])).
% 299.45/189.75 tff(767,plain,
% 299.45/189.75 (equiv(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))),
% 299.45/189.75 inference(unit_resolution,[status(thm)],[766, 92])).
% 299.45/189.75 tff(768,plain,
% 299.45/189.75 (and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) = equiv(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.45/189.75 inference(symmetry,[status(thm)],[767])).
% 299.45/189.75 tff(769,plain,
% 299.45/189.75 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))) = or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))),
% 299.45/189.75 inference(quant_inst,[status(thm)],[])).
% 299.45/189.75 tff(770,plain,
% 299.45/189.75 (implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))) = or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))),
% 299.45/189.75 inference(unit_resolution,[status(thm)],[769, 20])).
% 299.45/189.75 tff(771,plain,
% 299.45/189.75 (or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))) = implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))),
% 299.45/189.75 inference(symmetry,[status(thm)],[770])).
% 299.45/189.75 tff(772,plain,
% 299.45/189.75 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.45/189.75 inference(quant_inst,[status(thm)],[])).
% 299.45/189.75 tff(773,plain,
% 299.45/189.75 (implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.45/189.75 inference(unit_resolution,[status(thm)],[772, 41])).
% 299.45/189.75 tff(774,plain,
% 299.45/189.75 (not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.45/189.75 inference(symmetry,[status(thm)],[773])).
% 299.45/189.75 tff(775,plain,
% 299.45/189.75 (not(not(or(not(Y!0), not(not(X!1))))) = or(not(Y!0), X!1)),
% 299.45/189.75 inference(transitivity,[status(thm)],[232, 98, 68])).
% 299.45/189.75 tff(776,plain,
% 299.45/189.75 (and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))) = and(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))), or(not(Y!0), X!1))),
% 299.45/189.75 inference(monotonicity,[status(thm)],[693, 775])).
% 299.45/189.75 tff(777,plain,
% 299.45/189.75 (and(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))), or(not(Y!0), X!1)) = and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))),
% 299.45/189.75 inference(symmetry,[status(thm)],[776])).
% 299.45/189.75 tff(778,plain,
% 299.45/189.75 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))), or(not(Y!0), X!1)) = not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))),
% 299.45/189.75 inference(quant_inst,[status(thm)],[])).
% 299.45/189.75 tff(779,plain,
% 299.45/189.75 (and(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))), or(not(Y!0), X!1)) = not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))),
% 299.45/189.75 inference(unit_resolution,[status(thm)],[778, 125])).
% 299.45/189.75 tff(780,plain,
% 299.45/189.75 (not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))) = and(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))), or(not(Y!0), X!1))),
% 299.45/189.75 inference(symmetry,[status(thm)],[779])).
% 299.45/189.75 tff(781,plain,
% 299.45/189.75 (not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))) = and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))),
% 299.45/189.75 inference(transitivity,[status(thm)],[780, 777])).
% 299.45/189.75 tff(782,plain,
% 299.45/189.75 (not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))) = not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))),
% 299.45/189.75 inference(monotonicity,[status(thm)],[781])).
% 299.45/189.75 tff(783,plain,
% 299.45/189.75 (not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))) = or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))),
% 299.45/189.75 inference(transitivity,[status(thm)],[782, 762, 759, 757])).
% 299.45/189.75 tff(784,plain,
% 299.45/189.75 (and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))) = and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))),
% 299.45/189.75 inference(monotonicity,[status(thm)],[783])).
% 299.45/189.75 tff(785,plain,
% 299.45/189.75 (and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))) = and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))),
% 299.45/189.75 inference(symmetry,[status(thm)],[784])).
% 299.45/189.75 tff(786,plain,
% 299.45/189.75 (not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.45/189.75 inference(monotonicity,[status(thm)],[785])).
% 299.45/189.75 tff(787,plain,
% 299.45/189.75 (not(and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.45/189.75 inference(symmetry,[status(thm)],[786])).
% 299.45/189.75 tff(788,plain,
% 299.45/189.75 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = not(and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.45/189.75 inference(quant_inst,[status(thm)],[])).
% 299.45/189.75 tff(789,plain,
% 299.45/189.75 (or(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = not(and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.45/189.75 inference(unit_resolution,[status(thm)],[788, 63])).
% 299.45/189.75 tff(790,plain,
% 299.45/189.75 (or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))) = or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))),
% 299.45/189.75 inference(monotonicity,[status(thm)],[707, 70])).
% 299.45/189.75 tff(791,plain,
% 299.45/189.75 (or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))) = or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))),
% 299.45/189.75 inference(symmetry,[status(thm)],[790])).
% 299.45/189.75 tff(792,plain,
% 299.45/189.75 (not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))) = not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))),
% 299.45/189.75 inference(monotonicity,[status(thm)],[791])).
% 299.45/189.75 tff(793,plain,
% 299.45/189.75 (not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))) = not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))),
% 299.45/189.75 inference(symmetry,[status(thm)],[792])).
% 299.45/189.75 tff(794,plain,
% 299.45/189.75 (or(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.45/189.75 inference(monotonicity,[status(thm)],[793])).
% 299.45/189.75 tff(795,plain,
% 299.45/189.75 (or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = or(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.45/189.75 inference(symmetry,[status(thm)],[794])).
% 299.45/189.75 tff(796,plain,
% 299.45/189.75 (or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.45/189.75 inference(transitivity,[status(thm)],[795, 789, 787, 774])).
% 299.45/189.75 tff(797,plain,
% 299.45/189.75 (and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) = and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))),
% 299.56/189.75 inference(monotonicity,[status(thm)],[796, 771])).
% 299.56/189.75 tff(798,plain,
% 299.56/189.75 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) = not(or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.56/189.75 inference(quant_inst,[status(thm)],[])).
% 299.56/189.75 tff(799,plain,
% 299.56/189.75 (and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) = not(or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.56/189.75 inference(unit_resolution,[status(thm)],[798, 125])).
% 299.56/189.75 tff(800,plain,
% 299.56/189.75 (not(or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))) = and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))),
% 299.56/189.75 inference(symmetry,[status(thm)],[799])).
% 299.56/189.75 tff(801,plain,
% 299.56/189.75 (or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))) = or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))),
% 299.56/189.75 inference(monotonicity,[status(thm)],[783])).
% 299.56/189.75 tff(802,plain,
% 299.56/189.75 (or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))) = or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))),
% 299.56/189.75 inference(symmetry,[status(thm)],[801])).
% 299.56/189.75 tff(803,plain,
% 299.56/189.75 (not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) = not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))),
% 299.56/189.75 inference(monotonicity,[status(thm)],[802])).
% 299.56/189.75 tff(804,plain,
% 299.56/189.75 (or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))))),
% 299.56/189.75 inference(monotonicity,[status(thm)],[803])).
% 299.56/189.75 tff(805,plain,
% 299.56/189.75 (or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))) = or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.56/189.75 inference(symmetry,[status(thm)],[804])).
% 299.56/189.75 tff(806,plain,
% 299.56/189.75 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))) = or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))))),
% 299.56/189.75 inference(quant_inst,[status(thm)],[])).
% 299.56/189.75 tff(807,plain,
% 299.56/189.75 (implies(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))) = or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))))),
% 299.56/189.75 inference(unit_resolution,[status(thm)],[806, 20])).
% 299.56/189.75 tff(808,plain,
% 299.56/189.75 (and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))) = and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))),
% 299.56/189.75 inference(monotonicity,[status(thm)],[792])).
% 299.56/189.75 tff(809,plain,
% 299.56/189.75 (and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))) = and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.56/189.75 inference(symmetry,[status(thm)],[808])).
% 299.56/189.75 tff(810,plain,
% 299.56/189.75 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))) = not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))))),
% 299.56/189.75 inference(quant_inst,[status(thm)],[])).
% 299.56/189.75 tff(811,plain,
% 299.56/189.75 (and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))) = not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))),
% 299.56/189.75 inference(unit_resolution,[status(thm)],[810, 125])).
% 299.56/189.75 tff(812,plain,
% 299.56/189.75 (not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))) = and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))),
% 299.56/189.75 inference(symmetry,[status(thm)],[811])).
% 299.56/189.75 tff(813,plain,
% 299.56/189.75 (not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))) = and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.56/189.75 inference(transitivity,[status(thm)],[812, 809])).
% 299.56/189.75 tff(814,plain,
% 299.56/189.75 (implies(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))) = implies(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))),
% 299.56/189.76 inference(monotonicity,[status(thm)],[813])).
% 299.56/189.76 tff(815,plain,
% 299.56/189.76 (implies(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) = implies(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))))),
% 299.56/189.76 inference(symmetry,[status(thm)],[814])).
% 299.56/189.76 tff(816,plain,
% 299.56/189.76 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) = not(and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))))),
% 299.56/189.76 inference(quant_inst,[status(thm)],[])).
% 299.56/189.76 tff(817,plain,
% 299.56/189.76 (implies(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) = not(and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))),
% 299.56/189.76 inference(unit_resolution,[status(thm)],[816, 41])).
% 299.56/189.76 tff(818,plain,
% 299.56/189.76 (not(and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))) = implies(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))),
% 299.56/189.76 inference(symmetry,[status(thm)],[817])).
% 299.56/189.76 tff(819,plain,
% 299.56/189.76 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))) = not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))),
% 299.56/189.76 inference(quant_inst,[status(thm)],[])).
% 299.56/189.76 tff(820,plain,
% 299.56/189.76 (implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))) = not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))),
% 299.56/189.76 inference(unit_resolution,[status(thm)],[819, 41])).
% 299.56/189.76 tff(821,plain,
% 299.56/189.76 (not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) = implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))),
% 299.56/189.76 inference(symmetry,[status(thm)],[820])).
% 299.56/189.76 tff(822,plain,
% 299.56/189.76 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.56/189.76 inference(quant_inst,[status(thm)],[])).
% 299.56/189.76 tff(823,plain,
% 299.56/189.76 (implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.56/189.76 inference(unit_resolution,[status(thm)],[822, 41])).
% 299.56/189.76 tff(824,plain,
% 299.56/189.76 (not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.56/189.76 inference(symmetry,[status(thm)],[823])).
% 299.56/189.76 tff(825,plain,
% 299.56/189.76 (and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))) = and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.56/189.76 inference(monotonicity,[status(thm)],[824, 821])).
% 299.56/189.76 tff(826,plain,
% 299.56/189.76 (and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))) = and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))),
% 299.56/189.76 inference(symmetry,[status(thm)],[825])).
% 299.56/189.76 tff(827,plain,
% 299.56/189.76 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))),
% 299.56/189.76 inference(quant_inst,[status(thm)],[])).
% 299.56/189.76 tff(828,plain,
% 299.56/189.76 (implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.56/189.76 inference(unit_resolution,[status(thm)],[827, 20])).
% 299.56/189.76 tff(829,plain,
% 299.56/189.76 (or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.56/189.76 inference(symmetry,[status(thm)],[828])).
% 299.56/189.76 tff(830,plain,
% 299.56/189.76 (and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))) = and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.56/189.76 inference(monotonicity,[status(thm)],[829, 821])).
% 299.56/189.76 tff(831,plain,
% 299.56/189.76 (and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))) = and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))),
% 299.56/189.76 inference(transitivity,[status(thm)],[830, 826])).
% 299.56/189.76 tff(832,plain,
% 299.56/189.76 (not(and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))) = not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))),
% 299.56/189.76 inference(monotonicity,[status(thm)],[831])).
% 299.56/189.76 tff(833,plain,
% 299.56/189.76 (not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))) = not(and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))),
% 299.56/189.76 inference(symmetry,[status(thm)],[832])).
% 299.56/189.76 tff(834,plain,
% 299.56/189.76 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))) = or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.56/189.76 inference(quant_inst,[status(thm)],[])).
% 299.56/189.76 tff(835,plain,
% 299.56/189.76 (implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))) = or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))),
% 299.56/189.76 inference(unit_resolution,[status(thm)],[834, 20])).
% 299.56/189.76 tff(836,plain,
% 299.56/189.76 (or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))) = implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))),
% 299.56/189.76 inference(symmetry,[status(thm)],[835])).
% 299.56/189.76 tff(837,plain,
% 299.56/189.76 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))) = not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))),
% 299.56/189.76 inference(quant_inst,[status(thm)],[])).
% 299.56/189.76 tff(838,plain,
% 299.56/189.76 (or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))) = not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))),
% 299.56/189.76 inference(unit_resolution,[status(thm)],[837, 63])).
% 299.56/189.76 tff(839,plain,
% 299.56/189.76 (not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))) = or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))),
% 299.56/189.76 inference(symmetry,[status(thm)],[838])).
% 299.56/189.76 tff(840,plain,
% 299.56/189.76 (not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))),
% 299.56/189.76 inference(monotonicity,[status(thm)],[619])).
% 299.56/189.76 tff(841,plain,
% 299.56/189.76 (not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))) = not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.56/189.76 inference(symmetry,[status(thm)],[840])).
% 299.56/189.76 tff(842,plain,
% 299.56/189.76 (or(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))) = or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))),
% 299.56/189.76 inference(monotonicity,[status(thm)],[841, 839])).
% 299.56/189.76 tff(843,plain,
% 299.56/189.76 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))) = not(and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))))))),
% 299.56/189.76 inference(quant_inst,[status(thm)],[])).
% 299.56/189.76 tff(844,plain,
% 299.56/189.76 (or(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))) = not(and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))))),
% 299.56/189.76 inference(unit_resolution,[status(thm)],[843, 63])).
% 299.56/189.76 tff(845,plain,
% 299.56/189.76 (not(and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))))) = or(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))),
% 299.56/189.76 inference(symmetry,[status(thm)],[844])).
% 299.56/189.76 tff(846,plain,
% 299.56/189.76 (not(and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))))) = implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))),
% 299.56/189.76 inference(transitivity,[status(thm)],[845, 842, 836])).
% 299.56/189.76 tff(847,plain,
% 299.56/189.76 (not(and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = or(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.56/189.76 inference(symmetry,[status(thm)],[789])).
% 299.56/189.76 tff(848,plain,
% 299.56/189.76 (not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.56/189.76 inference(transitivity,[status(thm)],[786, 847, 794, 829])).
% 299.56/189.76 tff(849,plain,
% 299.56/189.76 (and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))))) = and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.56/189.76 inference(monotonicity,[status(thm)],[848, 846])).
% 299.56/189.76 tff(850,plain,
% 299.56/189.76 (and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))))) = and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))),
% 299.56/189.76 inference(transitivity,[status(thm)],[849, 826])).
% 299.56/189.76 tff(851,plain,
% 299.56/189.76 (not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))))))) = not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))),
% 299.56/189.76 inference(monotonicity,[status(thm)],[850])).
% 299.56/189.76 tff(852,plain,
% 299.56/189.76 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))))) = not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))))))))),
% 299.56/189.76 inference(quant_inst,[status(thm)],[])).
% 299.56/189.76 tff(853,plain,
% 299.56/189.76 (or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))))) = not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))))))),
% 299.56/189.76 inference(unit_resolution,[status(thm)],[852, 63])).
% 299.56/189.76 tff(854,plain,
% 299.56/189.76 (not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))) = not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))),
% 299.56/189.76 inference(monotonicity,[status(thm)],[839])).
% 299.56/189.76 tff(855,plain,
% 299.56/189.76 (not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))) = not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))),
% 299.56/189.76 inference(symmetry,[status(thm)],[854])).
% 299.56/189.76 tff(856,plain,
% 299.56/189.76 (not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))) = not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))),
% 299.56/189.76 inference(transitivity,[status(thm)],[793, 855])).
% 299.56/189.76 tff(857,plain,
% 299.56/189.76 (and(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))), not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))) = and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))))),
% 299.56/189.76 inference(monotonicity,[status(thm)],[714, 856])).
% 299.56/189.76 tff(858,plain,
% 299.56/189.76 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))), not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))) = not(or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))))),
% 299.56/189.76 inference(quant_inst,[status(thm)],[])).
% 299.56/189.76 tff(859,plain,
% 299.56/189.76 (and(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))), not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))) = not(or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))),
% 299.56/189.76 inference(unit_resolution,[status(thm)],[858, 125])).
% 299.56/189.76 tff(860,plain,
% 299.56/189.76 (not(or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))) = and(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))), not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))),
% 299.56/189.77 inference(symmetry,[status(thm)],[859])).
% 299.56/189.77 tff(861,plain,
% 299.56/189.77 (not(or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))) = and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))))),
% 299.56/189.77 inference(transitivity,[status(thm)],[860, 857])).
% 299.56/189.77 tff(862,plain,
% 299.56/189.77 (and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))),
% 299.56/189.77 inference(monotonicity,[status(thm)],[763, 841])).
% 299.56/189.77 tff(863,plain,
% 299.56/189.77 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.56/189.77 inference(quant_inst,[status(thm)],[])).
% 299.56/189.77 tff(864,plain,
% 299.56/189.77 (and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.56/189.77 inference(unit_resolution,[status(thm)],[863, 125])).
% 299.56/189.77 tff(865,plain,
% 299.56/189.77 (not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.56/189.77 inference(symmetry,[status(thm)],[864])).
% 299.56/189.77 tff(866,plain,
% 299.56/189.77 (not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))),
% 299.56/189.77 inference(transitivity,[status(thm)],[865, 862])).
% 299.56/189.77 tff(867,plain,
% 299.56/189.77 (or(not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))) = or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))), not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))))),
% 299.56/189.77 inference(monotonicity,[status(thm)],[866, 861])).
% 299.56/189.77 tff(868,plain,
% 299.56/189.77 (or(not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))) = or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.56/189.77 inference(transitivity,[status(thm)],[867, 853, 851, 833, 818, 815, 807, 805])).
% 299.56/189.77 tff(869,plain,
% 299.56/189.77 (not(or(not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))))) = not(or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.56/189.77 inference(monotonicity,[status(thm)],[868])).
% 299.56/189.77 tff(870,plain,
% 299.56/189.77 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))) = not(or(not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))))))),
% 299.56/189.77 inference(quant_inst,[status(thm)],[])).
% 299.56/189.77 tff(871,plain,
% 299.56/189.77 (and(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))) = not(or(not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))), not(or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))))),
% 299.56/189.77 inference(unit_resolution,[status(thm)],[870, 125])).
% 299.56/189.77 tff(872,plain,
% 299.56/189.77 (or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))) = or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.56/189.77 inference(monotonicity,[status(thm)],[782])).
% 299.56/189.77 tff(873,plain,
% 299.56/189.77 (or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))),
% 299.56/189.77 inference(symmetry,[status(thm)],[872])).
% 299.56/189.77 tff(874,plain,
% 299.56/189.77 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))),
% 299.56/189.77 inference(quant_inst,[status(thm)],[])).
% 299.56/189.77 tff(875,plain,
% 299.56/189.77 (implies(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.56/189.77 inference(unit_resolution,[status(thm)],[874, 20])).
% 299.56/189.77 tff(876,plain,
% 299.56/189.77 (implies(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))),
% 299.56/189.77 inference(transitivity,[status(thm)],[875, 873])).
% 299.56/189.77 tff(877,plain,
% 299.56/189.77 (or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))),
% 299.56/189.77 inference(monotonicity,[status(thm)],[713])).
% 299.56/189.77 tff(878,plain,
% 299.56/189.77 (or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.56/189.77 inference(symmetry,[status(thm)],[877])).
% 299.56/189.77 tff(879,plain,
% 299.56/189.77 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))),
% 299.56/189.77 inference(quant_inst,[status(thm)],[])).
% 299.56/189.77 tff(880,plain,
% 299.56/189.77 (implies(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))),
% 299.56/189.77 inference(unit_resolution,[status(thm)],[879, 20])).
% 299.56/189.77 tff(881,plain,
% 299.56/189.77 (implies(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.56/189.77 inference(transitivity,[status(thm)],[880, 878])).
% 299.56/189.77 tff(882,plain,
% 299.56/189.77 (and(implies(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), implies(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))) = and(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))), or(not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))),
% 299.56/189.77 inference(monotonicity,[status(thm)],[881, 876])).
% 299.56/189.77 tff(883,plain,
% 299.56/189.77 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = and(implies(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), implies(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))))),
% 299.56/189.77 inference(quant_inst,[status(thm)],[])).
% 299.56/189.77 tff(884,plain,
% 299.56/189.77 (equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = and(implies(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))), implies(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))),
% 299.56/189.77 inference(unit_resolution,[status(thm)],[883, 92])).
% 299.56/189.77 tff(885,plain,
% 299.56/189.77 (equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.56/189.77 inference(transitivity,[status(thm)],[884, 882, 871, 869, 800, 797, 768, 765])).
% 299.56/189.77 tff(886,plain,
% 299.56/189.77 (is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))) <=> is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))),
% 299.56/189.77 inference(monotonicity,[status(thm)],[885])).
% 299.56/189.77 tff(887,plain,
% 299.56/189.77 (is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))) <=> is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))),
% 299.56/189.77 inference(symmetry,[status(thm)],[886])).
% 299.56/189.77 tff(888,plain,
% 299.56/189.77 (and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) = equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.56/189.77 inference(transitivity,[status(thm)],[768, 765])).
% 299.56/189.77 tff(889,plain,
% 299.56/189.77 (is_a_theorem(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) <=> is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))),
% 299.56/189.77 inference(monotonicity,[status(thm)],[888])).
% 299.56/189.77 tff(890,plain,
% 299.56/189.77 (is_a_theorem(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) <=> is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))),
% 299.56/189.77 inference(transitivity,[status(thm)],[889, 887])).
% 299.56/189.77 tff(891,plain,
% 299.56/189.77 (and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))) = and(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.56/189.77 inference(monotonicity,[status(thm)],[838, 840])).
% 299.56/189.77 tff(892,plain,
% 299.56/189.77 (and(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))),
% 299.56/189.77 inference(symmetry,[status(thm)],[891])).
% 299.56/189.77 tff(893,plain,
% 299.56/189.77 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(or(not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.56/189.77 inference(quant_inst,[status(thm)],[])).
% 299.56/189.77 tff(894,plain,
% 299.56/189.77 (and(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(or(not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.56/189.77 inference(unit_resolution,[status(thm)],[893, 125])).
% 299.56/189.77 tff(895,plain,
% 299.56/189.77 (not(or(not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = and(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.56/189.77 inference(symmetry,[status(thm)],[894])).
% 299.56/189.77 tff(896,plain,
% 299.56/189.77 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))))),
% 299.56/189.78 inference(quant_inst,[status(thm)],[])).
% 299.56/189.78 tff(897,plain,
% 299.56/189.78 (implies(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))),
% 299.56/189.78 inference(unit_resolution,[status(thm)],[896, 41])).
% 299.56/189.78 tff(898,plain,
% 299.56/189.78 (not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) = implies(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))),
% 299.56/189.78 inference(symmetry,[status(thm)],[897])).
% 299.56/189.78 tff(899,plain,
% 299.56/189.78 (not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))) = not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))),
% 299.56/189.78 inference(symmetry,[status(thm)],[782])).
% 299.56/189.78 tff(900,plain,
% 299.56/189.78 (and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))) = and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))),
% 299.56/189.78 inference(monotonicity,[status(thm)],[899])).
% 299.56/189.78 tff(901,plain,
% 299.56/189.78 (and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))) = and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))),
% 299.56/189.78 inference(symmetry,[status(thm)],[900])).
% 299.56/189.78 tff(902,plain,
% 299.56/189.78 (not(and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) = not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))),
% 299.56/189.78 inference(monotonicity,[status(thm)],[901])).
% 299.56/189.78 tff(903,plain,
% 299.56/189.78 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = not(and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))))),
% 299.56/189.78 inference(quant_inst,[status(thm)],[])).
% 299.56/189.78 tff(904,plain,
% 299.56/189.78 (or(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = not(and(not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))),
% 299.56/189.78 inference(unit_resolution,[status(thm)],[903, 63])).
% 299.56/189.78 tff(905,plain,
% 299.56/189.78 (not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))) = not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))),
% 299.56/189.78 inference(transitivity,[status(thm)],[854, 792])).
% 299.56/189.78 tff(906,plain,
% 299.56/189.78 (or(not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = or(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))),
% 299.56/189.78 inference(monotonicity,[status(thm)],[905, 713])).
% 299.56/189.78 tff(907,plain,
% 299.56/189.78 (or(not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) = or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.56/189.78 inference(transitivity,[status(thm)],[906, 904, 902, 898, 880, 878])).
% 299.56/189.78 tff(908,plain,
% 299.56/189.78 (not(or(not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.56/189.78 inference(monotonicity,[status(thm)],[907])).
% 299.56/189.78 tff(909,plain,
% 299.56/189.78 (not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))) = not(or(not(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.56/189.78 inference(symmetry,[status(thm)],[908])).
% 299.56/189.78 tff(910,plain,
% 299.56/189.78 (not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) = or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.56/189.78 inference(transitivity,[status(thm)],[898, 880, 878])).
% 299.56/189.78 tff(911,plain,
% 299.56/189.78 (not(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))) = not(or(not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))), not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.56/189.78 inference(monotonicity,[status(thm)],[910])).
% 299.56/189.78 tff(912,plain,
% 299.56/189.78 (not(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))) = and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))),
% 299.56/189.78 inference(transitivity,[status(thm)],[911, 909, 895, 892])).
% 299.56/189.78 tff(913,plain,
% 299.56/189.78 (or(not(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) = or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.56/189.78 inference(monotonicity,[status(thm)],[912])).
% 299.56/189.78 tff(914,plain,
% 299.56/189.78 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) = or(not(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.56/189.78 inference(quant_inst,[status(thm)],[])).
% 299.56/189.78 tff(915,plain,
% 299.56/189.78 (implies(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) = or(not(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.56/189.78 inference(unit_resolution,[status(thm)],[914, 20])).
% 299.56/189.78 tff(916,plain,
% 299.56/189.78 (implies(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) = or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.56/189.78 inference(transitivity,[status(thm)],[915, 913])).
% 299.56/189.78 tff(917,plain,
% 299.56/189.78 (is_a_theorem(implies(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))) <=> is_a_theorem(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.56/189.78 inference(monotonicity,[status(thm)],[916])).
% 299.56/189.78 tff(918,plain,
% 299.56/189.78 (is_a_theorem(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))) <=> is_a_theorem(implies(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.56/189.78 inference(symmetry,[status(thm)],[917])).
% 299.56/189.78 tff(919,plain,
% 299.56/189.78 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.56/189.78 inference(quant_inst,[status(thm)],[])).
% 299.56/189.78 tff(920,plain,
% 299.56/189.78 (or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.56/189.78 inference(unit_resolution,[status(thm)],[919, 63])).
% 299.56/189.78 tff(921,plain,
% 299.56/189.78 (implies(or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))) = implies(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.56/189.78 inference(monotonicity,[status(thm)],[920])).
% 299.56/189.78 tff(922,plain,
% 299.56/189.78 (is_a_theorem(implies(or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))) <=> is_a_theorem(implies(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.56/189.78 inference(monotonicity,[status(thm)],[921])).
% 299.56/189.78 tff(923,plain,
% 299.56/189.78 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.56/189.79 inference(quant_inst,[status(thm)],[])).
% 299.56/189.79 tff(924,plain,
% 299.56/189.79 (is_a_theorem(implies(or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.56/189.79 inference(unit_resolution,[status(thm)],[923, 518])).
% 299.56/189.79 tff(925,plain,
% 299.56/189.79 (is_a_theorem(implies(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.56/189.79 inference(modus_ponens,[status(thm)],[924, 922])).
% 299.56/189.79 tff(926,plain,
% 299.56/189.79 (or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))) = or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))),
% 299.56/189.79 inference(monotonicity,[status(thm)],[839])).
% 299.56/189.79 tff(927,plain,
% 299.56/189.79 (not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))) = not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.56/189.79 inference(monotonicity,[status(thm)],[926])).
% 299.56/189.79 tff(928,plain,
% 299.56/189.79 (not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))) = not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1)))))))),
% 299.56/189.79 inference(symmetry,[status(thm)],[927])).
% 299.56/189.79 tff(929,plain,
% 299.56/189.79 (or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))) = or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.56/189.79 inference(monotonicity,[status(thm)],[928])).
% 299.56/189.79 tff(930,plain,
% 299.56/189.79 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))) = or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.56/189.79 inference(quant_inst,[status(thm)],[])).
% 299.56/189.79 tff(931,plain,
% 299.56/189.79 (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))) = or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.56/189.79 inference(unit_resolution,[status(thm)],[930, 20])).
% 299.56/189.79 tff(932,plain,
% 299.56/189.79 (not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))) = or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.56/189.79 inference(symmetry,[status(thm)],[920])).
% 299.56/189.79 tff(933,plain,
% 299.56/189.79 (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) = implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.56/189.79 inference(monotonicity,[status(thm)],[932])).
% 299.56/189.79 tff(934,plain,
% 299.56/189.79 (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) = or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.56/189.79 inference(transitivity,[status(thm)],[933, 931, 929])).
% 299.56/189.79 tff(935,plain,
% 299.56/189.79 (is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))) <=> is_a_theorem(or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.56/189.79 inference(monotonicity,[status(thm)],[934])).
% 299.56/189.79 tff(936,plain,
% 299.56/189.79 (is_a_theorem(or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))) <=> is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))),
% 299.56/189.79 inference(symmetry,[status(thm)],[935])).
% 299.56/189.79 tff(937,plain,
% 299.56/189.79 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.56/189.79 inference(quant_inst,[status(thm)],[])).
% 299.56/189.79 tff(938,plain,
% 299.56/189.79 (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.56/189.79 inference(unit_resolution,[status(thm)],[937, 41])).
% 299.56/189.79 tff(939,plain,
% 299.56/189.79 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.56/189.79 inference(quant_inst,[status(thm)],[])).
% 299.56/189.79 tff(940,plain,
% 299.56/189.79 (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.56/189.79 inference(unit_resolution,[status(thm)],[939, 20])).
% 299.56/189.79 tff(941,plain,
% 299.56/189.79 (or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.56/189.79 inference(symmetry,[status(thm)],[940])).
% 299.56/189.79 tff(942,plain,
% 299.56/189.79 (not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) = and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.56/189.79 inference(transitivity,[status(thm)],[803, 812, 809])).
% 299.56/189.79 tff(943,plain,
% 299.56/189.79 (or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = or(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.56/189.80 inference(monotonicity,[status(thm)],[942])).
% 299.56/189.80 tff(944,plain,
% 299.56/189.80 (or(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.56/189.80 inference(symmetry,[status(thm)],[943])).
% 299.56/189.80 tff(945,plain,
% 299.56/189.80 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.56/189.80 inference(quant_inst,[status(thm)],[])).
% 299.56/189.80 tff(946,plain,
% 299.56/189.80 (or(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.56/189.80 inference(unit_resolution,[status(thm)],[945, 63])).
% 299.56/189.80 tff(947,plain,
% 299.56/189.80 (not(and(not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))) = or(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.56/189.80 inference(symmetry,[status(thm)],[946])).
% 299.56/189.80 tff(948,plain,
% 299.56/189.80 (and(not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))) = and(implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))),
% 299.56/189.80 inference(monotonicity,[status(thm)],[821, 824])).
% 299.56/189.80 tff(949,plain,
% 299.56/189.80 (and(implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))) = and(not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.56/189.80 inference(symmetry,[status(thm)],[948])).
% 299.56/189.80 tff(950,plain,
% 299.56/189.80 (and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))) = and(implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))),
% 299.56/189.80 inference(monotonicity,[status(thm)],[836, 824])).
% 299.56/189.80 tff(951,plain,
% 299.56/189.80 (and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))) = and(not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.56/189.80 inference(transitivity,[status(thm)],[950, 949])).
% 299.56/189.80 tff(952,plain,
% 299.56/189.80 (not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))) = not(and(not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.56/189.80 inference(monotonicity,[status(thm)],[951])).
% 299.56/189.80 tff(953,plain,
% 299.56/189.80 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.56/189.80 inference(quant_inst,[status(thm)],[])).
% 299.56/189.80 tff(954,plain,
% 299.56/189.80 (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.56/189.80 inference(unit_resolution,[status(thm)],[953, 41])).
% 299.56/189.80 tff(955,plain,
% 299.56/189.80 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.56/189.80 inference(quant_inst,[status(thm)],[])).
% 299.56/189.80 tff(956,plain,
% 299.56/189.80 (implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.56/189.80 inference(unit_resolution,[status(thm)],[955, 20])).
% 299.56/189.80 tff(957,plain,
% 299.56/189.80 (or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.56/189.80 inference(symmetry,[status(thm)],[956])).
% 299.56/189.80 tff(958,plain,
% 299.56/189.80 (or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.56/189.80 inference(monotonicity,[status(thm)],[927])).
% 299.56/189.80 tff(959,plain,
% 299.56/189.80 (or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.56/189.80 inference(transitivity,[status(thm)],[958, 957, 954, 952, 947, 944, 941, 938])).
% 299.56/189.80 tff(960,plain,
% 299.56/189.80 (not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))) = or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.56/189.80 inference(transitivity,[status(thm)],[833, 818, 815, 807, 805])).
% 299.56/189.80 tff(961,plain,
% 299.56/189.80 (not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))) = not(or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.56/189.80 inference(monotonicity,[status(thm)],[960])).
% 299.56/189.80 tff(962,plain,
% 299.56/189.80 (not(or(not(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))) = not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))))),
% 299.56/189.80 inference(symmetry,[status(thm)],[961])).
% 299.56/189.80 tff(963,plain,
% 299.56/189.80 (and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) = and(or(not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))),
% 299.56/189.80 inference(symmetry,[status(thm)],[797])).
% 299.56/189.80 tff(964,plain,
% 299.56/189.80 (and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) = not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))))),
% 299.56/189.80 inference(transitivity,[status(thm)],[963, 799, 962])).
% 299.56/189.80 tff(965,plain,
% 299.56/189.80 (or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))) = or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.56/189.80 inference(monotonicity,[status(thm)],[964, 959])).
% 299.56/189.80 tff(966,plain,
% 299.56/189.80 (implies(or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))) = implies(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.56/189.80 inference(monotonicity,[status(thm)],[965])).
% 299.56/189.80 tff(967,plain,
% 299.56/189.80 (is_a_theorem(implies(or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) <=> is_a_theorem(implies(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.56/189.80 inference(monotonicity,[status(thm)],[966])).
% 299.56/189.80 tff(968,plain,
% 299.56/189.80 ((~![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(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.56/189.80 inference(quant_inst,[status(thm)],[])).
% 299.56/189.80 tff(969,plain,
% 299.56/189.80 (is_a_theorem(implies(or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.56/189.81 inference(unit_resolution,[status(thm)],[968, 570])).
% 299.56/189.81 tff(970,plain,
% 299.56/189.81 (is_a_theorem(implies(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.56/189.81 inference(modus_ponens,[status(thm)],[969, 967])).
% 299.56/189.81 tff(971,plain,
% 299.56/189.81 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) = or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))),
% 299.56/189.81 inference(quant_inst,[status(thm)],[])).
% 299.56/189.81 tff(972,plain,
% 299.56/189.81 (implies(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) = or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.56/189.81 inference(unit_resolution,[status(thm)],[971, 20])).
% 299.56/189.81 tff(973,plain,
% 299.56/189.81 (or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) = implies(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.56/189.81 inference(symmetry,[status(thm)],[972])).
% 299.56/189.81 tff(974,plain,
% 299.56/189.81 (is_a_theorem(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))) <=> is_a_theorem(implies(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))),
% 299.56/189.81 inference(monotonicity,[status(thm)],[973])).
% 299.56/189.81 tff(975,plain,
% 299.56/189.81 (is_a_theorem(implies(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))) <=> is_a_theorem(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))),
% 299.56/189.81 inference(symmetry,[status(thm)],[974])).
% 299.56/189.81 tff(976,plain,
% 299.56/189.81 (or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = or(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.56/189.81 inference(monotonicity,[status(thm)],[813])).
% 299.56/189.81 tff(977,plain,
% 299.56/189.81 (or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.56/189.81 inference(transitivity,[status(thm)],[976, 944, 941, 938])).
% 299.56/189.81 tff(978,plain,
% 299.56/189.81 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) = not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))))),
% 299.56/189.81 inference(quant_inst,[status(thm)],[])).
% 299.56/189.81 tff(979,plain,
% 299.56/189.81 (or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) = not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))),
% 299.56/189.81 inference(unit_resolution,[status(thm)],[978, 63])).
% 299.56/189.81 tff(980,plain,
% 299.56/189.81 (or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))) = or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))),
% 299.56/189.81 inference(monotonicity,[status(thm)],[813])).
% 299.56/189.81 tff(981,plain,
% 299.56/189.81 (or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))) = not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))),
% 299.56/189.81 inference(transitivity,[status(thm)],[980, 979])).
% 299.56/189.81 tff(982,plain,
% 299.56/189.81 (implies(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))) = implies(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.62/189.81 inference(monotonicity,[status(thm)],[981, 977])).
% 299.62/189.81 tff(983,plain,
% 299.62/189.81 (is_a_theorem(implies(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))) <=> is_a_theorem(implies(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))),
% 299.62/189.81 inference(monotonicity,[status(thm)],[982])).
% 299.62/189.81 tff(984,plain,
% 299.62/189.81 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.62/189.81 inference(quant_inst,[status(thm)],[])).
% 299.62/189.81 tff(985,plain,
% 299.62/189.81 (is_a_theorem(implies(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(not(or(not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))), not(or(not(Y!0), X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.62/189.81 inference(unit_resolution,[status(thm)],[984, 518])).
% 299.62/189.81 tff(986,plain,
% 299.62/189.81 (is_a_theorem(implies(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))),
% 299.62/189.82 inference(modus_ponens,[status(thm)],[985, 983])).
% 299.62/189.82 tff(987,plain,
% 299.62/189.82 (is_a_theorem(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))),
% 299.62/189.82 inference(modus_ponens,[status(thm)],[986, 975])).
% 299.62/189.82 tff(988,plain,
% 299.62/189.82 (((~![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(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))) | (~is_a_theorem(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))) | (~is_a_theorem(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))))),
% 299.62/189.82 inference(rewrite,[status(thm)],[])).
% 299.62/189.82 tff(989,plain,
% 299.62/189.82 ((~![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(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))) | (~is_a_theorem(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))))),
% 299.62/189.82 inference(quant_inst,[status(thm)],[])).
% 299.62/189.82 tff(990,plain,
% 299.62/189.82 ((~![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(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))) | (~is_a_theorem(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))),
% 299.62/189.82 inference(modus_ponens,[status(thm)],[989, 988])).
% 299.62/189.82 tff(991,plain,
% 299.62/189.82 (is_a_theorem(or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))) | (~is_a_theorem(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))) | (~is_a_theorem(implies(or(not(not(and(not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))), not(and(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))))))), not(and(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))), or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))),
% 299.62/189.82 inference(unit_resolution,[status(thm)],[990, 610])).
% 299.62/189.82 tff(992,plain,
% 299.62/189.82 (is_a_theorem(or(not(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(implies(Y!0, X!1))))))), or(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))), and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))),
% 299.62/189.82 inference(unit_resolution,[status(thm)],[991, 987, 970])).
% 299.62/189.82 tff(993,plain,
% 299.62/189.82 (is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))),
% 299.62/189.82 inference(modus_ponens,[status(thm)],[992, 936])).
% 299.62/189.82 tff(994,plain,
% 299.62/189.82 (is_a_theorem(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))) <=> is_a_theorem(implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.62/189.82 inference(monotonicity,[status(thm)],[836])).
% 299.62/189.82 tff(995,plain,
% 299.62/189.82 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))) <=> is_a_theorem(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.62/189.82 inference(symmetry,[status(thm)],[994])).
% 299.62/189.82 tff(996,plain,
% 299.62/189.82 (implies(or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))) = implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))),
% 299.62/189.82 inference(monotonicity,[status(thm)],[620])).
% 299.62/189.82 tff(997,plain,
% 299.62/189.82 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))))) <=> is_a_theorem(implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.62/189.82 inference(monotonicity,[status(thm)],[996])).
% 299.62/189.82 tff(998,plain,
% 299.62/189.82 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.62/189.82 inference(quant_inst,[status(thm)],[])).
% 299.62/189.82 tff(999,plain,
% 299.62/189.82 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), and(implies(X!1, Y!0), implies(Y!0, X!1))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.62/189.82 inference(unit_resolution,[status(thm)],[998, 518])).
% 299.62/189.82 tff(1000,plain,
% 299.62/189.82 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.62/189.82 inference(modus_ponens,[status(thm)],[999, 997])).
% 299.62/189.82 tff(1001,plain,
% 299.62/189.82 (is_a_theorem(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))),
% 299.62/189.82 inference(modus_ponens,[status(thm)],[1000, 995])).
% 299.62/189.82 tff(1002,plain,
% 299.62/189.82 (((~![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(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) | is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) | (~is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) | is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) | (~is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))))),
% 299.62/189.82 inference(rewrite,[status(thm)],[])).
% 299.62/189.82 tff(1003,plain,
% 299.62/189.82 ((is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) | (~is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))))) <=> ((~is_a_theorem(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) | is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) | (~is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))))),
% 299.62/189.83 inference(rewrite,[status(thm)],[])).
% 299.62/189.83 tff(1004,plain,
% 299.62/189.83 (((~![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(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) | (~is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) | is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) | (~is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))))))),
% 299.62/189.83 inference(monotonicity,[status(thm)],[1003])).
% 299.62/189.83 tff(1005,plain,
% 299.62/189.83 (((~![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(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) | (~is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) | is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) | (~is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))))),
% 299.62/189.83 inference(transitivity,[status(thm)],[1004, 1002])).
% 299.62/189.83 tff(1006,plain,
% 299.62/189.83 ((~![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(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) | (~is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))))))),
% 299.62/189.83 inference(quant_inst,[status(thm)],[])).
% 299.62/189.83 tff(1007,plain,
% 299.62/189.83 ((~![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(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))))) | is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) | (~is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))))),
% 299.62/189.83 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 299.62/189.83 tff(1008,plain,
% 299.62/189.83 (is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))))) | (~is_a_theorem(implies(or(not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1)))), not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))))),
% 299.62/189.83 inference(unit_resolution,[status(thm)],[1007, 610, 1001])).
% 299.62/189.83 tff(1009,plain,
% 299.62/189.83 (is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))),
% 299.62/189.83 inference(unit_resolution,[status(thm)],[1008, 993])).
% 299.62/189.83 tff(1010,plain,
% 299.62/189.83 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))) | (~is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))) | (~is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))))),
% 299.62/189.83 inference(rewrite,[status(thm)],[])).
% 299.62/189.83 tff(1011,plain,
% 299.62/189.83 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))) | (~is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))))),
% 299.62/189.83 inference(quant_inst,[status(thm)],[])).
% 299.62/189.83 tff(1012,plain,
% 299.62/189.83 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))) | (~is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))))),
% 299.62/189.84 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 299.62/189.84 tff(1013,plain,
% 299.62/189.84 (is_a_theorem(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))) | (~is_a_theorem(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))), not(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))), or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))))),
% 299.62/189.84 inference(unit_resolution,[status(thm)],[1012, 610])).
% 299.62/189.84 tff(1014,plain,
% 299.62/189.84 (is_a_theorem(or(and(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(implies(Y!0, X!1))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.62/189.84 inference(unit_resolution,[status(thm)],[1013, 1009, 925])).
% 299.62/189.84 tff(1015,plain,
% 299.62/189.84 (is_a_theorem(implies(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.62/189.84 inference(modus_ponens,[status(thm)],[1014, 918])).
% 299.62/189.84 tff(1016,plain,
% 299.62/189.84 (or(not(or(not(Y!0), not(not(X!1)))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1))))))) = or(not(or(not(Y!0), not(not(X!1)))), and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))),
% 299.62/189.84 inference(monotonicity,[status(thm)],[743])).
% 299.62/189.84 tff(1017,plain,
% 299.62/189.84 (or(not(or(not(Y!0), not(not(X!1)))), and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))) = or(not(or(not(Y!0), not(not(X!1)))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))))),
% 299.62/189.84 inference(symmetry,[status(thm)],[1016])).
% 299.62/189.84 tff(1018,plain,
% 299.62/189.84 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(Y!0), not(not(X!1)))), and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))) = not(and(not(not(or(not(Y!0), not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))),
% 299.62/189.84 inference(quant_inst,[status(thm)],[])).
% 299.62/189.84 tff(1019,plain,
% 299.62/189.84 (or(not(or(not(Y!0), not(not(X!1)))), and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))) = not(and(not(not(or(not(Y!0), not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))),
% 299.62/189.84 inference(unit_resolution,[status(thm)],[1018, 63])).
% 299.62/189.84 tff(1020,plain,
% 299.62/189.84 (not(and(not(not(or(not(Y!0), not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))) = or(not(or(not(Y!0), not(not(X!1)))), and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))),
% 299.62/189.84 inference(symmetry,[status(thm)],[1019])).
% 299.62/189.84 tff(1021,plain,
% 299.62/189.84 (not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))) = equiv(X!1, Y!0)),
% 299.62/189.84 inference(transitivity,[status(thm)],[706, 703, 95])).
% 299.62/189.84 tff(1022,plain,
% 299.62/189.84 (or(not(or(not(Y!0), X!1)), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))) = or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))),
% 299.62/189.84 inference(monotonicity,[status(thm)],[70, 1021])).
% 299.62/189.84 tff(1023,plain,
% 299.62/189.84 (or(not(or(not(Y!0), X!1)), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))) = implies(implies(Y!0, X!1), equiv(X!1, Y!0))),
% 299.62/189.84 inference(transitivity,[status(thm)],[1022, 619])).
% 299.62/189.84 tff(1024,plain,
% 299.62/189.84 (not(or(not(or(not(Y!0), X!1)), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))))) = not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))),
% 299.62/189.84 inference(monotonicity,[status(thm)],[1023])).
% 299.62/189.84 tff(1025,plain,
% 299.62/189.84 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(Y!0), X!1), or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))) = not(or(not(or(not(Y!0), X!1)), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))))))),
% 299.62/189.84 inference(quant_inst,[status(thm)],[])).
% 299.62/189.84 tff(1026,plain,
% 299.62/189.84 (and(or(not(Y!0), X!1), or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))) = not(or(not(or(not(Y!0), X!1)), not(or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))))),
% 299.62/189.84 inference(unit_resolution,[status(thm)],[1025, 125])).
% 299.62/189.84 tff(1027,plain,
% 299.62/189.84 (and(not(not(or(not(Y!0), not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))) = and(or(not(Y!0), X!1), or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))))),
% 299.62/189.84 inference(monotonicity,[status(thm)],[775, 693])).
% 299.62/189.84 tff(1028,plain,
% 299.62/189.84 (and(not(not(or(not(Y!0), not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))) = not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))),
% 299.62/189.84 inference(transitivity,[status(thm)],[1027, 1026, 1024])).
% 299.62/189.84 tff(1029,plain,
% 299.62/189.84 (not(and(not(not(or(not(Y!0), not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))) = not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.62/189.84 inference(monotonicity,[status(thm)],[1028])).
% 299.62/189.84 tff(1030,plain,
% 299.62/189.84 (not(not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) = not(and(not(not(or(not(Y!0), not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))),
% 299.62/189.84 inference(symmetry,[status(thm)],[1029])).
% 299.62/189.84 tff(1031,plain,
% 299.62/189.84 (not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))) = or(not(or(not(Y!0), not(not(X!1)))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))))),
% 299.62/189.84 inference(transitivity,[status(thm)],[714, 1030, 1020, 1017])).
% 299.62/189.84 tff(1032,plain,
% 299.62/189.84 (or(not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1))))) = or(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))), not(or(not(Y!0), not(not(X!1)))))),
% 299.62/189.84 inference(monotonicity,[status(thm)],[743])).
% 299.62/189.84 tff(1033,plain,
% 299.62/189.84 (or(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))), not(or(not(Y!0), not(not(X!1))))) = or(not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1)))))),
% 299.62/189.84 inference(symmetry,[status(thm)],[1032])).
% 299.62/189.84 tff(1034,plain,
% 299.62/189.84 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))), not(or(not(Y!0), not(not(X!1))))) = not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.84 inference(quant_inst,[status(thm)],[])).
% 299.62/189.84 tff(1035,plain,
% 299.62/189.84 (or(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))), not(or(not(Y!0), not(not(X!1))))) = not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.84 inference(unit_resolution,[status(thm)],[1034, 63])).
% 299.62/189.84 tff(1036,plain,
% 299.62/189.84 (not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))) = or(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))), not(or(not(Y!0), not(not(X!1)))))),
% 299.62/189.84 inference(symmetry,[status(thm)],[1035])).
% 299.62/189.84 tff(1037,plain,
% 299.62/189.84 (not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))) = or(not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1)))))),
% 299.62/189.84 inference(transitivity,[status(thm)],[1036, 1033])).
% 299.62/189.84 tff(1038,plain,
% 299.62/189.84 (implies(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))) = implies(or(not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1))))), or(not(or(not(Y!0), not(not(X!1)))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1))))))))),
% 299.62/189.84 inference(monotonicity,[status(thm)],[1037, 1031])).
% 299.62/189.84 tff(1039,plain,
% 299.62/189.84 (not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) = implies(or(not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1))))), or(not(or(not(Y!0), not(not(X!1)))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1))))))))),
% 299.62/189.84 inference(transitivity,[status(thm)],[898, 1038])).
% 299.62/189.84 tff(1040,plain,
% 299.62/189.84 (is_a_theorem(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))))) <=> is_a_theorem(implies(or(not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1))))), or(not(or(not(Y!0), not(not(X!1)))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))))))),
% 299.62/189.84 inference(monotonicity,[status(thm)],[1039])).
% 299.62/189.84 tff(1041,plain,
% 299.62/189.84 (is_a_theorem(implies(or(not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1))))), or(not(or(not(Y!0), not(not(X!1)))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1))))))))) <=> is_a_theorem(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))))),
% 299.62/189.84 inference(symmetry,[status(thm)],[1040])).
% 299.62/189.84 tff(1042,plain,
% 299.62/189.84 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1))))), or(not(or(not(Y!0), not(not(X!1)))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))))))),
% 299.62/189.84 inference(quant_inst,[status(thm)],[])).
% 299.62/189.84 tff(1043,plain,
% 299.62/189.84 (is_a_theorem(implies(or(not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1))))), or(not(or(not(Y!0), not(not(X!1)))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))))))),
% 299.62/189.84 inference(unit_resolution,[status(thm)],[1042, 518])).
% 299.62/189.84 tff(1044,plain,
% 299.62/189.84 (is_a_theorem(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))))),
% 299.62/189.84 inference(modus_ponens,[status(thm)],[1043, 1041])).
% 299.62/189.84 tff(1045,plain,
% 299.62/189.84 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) | (~is_a_theorem(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))))) | (~is_a_theorem(implies(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) | (~is_a_theorem(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))))) | (~is_a_theorem(implies(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))))),
% 299.62/189.84 inference(rewrite,[status(thm)],[])).
% 299.62/189.84 tff(1046,plain,
% 299.62/189.84 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) | (~is_a_theorem(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))))) | (~is_a_theorem(implies(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))))),
% 299.62/189.84 inference(quant_inst,[status(thm)],[])).
% 299.62/189.84 tff(1047,plain,
% 299.62/189.84 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) | (~is_a_theorem(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))))) | (~is_a_theorem(implies(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.84 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 299.62/189.84 tff(1048,plain,
% 299.62/189.84 (is_a_theorem(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) | (~is_a_theorem(implies(not(and(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))), and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.84 inference(unit_resolution,[status(thm)],[1047, 610, 1044])).
% 299.62/189.84 tff(1049,plain,
% 299.62/189.84 (is_a_theorem(and(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))), implies(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.84 inference(unit_resolution,[status(thm)],[1048, 1015])).
% 299.62/189.84 tff(1050,plain,
% 299.62/189.84 (is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))),
% 299.62/189.84 inference(modus_ponens,[status(thm)],[1049, 890])).
% 299.62/189.84 tff(1051,plain,
% 299.62/189.84 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) | (not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))) = not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) | (not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))) = not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))),
% 299.62/189.84 inference(rewrite,[status(thm)],[])).
% 299.62/189.84 tff(1052,plain,
% 299.62/189.84 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) | (not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))) = not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))),
% 299.62/189.84 inference(quant_inst,[status(thm)],[])).
% 299.62/189.84 tff(1053,plain,
% 299.62/189.84 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) | (not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))) = not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))),
% 299.62/189.84 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 299.62/189.84 tff(1054,plain,
% 299.62/189.84 ((~is_a_theorem(equiv(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))), not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))))) | (not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))) = not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))))))),
% 299.62/189.84 inference(unit_resolution,[status(thm)],[1053, 677])).
% 299.62/189.84 tff(1055,plain,
% 299.62/189.84 (not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))) = not(and(not(and(not(not(Y!0)), not(not(not(X!1))))), not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))))),
% 299.62/189.84 inference(unit_resolution,[status(thm)],[1054, 1050])).
% 299.62/189.84 tff(1056,plain,
% 299.62/189.84 (or(not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))), not(or(not(Y!0), not(not(X!1))))) = implies(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))),
% 299.62/189.84 inference(symmetry,[status(thm)],[759])).
% 299.62/189.84 tff(1057,plain,
% 299.62/189.84 (or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))) = or(not(or(not(not(not(Y!0))), not(not(not(not(X!1)))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1)))))))),
% 299.62/189.85 inference(transitivity,[status(thm)],[756, 1056, 761, 1055, 751, 750])).
% 299.62/189.85 tff(1058,plain,
% 299.62/189.85 (or(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))) = or(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))), or(not(or(not(not(not(Y!0))), not(not(not(not(X!1)))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(not(implies(Y!0, X!1))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1057])).
% 299.62/189.85 tff(1059,plain,
% 299.62/189.85 (or(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[763])).
% 299.62/189.85 tff(1060,plain,
% 299.62/189.85 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = not(and(not(not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1061,plain,
% 299.62/189.85 (or(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = not(and(not(not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.85 inference(unit_resolution,[status(thm)],[1060, 63])).
% 299.62/189.85 tff(1062,plain,
% 299.62/189.85 (not(and(not(not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))) = or(not(or(not(not(not(X!1))), not(not(not(not(Y!0)))))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1061])).
% 299.62/189.85 tff(1063,plain,
% 299.62/189.85 (and(or(not(X!1), not(not(Y!0))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))) = and(not(not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[733])).
% 299.62/189.85 tff(1064,plain,
% 299.62/189.85 (not(and(or(not(X!1), not(not(Y!0))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))) = not(and(not(not(or(not(not(not(X!1))), not(not(not(not(Y!0))))))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1063])).
% 299.62/189.85 tff(1065,plain,
% 299.62/189.85 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(X!1), not(not(Y!0))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = not(and(or(not(X!1), not(not(Y!0))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1066,plain,
% 299.62/189.85 (implies(or(not(X!1), not(not(Y!0))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = not(and(or(not(X!1), not(not(Y!0))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.85 inference(unit_resolution,[status(thm)],[1065, 41])).
% 299.62/189.85 tff(1067,plain,
% 299.62/189.85 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(X!1), not(not(Y!0))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(X!1), not(not(Y!0)))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1068,plain,
% 299.62/189.85 (implies(or(not(X!1), not(not(Y!0))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(X!1), not(not(Y!0)))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.85 inference(unit_resolution,[status(thm)],[1067, 20])).
% 299.62/189.85 tff(1069,plain,
% 299.62/189.85 (or(not(or(not(X!1), not(not(Y!0)))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = implies(or(not(X!1), not(not(Y!0))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1068])).
% 299.62/189.85 tff(1070,plain,
% 299.62/189.85 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(X!1), not(not(Y!0)))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1071,plain,
% 299.62/189.85 (or(not(or(not(X!1), not(not(Y!0)))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.85 inference(unit_resolution,[status(thm)],[1070, 63])).
% 299.62/189.85 tff(1072,plain,
% 299.62/189.85 (not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))) = or(not(or(not(X!1), not(not(Y!0)))), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1071])).
% 299.62/189.85 tff(1073,plain,
% 299.62/189.85 (and(or(not(X!1), Y!0), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))) = and(not(not(or(not(X!1), not(not(Y!0))))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[152])).
% 299.62/189.85 tff(1074,plain,
% 299.62/189.85 (not(and(or(not(X!1), Y!0), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1073])).
% 299.62/189.85 tff(1075,plain,
% 299.62/189.85 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(X!1), Y!0), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = not(and(or(not(X!1), Y!0), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1076,plain,
% 299.62/189.85 (implies(or(not(X!1), Y!0), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = not(and(or(not(X!1), Y!0), not(not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.85 inference(unit_resolution,[status(thm)],[1075, 41])).
% 299.62/189.85 tff(1077,plain,
% 299.62/189.85 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(X!1), Y!0), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(X!1), Y!0)), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1078,plain,
% 299.62/189.85 (implies(or(not(X!1), Y!0), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(X!1), Y!0)), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.85 inference(unit_resolution,[status(thm)],[1077, 20])).
% 299.62/189.85 tff(1079,plain,
% 299.62/189.85 (or(not(or(not(X!1), Y!0)), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))) = implies(or(not(X!1), Y!0), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1078])).
% 299.62/189.85 tff(1080,plain,
% 299.62/189.85 (or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))) = not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.85 inference(transitivity,[status(thm)],[756, 1056, 761])).
% 299.62/189.85 tff(1081,plain,
% 299.62/189.85 (or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))) = or(not(or(not(X!1), Y!0)), not(and(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[139, 1080])).
% 299.62/189.85 tff(1082,plain,
% 299.62/189.85 (or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))) = not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))),
% 299.62/189.85 inference(transitivity,[status(thm)],[1081, 1079, 1076, 1074, 1072, 1069, 1066, 1064, 1062, 1059, 1058, 749, 738, 736, 725, 722, 720, 718, 688, 685, 683])).
% 299.62/189.85 tff(1083,plain,
% 299.62/189.85 (is_a_theorem(or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) <=> is_a_theorem(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1082])).
% 299.62/189.85 tff(1084,plain,
% 299.62/189.85 (is_a_theorem(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))) <=> is_a_theorem(or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1083])).
% 299.62/189.85 tff(1085,plain,
% 299.62/189.85 ((~is_a_theorem(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))) <=> (~is_a_theorem(or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1084])).
% 299.62/189.85 tff(1086,plain,
% 299.62/189.85 (or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))),
% 299.62/189.85 inference(transitivity,[status(thm)],[159, 259, 256, 253, 251, 244])).
% 299.62/189.85 tff(1087,plain,
% 299.62/189.85 (is_a_theorem(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))) <=> is_a_theorem(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1086])).
% 299.62/189.85 tff(1088,plain,
% 299.62/189.85 ((~is_a_theorem(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))) <=> (~is_a_theorem(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0)))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1087])).
% 299.62/189.85 tff(1089,plain,
% 299.62/189.85 (and(not(not(or(not(X!1), not(not(Y!0))))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))) = and(or(not(X!1), Y!0), and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[716, 181])).
% 299.62/189.85 tff(1090,plain,
% 299.62/189.85 (and(not(not(or(not(X!1), not(not(Y!0))))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))) = not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))),
% 299.62/189.85 inference(transitivity,[status(thm)],[1089, 175])).
% 299.62/189.85 tff(1091,plain,
% 299.62/189.85 (not(and(not(not(or(not(X!1), not(not(Y!0))))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))) = not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1090])).
% 299.62/189.85 tff(1092,plain,
% 299.62/189.85 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(X!1), not(not(Y!0)))), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1093,plain,
% 299.62/189.85 (or(not(or(not(X!1), not(not(Y!0)))), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))),
% 299.62/189.85 inference(unit_resolution,[status(thm)],[1092, 63])).
% 299.62/189.85 tff(1094,plain,
% 299.62/189.85 (or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = or(not(or(not(X!1), not(not(Y!0)))), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[166])).
% 299.62/189.85 tff(1095,plain,
% 299.62/189.85 (or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) = not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))),
% 299.62/189.85 inference(transitivity,[status(thm)],[1094, 1093, 1091, 193])).
% 299.62/189.85 tff(1096,plain,
% 299.62/189.85 (implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))) = implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1095])).
% 299.62/189.85 tff(1097,plain,
% 299.62/189.85 (implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) = implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1096])).
% 299.62/189.85 tff(1098,plain,
% 299.62/189.85 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))) <=> is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1097])).
% 299.62/189.85 tff(1099,plain,
% 299.62/189.85 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))) <=> is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1098])).
% 299.62/189.85 tff(1100,plain,
% 299.62/189.85 ((~![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(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1101,plain,
% 299.62/189.85 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.85 inference(unit_resolution,[status(thm)],[1100, 570])).
% 299.62/189.85 tff(1102,plain,
% 299.62/189.85 (is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))),
% 299.62/189.85 inference(modus_ponens,[status(thm)],[1101, 1099])).
% 299.62/189.85 tff(1103,plain,
% 299.62/189.85 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))), not(or(not(X!1), not(not(Y!0))))) = not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0))))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1104,plain,
% 299.62/189.85 (or(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))), not(or(not(X!1), not(not(Y!0))))) = not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))),
% 299.62/189.85 inference(unit_resolution,[status(thm)],[1103, 63])).
% 299.62/189.85 tff(1105,plain,
% 299.62/189.85 (not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0))))))) = or(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))), not(or(not(X!1), not(not(Y!0)))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1104])).
% 299.62/189.85 tff(1106,plain,
% 299.62/189.85 (not(and(not(not(or(not(X!1), not(not(Y!0))))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))) = or(not(or(not(X!1), not(not(Y!0)))), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1093])).
% 299.62/189.85 tff(1107,plain,
% 299.62/189.85 (not(not(or(not(or(not(X!1), Y!0)), not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1091])).
% 299.62/189.85 tff(1108,plain,
% 299.62/189.85 (not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))) = or(not(or(not(X!1), not(not(Y!0)))), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))),
% 299.62/189.85 inference(transitivity,[status(thm)],[194, 1107, 1106])).
% 299.62/189.85 tff(1109,plain,
% 299.62/189.85 (implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))) = implies(or(not(or(not(X!1), not(not(Y!0)))), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), or(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))), not(or(not(X!1), not(not(Y!0))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1108, 1105])).
% 299.62/189.85 tff(1110,plain,
% 299.62/189.85 (is_a_theorem(implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0))))))))) <=> is_a_theorem(implies(or(not(or(not(X!1), not(not(Y!0)))), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), or(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))), not(or(not(X!1), not(not(Y!0)))))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1109])).
% 299.62/189.85 tff(1111,plain,
% 299.62/189.85 (is_a_theorem(implies(or(not(or(not(X!1), not(not(Y!0)))), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), or(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))), not(or(not(X!1), not(not(Y!0))))))) <=> is_a_theorem(implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1110])).
% 299.62/189.85 tff(1112,plain,
% 299.62/189.85 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(X!1), not(not(Y!0)))), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), or(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))), not(or(not(X!1), not(not(Y!0)))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1113,plain,
% 299.62/189.85 (is_a_theorem(implies(or(not(or(not(X!1), not(not(Y!0)))), or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), or(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))), not(or(not(X!1), not(not(Y!0)))))))),
% 299.62/189.85 inference(unit_resolution,[status(thm)],[1112, 518])).
% 299.62/189.85 tff(1114,plain,
% 299.62/189.85 (is_a_theorem(implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))))),
% 299.62/189.85 inference(modus_ponens,[status(thm)],[1113, 1111])).
% 299.62/189.85 tff(1115,plain,
% 299.62/189.85 (not(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))) = not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[181])).
% 299.62/189.85 tff(1116,plain,
% 299.62/189.85 (not(and(implies(Y!0, X!1), not(equiv(X!1, Y!0)))) = not(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1115])).
% 299.62/189.85 tff(1117,plain,
% 299.62/189.85 (or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)) = not(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))),
% 299.62/189.85 inference(transitivity,[status(thm)],[619, 313, 1116])).
% 299.62/189.85 tff(1118,plain,
% 299.62/189.85 (or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))) = or(not(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))), not(or(not(X!1), not(not(Y!0)))))),
% 299.62/189.85 inference(monotonicity,[status(thm)],[1117])).
% 299.62/189.85 tff(1119,plain,
% 299.62/189.85 (or(not(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))), not(or(not(X!1), not(not(Y!0))))) = or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0)))))),
% 299.62/189.85 inference(symmetry,[status(thm)],[1118])).
% 299.62/189.85 tff(1120,plain,
% 299.62/189.85 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(or(not(X!1), not(not(Y!0))))) = or(not(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))), not(or(not(X!1), not(not(Y!0))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1121,plain,
% 299.62/189.85 (implies(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(or(not(X!1), not(not(Y!0))))) = or(not(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))), not(or(not(X!1), not(not(Y!0)))))),
% 299.62/189.85 inference(unit_resolution,[status(thm)],[1120, 20])).
% 299.62/189.85 tff(1122,plain,
% 299.62/189.85 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(or(not(X!1), not(not(Y!0))))) = not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0))))))))),
% 299.62/189.85 inference(quant_inst,[status(thm)],[])).
% 299.62/189.85 tff(1123,plain,
% 299.62/189.85 (implies(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(or(not(X!1), not(not(Y!0))))) = not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1122, 41])).
% 299.62/189.86 tff(1124,plain,
% 299.62/189.86 (not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0))))))) = implies(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(or(not(X!1), not(not(Y!0)))))),
% 299.62/189.86 inference(symmetry,[status(thm)],[1123])).
% 299.62/189.86 tff(1125,plain,
% 299.62/189.86 (not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0))))))) = or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0)))))),
% 299.62/189.86 inference(transitivity,[status(thm)],[1124, 1121, 1119])).
% 299.62/189.86 tff(1126,plain,
% 299.62/189.86 (is_a_theorem(not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))) <=> is_a_theorem(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1125])).
% 299.62/189.86 tff(1127,plain,
% 299.62/189.86 (is_a_theorem(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0)))))) <=> is_a_theorem(not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0))))))))),
% 299.62/189.86 inference(symmetry,[status(thm)],[1126])).
% 299.62/189.86 tff(1128,plain,
% 299.62/189.86 ((~is_a_theorem(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))))) <=> (~is_a_theorem(not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1127])).
% 299.62/189.86 tff(1129,plain,
% 299.62/189.86 (and(not(and(X!1, not(Y!0))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))) = and(implies(X!1, Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[101, 840])).
% 299.62/189.86 tff(1130,plain,
% 299.62/189.86 (not(and(not(and(X!1, not(Y!0))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) = not(and(implies(X!1, Y!0), not(implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1129])).
% 299.62/189.86 tff(1131,plain,
% 299.62/189.86 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(X!1, not(Y!0)), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = not(and(not(and(X!1, not(Y!0))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))))),
% 299.62/189.86 inference(quant_inst,[status(thm)],[])).
% 299.62/189.86 tff(1132,plain,
% 299.62/189.86 (or(and(X!1, not(Y!0)), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = not(and(not(and(X!1, not(Y!0))), not(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1131, 63])).
% 299.62/189.86 tff(1133,plain,
% 299.62/189.86 (or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = or(and(X!1, not(Y!0)), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[131])).
% 299.62/189.86 tff(1134,plain,
% 299.62/189.86 (or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))) = or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))),
% 299.62/189.86 inference(transitivity,[status(thm)],[1133, 1132, 1130, 384, 381])).
% 299.62/189.86 tff(1135,plain,
% 299.62/189.86 (implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))) = implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1134])).
% 299.62/189.86 tff(1136,plain,
% 299.62/189.86 (is_a_theorem(implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0))))) <=> is_a_theorem(implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1135])).
% 299.62/189.86 tff(1137,plain,
% 299.62/189.86 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.62/189.86 inference(quant_inst,[status(thm)],[])).
% 299.62/189.86 tff(1138,plain,
% 299.62/189.86 (is_a_theorem(implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(or(not(X!1), not(not(Y!0)))), or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1137, 518])).
% 299.62/189.86 tff(1139,plain,
% 299.62/189.86 (is_a_theorem(implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1138, 1136])).
% 299.62/189.86 tff(1140,plain,
% 299.62/189.86 (or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))) = implies(implies(X!1, Y!0), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))),
% 299.62/189.86 inference(symmetry,[status(thm)],[381])).
% 299.62/189.86 tff(1141,plain,
% 299.62/189.86 (is_a_theorem(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) <=> is_a_theorem(implies(implies(X!1, Y!0), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1140])).
% 299.62/189.86 tff(1142,plain,
% 299.62/189.86 (is_a_theorem(implies(implies(X!1, Y!0), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) <=> is_a_theorem(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.62/189.86 inference(symmetry,[status(thm)],[1141])).
% 299.62/189.86 tff(1143,plain,
% 299.62/189.86 ((~is_a_theorem(implies(implies(X!1, Y!0), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))) <=> (~is_a_theorem(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1142])).
% 299.62/189.86 tff(1144,plain,
% 299.62/189.86 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y)))))),
% 299.62/189.86 inference(rewrite,[status(thm)],[])).
% 299.62/189.86 tff(1145,plain,
% 299.62/189.86 (($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y)))))),
% 299.62/189.86 inference(rewrite,[status(thm)],[])).
% 299.62/189.86 tff(1146,axiom,(~equivalence_3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hilbert_equivalence_3')).
% 299.62/189.86 tff(1147,plain,
% 299.62/189.86 (equivalence_3 <=> $false),
% 299.62/189.86 inference(iff_false,[status(thm)],[1146])).
% 299.62/189.86 tff(1148,plain,
% 299.62/189.86 ((equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))) <=> ($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y)))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1147])).
% 299.62/189.86 tff(1149,plain,
% 299.62/189.86 ((equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y)))))),
% 299.62/189.86 inference(transitivity,[status(thm)],[1148, 1145])).
% 299.62/189.86 tff(1150,plain,
% 299.62/189.86 ((equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))) <=> (equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y)))))),
% 299.62/189.86 inference(rewrite,[status(thm)],[])).
% 299.62/189.86 tff(1151,axiom,(equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','equivalence_3')).
% 299.62/189.86 tff(1152,plain,
% 299.62/189.86 (equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 299.62/189.86 tff(1153,plain,
% 299.62/189.86 (equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1152, 1150])).
% 299.62/189.86 tff(1154,plain,
% 299.62/189.86 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1153, 1149])).
% 299.62/189.86 tff(1155,plain,
% 299.62/189.86 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1154, 1144])).
% 299.62/189.86 tff(1156,plain,
% 299.62/189.86 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1155, 1144])).
% 299.62/189.86 tff(1157,plain,
% 299.62/189.86 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1156, 1144])).
% 299.62/189.86 tff(1158,plain,
% 299.62/189.86 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1157, 1144])).
% 299.62/189.86 tff(1159,plain,
% 299.62/189.86 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1158, 1144])).
% 299.62/189.86 tff(1160,plain,
% 299.62/189.86 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1159, 1144])).
% 299.62/189.86 tff(1161,plain,(
% 299.62/189.86 ~is_a_theorem(implies(implies(X!1, Y!0), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.62/189.86 inference(skolemize,[status(sab)],[1160])).
% 299.62/189.86 tff(1162,plain,
% 299.62/189.86 (~is_a_theorem(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1161, 1143])).
% 299.62/189.86 tff(1163,plain,
% 299.62/189.86 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) | (~is_a_theorem(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))))) | (~is_a_theorem(implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) | (~is_a_theorem(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))))) | (~is_a_theorem(implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.62/189.86 inference(rewrite,[status(thm)],[])).
% 299.62/189.86 tff(1164,plain,
% 299.62/189.86 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) | (~is_a_theorem(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))))) | (~is_a_theorem(implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))))))),
% 299.62/189.86 inference(quant_inst,[status(thm)],[])).
% 299.62/189.86 tff(1165,plain,
% 299.62/189.86 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0)))) | (~is_a_theorem(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))))) | (~is_a_theorem(implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 299.62/189.86 tff(1166,plain,
% 299.62/189.86 ((~is_a_theorem(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))))) | (~is_a_theorem(implies(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))), or(not(implies(X!1, Y!0)), implies(implies(Y!0, X!1), equiv(X!1, Y!0))))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1165, 610, 1162])).
% 299.62/189.86 tff(1167,plain,
% 299.62/189.86 (~is_a_theorem(or(or(not(implies(Y!0, X!1)), equiv(X!1, Y!0)), not(or(not(X!1), not(not(Y!0))))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1166, 1139])).
% 299.62/189.86 tff(1168,plain,
% 299.62/189.86 (~is_a_theorem(not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0))))))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1167, 1128])).
% 299.62/189.86 tff(1169,plain,
% 299.62/189.86 (((~![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(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))) | (~is_a_theorem(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))))))) <=> ((~![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(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))) | (~is_a_theorem(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))))))),
% 299.62/189.86 inference(rewrite,[status(thm)],[])).
% 299.62/189.86 tff(1170,plain,
% 299.62/189.86 ((~![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(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))) | (~is_a_theorem(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))))))),
% 299.62/189.86 inference(quant_inst,[status(thm)],[])).
% 299.62/189.86 tff(1171,plain,
% 299.62/189.86 ((~![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(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))) | (~is_a_theorem(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0))))))))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 299.62/189.86 tff(1172,plain,
% 299.62/189.86 (is_a_theorem(not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0)))))))) | (~is_a_theorem(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))) | (~is_a_theorem(implies(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))), not(and(not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))), not(not(or(not(X!1), not(not(Y!0))))))))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1171, 610])).
% 299.62/189.86 tff(1173,plain,
% 299.62/189.86 (~is_a_theorem(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1172, 1168, 1114])).
% 299.62/189.86 tff(1174,plain,
% 299.62/189.86 (((~![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(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))) | (~is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))) | (~is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))))),
% 299.62/189.86 inference(rewrite,[status(thm)],[])).
% 299.62/189.86 tff(1175,plain,
% 299.62/189.86 ((~![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(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))) | (~is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))))))),
% 299.62/189.86 inference(quant_inst,[status(thm)],[])).
% 299.62/189.86 tff(1176,plain,
% 299.62/189.86 ((~![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(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))) | (~is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 299.62/189.86 tff(1177,plain,
% 299.62/189.86 (is_a_theorem(not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0)))))))) | (~is_a_theorem(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))) | (~is_a_theorem(implies(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))), not(and(not(and(not(not(X!1)), not(Y!0))), not(or(not(or(not(Y!0), X!1)), not(not(equiv(X!1, Y!0))))))))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1176, 610])).
% 299.62/189.86 tff(1178,plain,
% 299.62/189.86 (~is_a_theorem(or(not(implies(Y!0, X!1)), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1177, 1173, 1102])).
% 299.62/189.86 tff(1179,plain,
% 299.62/189.86 (~is_a_theorem(not(and(not(and(not(not(not(not(Y!0)))), not(not(not(X!1))))), not(or(not(not(not(implies(X!1, Y!0)))), not(not(equiv(X!1, Y!0))))))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1178, 1088])).
% 299.62/189.86 tff(1180,plain,
% 299.62/189.86 (~is_a_theorem(or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.86 inference(modus_ponens,[status(thm)],[1179, 1085])).
% 299.62/189.86 tff(1181,plain,
% 299.62/189.86 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(equiv(X!1, Y!0))) = not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))))),
% 299.62/189.86 inference(quant_inst,[status(thm)],[])).
% 299.62/189.86 tff(1182,plain,
% 299.62/189.86 (or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(equiv(X!1, Y!0))) = not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1181, 63])).
% 299.62/189.86 tff(1183,plain,
% 299.62/189.86 (and(or(not(X!1), Y!0), not(and(Y!0, not(X!1)))) = and(implies(X!1, Y!0), implies(Y!0, X!1))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[137, 98])).
% 299.62/189.86 tff(1184,plain,
% 299.62/189.86 (and(or(not(X!1), Y!0), not(and(Y!0, not(X!1)))) = equiv(X!1, Y!0)),
% 299.62/189.86 inference(transitivity,[status(thm)],[1183, 95])).
% 299.62/189.86 tff(1185,plain,
% 299.62/189.86 (not(and(or(not(X!1), Y!0), not(and(Y!0, not(X!1))))) = not(equiv(X!1, Y!0))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1184])).
% 299.62/189.86 tff(1186,plain,
% 299.62/189.86 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(X!1), Y!0), and(Y!0, not(X!1))) = not(and(or(not(X!1), Y!0), not(and(Y!0, not(X!1))))))),
% 299.62/189.86 inference(quant_inst,[status(thm)],[])).
% 299.62/189.86 tff(1187,plain,
% 299.62/189.86 (implies(or(not(X!1), Y!0), and(Y!0, not(X!1))) = not(and(or(not(X!1), Y!0), not(and(Y!0, not(X!1)))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1186, 41])).
% 299.62/189.86 tff(1188,plain,
% 299.62/189.86 (implies(or(not(X!1), Y!0), not(or(not(Y!0), not(not(X!1))))) = implies(or(not(X!1), Y!0), and(Y!0, not(X!1)))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[128])).
% 299.62/189.86 tff(1189,plain,
% 299.62/189.86 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(X!1), Y!0), not(or(not(Y!0), not(not(X!1))))) = or(not(or(not(X!1), Y!0)), not(or(not(Y!0), not(not(X!1))))))),
% 299.62/189.86 inference(quant_inst,[status(thm)],[])).
% 299.62/189.86 tff(1190,plain,
% 299.62/189.86 (implies(or(not(X!1), Y!0), not(or(not(Y!0), not(not(X!1))))) = or(not(or(not(X!1), Y!0)), not(or(not(Y!0), not(not(X!1)))))),
% 299.62/189.86 inference(unit_resolution,[status(thm)],[1189, 20])).
% 299.62/189.86 tff(1191,plain,
% 299.62/189.86 (or(not(or(not(X!1), Y!0)), not(or(not(Y!0), not(not(X!1))))) = implies(or(not(X!1), Y!0), not(or(not(Y!0), not(not(X!1)))))),
% 299.62/189.86 inference(symmetry,[status(thm)],[1190])).
% 299.62/189.86 tff(1192,plain,
% 299.62/189.86 (or(not(implies(X!1, Y!0)), not(or(not(Y!0), not(not(X!1))))) = or(not(or(not(X!1), Y!0)), not(or(not(Y!0), not(not(X!1)))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[139])).
% 299.62/189.86 tff(1193,plain,
% 299.62/189.86 (or(not(implies(X!1, Y!0)), not(or(not(Y!0), not(not(X!1))))) = not(equiv(X!1, Y!0))),
% 299.62/189.86 inference(transitivity,[status(thm)],[1192, 1191, 1188, 1187, 1185])).
% 299.62/189.86 tff(1194,plain,
% 299.62/189.86 (or(and(implies(X!1, Y!0), implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(Y!0), not(not(X!1)))))) = or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(equiv(X!1, Y!0)))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1193])).
% 299.62/189.86 tff(1195,plain,
% 299.62/189.86 (or(and(implies(X!1, Y!0), implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(Y!0), not(not(X!1)))))) = not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))),
% 299.62/189.86 inference(transitivity,[status(thm)],[1194, 1182])).
% 299.62/189.86 tff(1196,plain,
% 299.62/189.86 (implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(Y!0), not(not(X!1)))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) = implies(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1195])).
% 299.62/189.86 tff(1197,plain,
% 299.62/189.86 (is_a_theorem(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(Y!0), not(not(X!1)))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))) <=> is_a_theorem(implies(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.86 inference(monotonicity,[status(thm)],[1196])).
% 299.62/189.86 tff(1198,plain,
% 299.62/189.86 ((~![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(X!1, Y!0), implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(Y!0), not(not(X!1)))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.86 inference(quant_inst,[status(thm)],[])).
% 299.62/189.86 tff(1199,plain,
% 299.62/189.86 (is_a_theorem(implies(or(and(implies(X!1, Y!0), implies(Y!0, X!1)), or(not(implies(X!1, Y!0)), not(or(not(Y!0), not(not(X!1)))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.87 inference(unit_resolution,[status(thm)],[1198, 570])).
% 299.62/189.87 tff(1200,plain,
% 299.62/189.87 (is_a_theorem(implies(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.87 inference(modus_ponens,[status(thm)],[1199, 1197])).
% 299.62/189.87 tff(1201,plain,
% 299.62/189.87 (or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))) = or(not(implies(X!1, Y!0)), not(implies(Y!0, X!1)))),
% 299.62/189.87 inference(symmetry,[status(thm)],[689])).
% 299.62/189.87 tff(1202,plain,
% 299.62/189.87 (or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1))) = or(not(or(not(X!1), Y!0)), not(implies(Y!0, X!1)))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[70])).
% 299.62/189.87 tff(1203,plain,
% 299.62/189.87 (or(not(or(not(X!1), Y!0)), not(implies(Y!0, X!1))) = or(not(or(not(X!1), Y!0)), not(or(not(Y!0), X!1)))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1202])).
% 299.62/189.87 tff(1204,plain,
% 299.62/189.87 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(X!1), Y!0), not(implies(Y!0, X!1))) = or(not(or(not(X!1), Y!0)), not(implies(Y!0, X!1))))),
% 299.62/189.87 inference(quant_inst,[status(thm)],[])).
% 299.62/189.87 tff(1205,plain,
% 299.62/189.87 (implies(or(not(X!1), Y!0), not(implies(Y!0, X!1))) = or(not(or(not(X!1), Y!0)), not(implies(Y!0, X!1)))),
% 299.62/189.87 inference(unit_resolution,[status(thm)],[1204, 20])).
% 299.62/189.87 tff(1206,plain,
% 299.62/189.87 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(or(not(X!1), Y!0), not(implies(Y!0, X!1))) = not(and(or(not(X!1), Y!0), not(not(implies(Y!0, X!1))))))),
% 299.62/189.87 inference(quant_inst,[status(thm)],[])).
% 299.62/189.87 tff(1207,plain,
% 299.62/189.87 (implies(or(not(X!1), Y!0), not(implies(Y!0, X!1))) = not(and(or(not(X!1), Y!0), not(not(implies(Y!0, X!1)))))),
% 299.62/189.87 inference(unit_resolution,[status(thm)],[1206, 41])).
% 299.62/189.87 tff(1208,plain,
% 299.62/189.87 (not(and(or(not(X!1), Y!0), not(not(implies(Y!0, X!1))))) = implies(or(not(X!1), Y!0), not(implies(Y!0, X!1)))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1207])).
% 299.62/189.87 tff(1209,plain,
% 299.62/189.87 (and(not(not(or(not(X!1), not(not(Y!0))))), not(not(implies(Y!0, X!1)))) = and(or(not(X!1), Y!0), not(not(implies(Y!0, X!1))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[716])).
% 299.62/189.87 tff(1210,plain,
% 299.62/189.87 (not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(implies(Y!0, X!1))))) = not(and(or(not(X!1), Y!0), not(not(implies(Y!0, X!1)))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1209])).
% 299.62/189.87 tff(1211,plain,
% 299.62/189.87 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(X!1), not(not(Y!0)))), not(implies(Y!0, X!1))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(implies(Y!0, X!1))))))),
% 299.62/189.87 inference(quant_inst,[status(thm)],[])).
% 299.62/189.87 tff(1212,plain,
% 299.62/189.87 (or(not(or(not(X!1), not(not(Y!0)))), not(implies(Y!0, X!1))) = not(and(not(not(or(not(X!1), not(not(Y!0))))), not(not(implies(Y!0, X!1)))))),
% 299.62/189.87 inference(unit_resolution,[status(thm)],[1211, 63])).
% 299.62/189.87 tff(1213,plain,
% 299.62/189.87 (or(not(or(not(X!1), not(not(Y!0)))), not(implies(Y!0, X!1))) = not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))),
% 299.62/189.87 inference(transitivity,[status(thm)],[1212, 1210, 1208, 1205, 1203, 1201, 691])).
% 299.62/189.87 tff(1214,plain,
% 299.62/189.87 (implies(or(not(or(not(X!1), not(not(Y!0)))), not(implies(Y!0, X!1))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))) = implies(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(equiv(X!1, Y!0)))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1213, 133])).
% 299.62/189.87 tff(1215,plain,
% 299.62/189.87 (implies(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(equiv(X!1, Y!0))) = implies(or(not(or(not(X!1), not(not(Y!0)))), not(implies(Y!0, X!1))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1214])).
% 299.62/189.87 tff(1216,plain,
% 299.62/189.87 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(equiv(X!1, Y!0))) = or(not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))), not(equiv(X!1, Y!0))))),
% 299.62/189.87 inference(quant_inst,[status(thm)],[])).
% 299.62/189.87 tff(1217,plain,
% 299.62/189.87 (implies(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(equiv(X!1, Y!0))) = or(not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))), not(equiv(X!1, Y!0)))),
% 299.62/189.87 inference(unit_resolution,[status(thm)],[1216, 20])).
% 299.62/189.87 tff(1218,plain,
% 299.62/189.87 (or(not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))), not(equiv(X!1, Y!0))) = implies(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1))))), not(equiv(X!1, Y!0)))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1217])).
% 299.62/189.87 tff(1219,plain,
% 299.62/189.87 (not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))) = and(implies(X!1, Y!0), implies(Y!0, X!1))),
% 299.62/189.87 inference(transitivity,[status(thm)],[752, 706, 703])).
% 299.62/189.87 tff(1220,plain,
% 299.62/189.87 (or(not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))), not(equiv(X!1, Y!0))) = or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(equiv(X!1, Y!0)))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1219])).
% 299.62/189.87 tff(1221,plain,
% 299.62/189.87 (or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(equiv(X!1, Y!0))) = or(not(not(and(not(not(implies(X!1, Y!0))), not(not(implies(Y!0, X!1)))))), not(equiv(X!1, Y!0)))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1220])).
% 299.62/189.87 tff(1222,plain,
% 299.62/189.87 (not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))) = or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(equiv(X!1, Y!0)))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1182])).
% 299.62/189.87 tff(1223,plain,
% 299.62/189.87 (not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))) = implies(or(not(or(not(X!1), not(not(Y!0)))), not(implies(Y!0, X!1))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))),
% 299.62/189.87 inference(transitivity,[status(thm)],[1222, 1221, 1218, 1215])).
% 299.62/189.87 tff(1224,plain,
% 299.62/189.87 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))) = not(and(not(implies(Y!0, X!1)), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.87 inference(quant_inst,[status(thm)],[])).
% 299.62/189.87 tff(1225,plain,
% 299.62/189.87 (implies(not(implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))) = not(and(not(implies(Y!0, X!1)), not(not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.87 inference(unit_resolution,[status(thm)],[1224, 41])).
% 299.62/189.87 tff(1226,plain,
% 299.62/189.87 (not(and(not(implies(Y!0, X!1)), not(not(or(not(Y!0), not(not(X!1))))))) = implies(not(implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1225])).
% 299.62/189.87 tff(1227,plain,
% 299.62/189.87 (and(not(implies(Y!0, X!1)), not(not(or(not(Y!0), not(not(X!1)))))) = and(not(or(not(Y!0), X!1)), not(not(or(not(Y!0), not(not(X!1))))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[71])).
% 299.62/189.87 tff(1228,plain,
% 299.62/189.87 (not(and(not(implies(Y!0, X!1)), not(not(or(not(Y!0), not(not(X!1))))))) = not(and(not(or(not(Y!0), X!1)), not(not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1227])).
% 299.62/189.87 tff(1229,plain,
% 299.62/189.87 (not(and(not(or(not(Y!0), X!1)), not(not(or(not(Y!0), not(not(X!1))))))) = not(and(not(implies(Y!0, X!1)), not(not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1228])).
% 299.62/189.87 tff(1230,plain,
% 299.62/189.87 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))) = not(and(not(or(not(Y!0), X!1)), not(not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.87 inference(quant_inst,[status(thm)],[])).
% 299.62/189.87 tff(1231,plain,
% 299.62/189.87 (or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))) = not(and(not(or(not(Y!0), X!1)), not(not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.87 inference(unit_resolution,[status(thm)],[1230, 63])).
% 299.62/189.87 tff(1232,plain,
% 299.62/189.87 (or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))) = implies(not(implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))),
% 299.62/189.87 inference(transitivity,[status(thm)],[1231, 1229, 1226])).
% 299.62/189.87 tff(1233,plain,
% 299.62/189.87 (implies(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))) = implies(implies(not(implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), implies(or(not(or(not(X!1), not(not(Y!0)))), not(implies(Y!0, X!1))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1232, 1223])).
% 299.62/189.87 tff(1234,plain,
% 299.62/189.87 (is_a_theorem(implies(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))))) <=> is_a_theorem(implies(implies(not(implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), implies(or(not(or(not(X!1), not(not(Y!0)))), not(implies(Y!0, X!1))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1233])).
% 299.62/189.87 tff(1235,plain,
% 299.62/189.87 (is_a_theorem(implies(implies(not(implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), implies(or(not(or(not(X!1), not(not(Y!0)))), not(implies(Y!0, X!1))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))) <=> is_a_theorem(implies(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1234])).
% 299.62/189.87 tff(1236,plain,
% 299.62/189.87 (^[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)))))),
% 299.62/189.87 inference(bind,[status(th)],[])).
% 299.62/189.87 tff(1237,plain,
% 299.62/189.87 (![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))))),
% 299.62/189.87 inference(quant_intro,[status(thm)],[1236])).
% 299.62/189.87 tff(1238,plain,
% 299.62/189.87 (![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: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 299.62/189.87 inference(rewrite,[status(thm)],[])).
% 299.62/189.87 tff(1239,plain,
% 299.62/189.87 (($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))))),
% 299.62/189.87 inference(rewrite,[status(thm)],[])).
% 299.62/189.87 tff(1240,axiom,(r5), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r5')).
% 299.62/189.87 tff(1241,plain,
% 299.62/189.87 (r5 <=> $true),
% 299.62/189.87 inference(iff_true,[status(thm)],[1240])).
% 299.62/189.87 tff(1242,plain,
% 299.62/189.87 ((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)))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1241])).
% 299.62/189.87 tff(1243,plain,
% 299.62/189.87 ((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))))),
% 299.62/189.87 inference(transitivity,[status(thm)],[1242, 1239])).
% 299.62/189.87 tff(1244,plain,
% 299.62/189.87 ((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)))))),
% 299.62/189.87 inference(rewrite,[status(thm)],[])).
% 299.62/189.87 tff(1245,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/sandbox/benchmark/Axioms/LCL006+0.ax','r5')).
% 299.62/189.87 tff(1246,plain,
% 299.62/189.87 (r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 299.62/189.87 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 299.62/189.87 tff(1247,plain,
% 299.62/189.87 (r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 299.62/189.87 inference(modus_ponens,[status(thm)],[1246, 1244])).
% 299.62/189.87 tff(1248,plain,
% 299.62/189.87 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 299.62/189.87 inference(modus_ponens,[status(thm)],[1247, 1243])).
% 299.62/189.87 tff(1249,plain,
% 299.62/189.87 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 299.62/189.87 inference(modus_ponens,[status(thm)],[1248, 1238])).
% 299.62/189.87 tff(1250,plain,(
% 299.62/189.87 ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 299.62/189.87 inference(skolemize,[status(sab)],[1249])).
% 299.62/189.87 tff(1251,plain,
% 299.62/189.87 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 299.62/189.87 inference(modus_ponens,[status(thm)],[1250, 1237])).
% 299.62/189.87 tff(1252,plain,
% 299.62/189.87 ((~![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(implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), implies(or(not(or(not(X!1), not(not(Y!0)))), not(implies(Y!0, X!1))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.87 inference(quant_inst,[status(thm)],[])).
% 299.62/189.87 tff(1253,plain,
% 299.62/189.87 (is_a_theorem(implies(implies(not(implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))), implies(or(not(or(not(X!1), not(not(Y!0)))), not(implies(Y!0, X!1))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.87 inference(unit_resolution,[status(thm)],[1252, 1251])).
% 299.62/189.87 tff(1254,plain,
% 299.62/189.87 (is_a_theorem(implies(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))))),
% 299.62/189.87 inference(modus_ponens,[status(thm)],[1253, 1235])).
% 299.62/189.87 tff(1255,plain,
% 299.62/189.87 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))) = not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.62/189.87 inference(quant_inst,[status(thm)],[])).
% 299.62/189.87 tff(1256,plain,
% 299.62/189.87 (or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))) = not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.87 inference(unit_resolution,[status(thm)],[1255, 63])).
% 299.62/189.87 tff(1257,plain,
% 299.62/189.87 (or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))) = or(or(not(Y!0), X!1), not(equiv(X!1, Y!0)))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[775, 198])).
% 299.62/189.87 tff(1258,plain,
% 299.62/189.87 (not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))) = not(or(or(not(Y!0), X!1), not(equiv(X!1, Y!0))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1257])).
% 299.62/189.87 tff(1259,plain,
% 299.62/189.87 (not(or(or(not(Y!0), X!1), not(equiv(X!1, Y!0)))) = not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1258])).
% 299.62/189.87 tff(1260,plain,
% 299.62/189.87 (or(or(not(Y!0), X!1), not(equiv(X!1, Y!0))) = or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0)))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[234])).
% 299.62/189.87 tff(1261,plain,
% 299.62/189.87 (or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))) = or(or(not(Y!0), X!1), not(equiv(X!1, Y!0)))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1260])).
% 299.62/189.87 tff(1262,plain,
% 299.62/189.87 (not(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0)))) = not(or(or(not(Y!0), X!1), not(equiv(X!1, Y!0))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1261])).
% 299.62/189.87 tff(1263,plain,
% 299.62/189.87 (not(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0)))) = not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))),
% 299.62/189.87 inference(transitivity,[status(thm)],[1262, 1259])).
% 299.62/189.87 tff(1264,plain,
% 299.62/189.87 (or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0)))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))) = or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1263])).
% 299.62/189.87 tff(1265,plain,
% 299.62/189.87 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))) = or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0)))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.87 inference(quant_inst,[status(thm)],[])).
% 299.62/189.87 tff(1266,plain,
% 299.62/189.87 (implies(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))) = or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0)))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))),
% 299.62/189.87 inference(unit_resolution,[status(thm)],[1265, 20])).
% 299.62/189.87 tff(1267,plain,
% 299.62/189.87 (implies(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))) = not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.87 inference(transitivity,[status(thm)],[1266, 1264, 1256])).
% 299.62/189.87 tff(1268,plain,
% 299.62/189.87 (is_a_theorem(implies(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))) <=> is_a_theorem(not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1267])).
% 299.62/189.87 tff(1269,plain,
% 299.62/189.87 (is_a_theorem(not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))) <=> is_a_theorem(implies(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))),
% 299.62/189.87 inference(symmetry,[status(thm)],[1268])).
% 299.62/189.87 tff(1270,plain,
% 299.62/189.87 (implies(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))) = implies(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1256])).
% 299.62/189.87 tff(1271,plain,
% 299.62/189.87 (is_a_theorem(implies(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))) <=> is_a_theorem(implies(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.62/189.87 inference(monotonicity,[status(thm)],[1270])).
% 299.62/189.87 tff(1272,plain,
% 299.62/189.87 ((~![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(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.87 inference(quant_inst,[status(thm)],[])).
% 299.62/189.87 tff(1273,plain,
% 299.62/189.87 (is_a_theorem(implies(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))),
% 299.62/189.87 inference(unit_resolution,[status(thm)],[1272, 570])).
% 299.62/189.87 tff(1274,plain,
% 299.68/189.87 (is_a_theorem(implies(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.68/189.87 inference(modus_ponens,[status(thm)],[1273, 1271])).
% 299.68/189.87 tff(1275,plain,
% 299.68/189.87 (or(not(not(or(not(Y!0), not(not(X!1))))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))) = or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1))))))),
% 299.68/189.87 inference(monotonicity,[status(thm)],[775])).
% 299.68/189.87 tff(1276,plain,
% 299.68/189.87 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(Y!0), not(not(X!1)))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))) = or(not(not(or(not(Y!0), not(not(X!1))))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.68/189.87 inference(quant_inst,[status(thm)],[])).
% 299.68/189.87 tff(1277,plain,
% 299.68/189.87 (implies(not(or(not(Y!0), not(not(X!1)))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))) = or(not(not(or(not(Y!0), not(not(X!1))))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1))))))),
% 299.68/189.87 inference(unit_resolution,[status(thm)],[1276, 20])).
% 299.68/189.87 tff(1278,plain,
% 299.68/189.87 (implies(not(or(not(Y!0), not(not(X!1)))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))) = or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1))))))),
% 299.68/189.87 inference(transitivity,[status(thm)],[1277, 1275])).
% 299.68/189.87 tff(1279,plain,
% 299.68/189.87 (is_a_theorem(implies(not(or(not(Y!0), not(not(X!1)))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1))))))) <=> is_a_theorem(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.68/189.87 inference(monotonicity,[status(thm)],[1278])).
% 299.68/189.87 tff(1280,plain,
% 299.68/189.87 (^[P: $i, Q: $i] : refl(is_a_theorem(implies(Q, or(P, Q))) <=> is_a_theorem(implies(Q, or(P, Q))))),
% 299.68/189.87 inference(bind,[status(th)],[])).
% 299.68/189.87 tff(1281,plain,
% 299.68/189.87 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 299.68/189.87 inference(quant_intro,[status(thm)],[1280])).
% 299.68/189.87 tff(1282,plain,
% 299.68/189.87 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 299.68/189.87 inference(rewrite,[status(thm)],[])).
% 299.68/189.87 tff(1283,plain,
% 299.68/189.87 (($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 299.68/189.87 inference(rewrite,[status(thm)],[])).
% 299.68/189.87 tff(1284,axiom,(r2), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r2')).
% 299.68/189.87 tff(1285,plain,
% 299.68/189.87 (r2 <=> $true),
% 299.68/189.87 inference(iff_true,[status(thm)],[1284])).
% 299.68/189.87 tff(1286,plain,
% 299.68/189.87 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 299.68/189.87 inference(monotonicity,[status(thm)],[1285])).
% 299.68/189.87 tff(1287,plain,
% 299.68/189.87 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 299.68/189.87 inference(transitivity,[status(thm)],[1286, 1283])).
% 299.68/189.87 tff(1288,plain,
% 299.68/189.87 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 299.68/189.87 inference(rewrite,[status(thm)],[])).
% 299.68/189.87 tff(1289,axiom,(r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','r2')).
% 299.68/189.87 tff(1290,plain,
% 299.68/189.87 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 299.68/189.87 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 299.68/189.87 tff(1291,plain,
% 299.68/189.87 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 299.68/189.87 inference(modus_ponens,[status(thm)],[1290, 1288])).
% 299.68/189.87 tff(1292,plain,
% 299.68/189.87 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 299.68/189.87 inference(modus_ponens,[status(thm)],[1291, 1287])).
% 299.68/189.87 tff(1293,plain,
% 299.68/189.87 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 299.68/189.87 inference(modus_ponens,[status(thm)],[1292, 1282])).
% 299.68/189.87 tff(1294,plain,(
% 299.68/189.87 ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 299.68/189.87 inference(skolemize,[status(sab)],[1293])).
% 299.68/189.87 tff(1295,plain,
% 299.68/189.87 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 299.68/189.87 inference(modus_ponens,[status(thm)],[1294, 1281])).
% 299.68/189.87 tff(1296,plain,
% 299.68/189.87 ((~![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) | is_a_theorem(implies(not(or(not(Y!0), not(not(X!1)))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.68/189.87 inference(quant_inst,[status(thm)],[])).
% 299.68/189.87 tff(1297,plain,
% 299.68/189.87 (is_a_theorem(implies(not(or(not(Y!0), not(not(X!1)))), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.68/189.87 inference(unit_resolution,[status(thm)],[1296, 1295])).
% 299.68/189.87 tff(1298,plain,
% 299.68/189.87 (is_a_theorem(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.68/189.87 inference(modus_ponens,[status(thm)],[1297, 1279])).
% 299.68/189.87 tff(1299,plain,
% 299.68/189.87 (((~![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(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))) | (~is_a_theorem(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))))) | (~is_a_theorem(implies(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!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(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))) | (~is_a_theorem(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))))) | (~is_a_theorem(implies(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))))))),
% 299.68/189.87 inference(rewrite,[status(thm)],[])).
% 299.68/189.87 tff(1300,plain,
% 299.68/189.87 ((~![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(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))) | (~is_a_theorem(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))))) | (~is_a_theorem(implies(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))))))),
% 299.68/189.88 inference(quant_inst,[status(thm)],[])).
% 299.68/189.88 tff(1301,plain,
% 299.68/189.88 ((~![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(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))) | (~is_a_theorem(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))))) | (~is_a_theorem(implies(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))))))),
% 299.68/189.88 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 299.68/189.88 tff(1302,plain,
% 299.68/189.88 (is_a_theorem(not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))) | (~is_a_theorem(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))))) | (~is_a_theorem(implies(or(or(not(Y!0), X!1), or(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1))))), not(or(not(Y!0), not(not(X!1)))))), not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))))))),
% 299.68/189.88 inference(unit_resolution,[status(thm)],[1301, 610])).
% 299.68/189.88 tff(1303,plain,
% 299.68/189.88 (is_a_theorem(not(and(not(not(or(not(not(or(not(Y!0), not(not(X!1))))), not(and(implies(X!1, Y!0), implies(Y!0, X!1)))))), not(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.68/189.88 inference(unit_resolution,[status(thm)],[1302, 1298, 1274])).
% 299.68/189.88 tff(1304,plain,
% 299.68/189.88 (is_a_theorem(implies(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))),
% 299.68/189.88 inference(modus_ponens,[status(thm)],[1303, 1269])).
% 299.68/189.88 tff(1305,plain,
% 299.68/189.88 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(Y!0), not(not(X!1)))), not(equiv(X!1, Y!0))) = or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))))),
% 299.68/189.88 inference(quant_inst,[status(thm)],[])).
% 299.68/189.88 tff(1306,plain,
% 299.68/189.88 (implies(not(or(not(Y!0), not(not(X!1)))), not(equiv(X!1, Y!0))) = or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0)))),
% 299.68/189.88 inference(unit_resolution,[status(thm)],[1305, 20])).
% 299.68/189.88 tff(1307,plain,
% 299.68/189.88 (or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))) = implies(not(or(not(Y!0), not(not(X!1)))), not(equiv(X!1, Y!0)))),
% 299.68/189.88 inference(symmetry,[status(thm)],[1306])).
% 299.68/189.88 tff(1308,plain,
% 299.68/189.88 (is_a_theorem(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0)))) <=> is_a_theorem(implies(not(or(not(Y!0), not(not(X!1)))), not(equiv(X!1, Y!0))))),
% 299.68/189.88 inference(monotonicity,[status(thm)],[1307])).
% 299.68/189.88 tff(1309,plain,
% 299.68/189.88 (is_a_theorem(implies(not(or(not(Y!0), not(not(X!1)))), not(equiv(X!1, Y!0)))) <=> is_a_theorem(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))))),
% 299.68/189.88 inference(symmetry,[status(thm)],[1308])).
% 299.68/189.88 tff(1310,plain,
% 299.68/189.88 (implies(not(or(not(Y!0), not(not(X!1)))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))) = implies(not(or(not(Y!0), not(not(X!1)))), not(equiv(X!1, Y!0)))),
% 299.68/189.88 inference(monotonicity,[status(thm)],[133])).
% 299.68/189.88 tff(1311,plain,
% 299.68/189.88 (is_a_theorem(implies(not(or(not(Y!0), not(not(X!1)))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1))))))) <=> is_a_theorem(implies(not(or(not(Y!0), not(not(X!1)))), not(equiv(X!1, Y!0))))),
% 299.68/189.88 inference(monotonicity,[status(thm)],[1310])).
% 299.68/189.88 tff(1312,plain,
% 299.68/189.88 ((~![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) | is_a_theorem(implies(not(or(not(Y!0), not(not(X!1)))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.68/189.88 inference(quant_inst,[status(thm)],[])).
% 299.68/189.88 tff(1313,plain,
% 299.68/189.88 (is_a_theorem(implies(not(or(not(Y!0), not(not(X!1)))), or(not(or(not(X!1), not(not(Y!0)))), not(or(not(Y!0), not(not(X!1)))))))),
% 299.68/189.88 inference(unit_resolution,[status(thm)],[1312, 1295])).
% 299.68/189.88 tff(1314,plain,
% 299.68/189.88 (is_a_theorem(implies(not(or(not(Y!0), not(not(X!1)))), not(equiv(X!1, Y!0))))),
% 299.68/189.88 inference(modus_ponens,[status(thm)],[1313, 1311])).
% 299.68/189.88 tff(1315,plain,
% 299.68/189.88 (is_a_theorem(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))))),
% 299.68/189.88 inference(modus_ponens,[status(thm)],[1314, 1309])).
% 299.68/189.88 tff(1316,plain,
% 299.68/189.88 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))) | (~is_a_theorem(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))))) | (~is_a_theorem(implies(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))) | (~is_a_theorem(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))))) | (~is_a_theorem(implies(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.68/189.88 inference(rewrite,[status(thm)],[])).
% 299.68/189.88 tff(1317,plain,
% 299.68/189.88 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))) | (~is_a_theorem(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))))) | (~is_a_theorem(implies(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.68/189.88 inference(quant_inst,[status(thm)],[])).
% 299.68/189.88 tff(1318,plain,
% 299.68/189.88 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))) | (~is_a_theorem(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))))) | (~is_a_theorem(implies(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))),
% 299.68/189.88 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 299.68/189.88 tff(1319,plain,
% 299.68/189.88 (is_a_theorem(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1)))))) | (~is_a_theorem(implies(or(not(not(or(not(Y!0), not(not(X!1))))), not(equiv(X!1, Y!0))), or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))))),
% 299.68/189.88 inference(unit_resolution,[status(thm)],[1318, 610, 1315])).
% 299.68/189.88 tff(1320,plain,
% 299.68/189.88 (is_a_theorem(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))),
% 299.68/189.88 inference(unit_resolution,[status(thm)],[1319, 1304])).
% 299.68/189.88 tff(1321,plain,
% 299.68/189.88 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))) | (~is_a_theorem(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))) | (~is_a_theorem(implies(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))) | (~is_a_theorem(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))) | (~is_a_theorem(implies(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))))))),
% 299.68/189.88 inference(rewrite,[status(thm)],[])).
% 299.68/189.88 tff(1322,plain,
% 299.68/189.88 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))) | (~is_a_theorem(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))) | (~is_a_theorem(implies(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))))))),
% 299.68/189.88 inference(quant_inst,[status(thm)],[])).
% 299.68/189.88 tff(1323,plain,
% 299.68/189.88 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))) | (~is_a_theorem(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))) | (~is_a_theorem(implies(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))))))),
% 299.68/189.88 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 299.68/189.88 tff(1324,plain,
% 299.68/189.88 (is_a_theorem(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0)))))) | (~is_a_theorem(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))))) | (~is_a_theorem(implies(or(or(not(Y!0), X!1), not(or(not(Y!0), not(not(X!1))))), not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))))))),
% 299.68/189.88 inference(unit_resolution,[status(thm)],[1323, 610])).
% 299.68/189.88 tff(1325,plain,
% 299.68/189.88 (is_a_theorem(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))))),
% 299.68/189.88 inference(unit_resolution,[status(thm)],[1324, 1320, 1254])).
% 299.68/189.88 tff(1326,plain,
% 299.68/189.88 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) | (~is_a_theorem(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))))) | (~is_a_theorem(implies(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) | (~is_a_theorem(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))))) | (~is_a_theorem(implies(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.68/189.88 inference(rewrite,[status(thm)],[])).
% 299.68/189.88 tff(1327,plain,
% 299.68/189.88 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) | (~is_a_theorem(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))))) | (~is_a_theorem(implies(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))))))),
% 299.68/189.88 inference(quant_inst,[status(thm)],[])).
% 299.68/189.88 tff(1328,plain,
% 299.68/189.88 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) | (~is_a_theorem(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))))) | (~is_a_theorem(implies(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.68/189.88 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 299.68/189.88 tff(1329,plain,
% 299.68/189.88 (is_a_theorem(or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1))))))) | (~is_a_theorem(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))))) | (~is_a_theorem(implies(not(and(not(and(implies(X!1, Y!0), implies(Y!0, X!1))), not(not(equiv(X!1, Y!0))))), or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))))),
% 299.68/189.95 inference(unit_resolution,[status(thm)],[1328, 610])).
% 299.68/189.95 tff(1330,plain,
% 299.68/189.95 (is_a_theorem(or(not(implies(X!1, Y!0)), or(and(implies(X!1, Y!0), implies(Y!0, X!1)), not(or(not(Y!0), not(not(X!1)))))))),
% 299.68/189.95 inference(unit_resolution,[status(thm)],[1329, 1325, 1200])).
% 299.68/189.95 tff(1331,plain,
% 299.68/189.95 ($false),
% 299.68/189.95 inference(unit_resolution,[status(thm)],[1330, 1180])).
% 299.68/189.95 % SZS output end Proof
%------------------------------------------------------------------------------