TSTP Solution File: LCL497+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL497+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 04:56:31 EDT 2022
% Result : Theorem 16.46s 10.68s
% Output : Proof 16.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL497+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 22:08:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 16.46/10.68 % SZS status Theorem
% 16.46/10.68 % SZS output start Proof
% 16.46/10.68 tff(is_a_theorem_type, type, (
% 16.46/10.68 is_a_theorem: $i > $o)).
% 16.46/10.68 tff(not_type, type, (
% 16.46/10.68 not: $i > $i)).
% 16.46/10.68 tff(and_type, type, (
% 16.46/10.68 and: ( $i * $i ) > $i)).
% 16.46/10.68 tff(or_type, type, (
% 16.46/10.68 or: ( $i * $i ) > $i)).
% 16.46/10.68 tff(tptp_fun_P_2_type, type, (
% 16.46/10.68 tptp_fun_P_2: $i)).
% 16.46/10.68 tff(tptp_fun_Q_1_type, type, (
% 16.46/10.68 tptp_fun_Q_1: $i)).
% 16.46/10.68 tff(op_or_type, type, (
% 16.46/10.68 op_or: $o)).
% 16.46/10.68 tff(implies_type, type, (
% 16.46/10.68 implies: ( $i * $i ) > $i)).
% 16.46/10.68 tff(op_implies_or_type, type, (
% 16.46/10.68 op_implies_or: $o)).
% 16.46/10.68 tff(equiv_type, type, (
% 16.46/10.68 equiv: ( $i * $i ) > $i)).
% 16.46/10.68 tff(op_equiv_type, type, (
% 16.46/10.68 op_equiv: $o)).
% 16.46/10.68 tff(op_and_type, type, (
% 16.46/10.68 op_and: $o)).
% 16.46/10.68 tff(r3_type, type, (
% 16.46/10.68 r3: $o)).
% 16.46/10.68 tff(r4_type, type, (
% 16.46/10.68 r4: $o)).
% 16.46/10.68 tff(modus_ponens_type, type, (
% 16.46/10.68 modus_ponens: $o)).
% 16.46/10.68 tff(substitution_of_equivalents_type, type, (
% 16.46/10.68 substitution_of_equivalents: $o)).
% 16.46/10.68 tff(cn2_type, type, (
% 16.46/10.68 cn2: $o)).
% 16.46/10.68 tff(r2_type, type, (
% 16.46/10.68 r2: $o)).
% 16.46/10.68 tff(1,plain,
% 16.46/10.68 (^[X: $i, Y: $i] : refl((or(X, Y) = not(and(not(X), not(Y)))) <=> (or(X, Y) = not(and(not(X), not(Y)))))),
% 16.46/10.68 inference(bind,[status(th)],[])).
% 16.46/10.68 tff(2,plain,
% 16.46/10.68 (![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))))),
% 16.46/10.68 inference(quant_intro,[status(thm)],[1])).
% 16.46/10.68 tff(3,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(4,plain,
% 16.46/10.68 (($false | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(5,plain,
% 16.46/10.68 ((~$true) <=> $false),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(6,axiom,(op_or), file('/export/starexec/sandbox/benchmark/theBenchmark.p','luka_op_or')).
% 16.46/10.68 tff(7,plain,
% 16.46/10.68 (op_or <=> $true),
% 16.46/10.68 inference(iff_true,[status(thm)],[6])).
% 16.46/10.68 tff(8,plain,
% 16.46/10.68 ((~op_or) <=> (~$true)),
% 16.46/10.68 inference(monotonicity,[status(thm)],[7])).
% 16.46/10.68 tff(9,plain,
% 16.46/10.68 ((~op_or) <=> $false),
% 16.46/10.68 inference(transitivity,[status(thm)],[8, 5])).
% 16.46/10.68 tff(10,plain,
% 16.46/10.68 (((~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)))))),
% 16.46/10.68 inference(monotonicity,[status(thm)],[9])).
% 16.46/10.68 tff(11,plain,
% 16.46/10.68 (((~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))))),
% 16.46/10.68 inference(transitivity,[status(thm)],[10, 4])).
% 16.46/10.68 tff(12,plain,
% 16.46/10.68 (((~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)))))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(13,plain,
% 16.46/10.68 ((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)))))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(14,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')).
% 16.46/10.68 tff(15,plain,
% 16.46/10.68 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[14, 13])).
% 16.46/10.68 tff(16,plain,
% 16.46/10.68 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[15, 12])).
% 16.46/10.68 tff(17,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[16, 11])).
% 16.46/10.68 tff(18,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[17, 3])).
% 16.46/10.68 tff(19,plain,(
% 16.46/10.68 ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 16.46/10.68 inference(skolemize,[status(sab)],[18])).
% 16.46/10.68 tff(20,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[19, 2])).
% 16.46/10.68 tff(21,plain,
% 16.46/10.68 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(Q!1, or(not(P!2), not(not(P!2)))) = not(and(not(Q!1), not(or(not(P!2), not(not(P!2)))))))),
% 16.46/10.68 inference(quant_inst,[status(thm)],[])).
% 16.46/10.68 tff(22,plain,
% 16.46/10.68 (or(Q!1, or(not(P!2), not(not(P!2)))) = not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))),
% 16.46/10.68 inference(unit_resolution,[status(thm)],[21, 20])).
% 16.46/10.68 tff(23,plain,
% 16.46/10.68 (not(and(not(Q!1), not(or(not(P!2), not(not(P!2)))))) = or(Q!1, or(not(P!2), not(not(P!2))))),
% 16.46/10.68 inference(symmetry,[status(thm)],[22])).
% 16.46/10.68 tff(24,plain,
% 16.46/10.68 (is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) <=> is_a_theorem(or(Q!1, or(not(P!2), not(not(P!2)))))),
% 16.46/10.68 inference(monotonicity,[status(thm)],[23])).
% 16.46/10.68 tff(25,plain,
% 16.46/10.68 (is_a_theorem(or(Q!1, or(not(P!2), not(not(P!2))))) <=> is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2)))))))),
% 16.46/10.68 inference(symmetry,[status(thm)],[24])).
% 16.46/10.68 tff(26,plain,
% 16.46/10.68 ((~is_a_theorem(or(Q!1, or(not(P!2), not(not(P!2)))))) <=> (~is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))))),
% 16.46/10.68 inference(monotonicity,[status(thm)],[25])).
% 16.46/10.68 tff(27,plain,
% 16.46/10.68 (^[X: $i, Y: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 16.46/10.68 inference(bind,[status(th)],[])).
% 16.46/10.68 tff(28,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 16.46/10.68 inference(quant_intro,[status(thm)],[27])).
% 16.46/10.68 tff(29,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(30,plain,
% 16.46/10.68 (($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(31,axiom,(op_implies_or), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_op_implies_or')).
% 16.46/10.68 tff(32,plain,
% 16.46/10.68 (op_implies_or <=> $true),
% 16.46/10.68 inference(iff_true,[status(thm)],[31])).
% 16.46/10.68 tff(33,plain,
% 16.46/10.68 ((~op_implies_or) <=> (~$true)),
% 16.46/10.68 inference(monotonicity,[status(thm)],[32])).
% 16.46/10.68 tff(34,plain,
% 16.46/10.68 ((~op_implies_or) <=> $false),
% 16.46/10.68 inference(transitivity,[status(thm)],[33, 5])).
% 16.46/10.68 tff(35,plain,
% 16.46/10.68 (((~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)))),
% 16.46/10.68 inference(monotonicity,[status(thm)],[34])).
% 16.46/10.68 tff(36,plain,
% 16.46/10.68 (((~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))),
% 16.46/10.68 inference(transitivity,[status(thm)],[35, 30])).
% 16.46/10.68 tff(37,plain,
% 16.46/10.68 (((~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)))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(38,plain,
% 16.46/10.68 ((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)))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(39,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')).
% 16.46/10.68 tff(40,plain,
% 16.46/10.68 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[39, 38])).
% 16.46/10.68 tff(41,plain,
% 16.46/10.68 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[40, 37])).
% 16.46/10.68 tff(42,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[41, 36])).
% 16.46/10.68 tff(43,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[42, 29])).
% 16.46/10.68 tff(44,plain,(
% 16.46/10.68 ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 16.46/10.68 inference(skolemize,[status(sab)],[43])).
% 16.46/10.68 tff(45,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[44, 28])).
% 16.46/10.68 tff(46,plain,
% 16.46/10.68 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(P!2), Q!1) = or(not(not(P!2)), Q!1))),
% 16.46/10.68 inference(quant_inst,[status(thm)],[])).
% 16.46/10.68 tff(47,plain,
% 16.46/10.68 (implies(not(P!2), Q!1) = or(not(not(P!2)), Q!1)),
% 16.46/10.68 inference(unit_resolution,[status(thm)],[46, 45])).
% 16.46/10.68 tff(48,plain,
% 16.46/10.68 (or(not(not(P!2)), Q!1) = implies(not(P!2), Q!1)),
% 16.46/10.68 inference(symmetry,[status(thm)],[47])).
% 16.46/10.68 tff(49,plain,
% 16.46/10.68 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(Q!1, not(not(P!2))) = not(and(not(Q!1), not(not(not(P!2))))))),
% 16.46/10.68 inference(quant_inst,[status(thm)],[])).
% 16.46/10.68 tff(50,plain,
% 16.46/10.68 (or(Q!1, not(not(P!2))) = not(and(not(Q!1), not(not(not(P!2)))))),
% 16.46/10.68 inference(unit_resolution,[status(thm)],[49, 20])).
% 16.46/10.68 tff(51,plain,
% 16.46/10.68 (not(and(not(Q!1), not(not(not(P!2))))) = or(Q!1, not(not(P!2)))),
% 16.46/10.68 inference(symmetry,[status(thm)],[50])).
% 16.46/10.68 tff(52,plain,
% 16.46/10.68 (equiv(not(and(not(Q!1), not(not(not(P!2))))), or(not(not(P!2)), Q!1)) = equiv(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1))),
% 16.46/10.68 inference(monotonicity,[status(thm)],[51])).
% 16.46/10.68 tff(53,plain,
% 16.46/10.68 (equiv(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)) = equiv(not(and(not(Q!1), not(not(not(P!2))))), or(not(not(P!2)), Q!1))),
% 16.46/10.68 inference(symmetry,[status(thm)],[52])).
% 16.46/10.68 tff(54,plain,
% 16.46/10.68 (^[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))))),
% 16.46/10.68 inference(bind,[status(th)],[])).
% 16.46/10.68 tff(55,plain,
% 16.46/10.68 (![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)))),
% 16.46/10.68 inference(quant_intro,[status(thm)],[54])).
% 16.46/10.68 tff(56,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(57,plain,
% 16.46/10.68 (($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)))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(58,axiom,(op_equiv), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_op_equiv')).
% 16.46/10.68 tff(59,plain,
% 16.46/10.68 (op_equiv <=> $true),
% 16.46/10.68 inference(iff_true,[status(thm)],[58])).
% 16.46/10.68 tff(60,plain,
% 16.46/10.68 ((~op_equiv) <=> (~$true)),
% 16.46/10.68 inference(monotonicity,[status(thm)],[59])).
% 16.46/10.68 tff(61,plain,
% 16.46/10.68 ((~op_equiv) <=> $false),
% 16.46/10.68 inference(transitivity,[status(thm)],[60, 5])).
% 16.46/10.68 tff(62,plain,
% 16.46/10.68 (((~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))))),
% 16.46/10.68 inference(monotonicity,[status(thm)],[61])).
% 16.46/10.68 tff(63,plain,
% 16.46/10.68 (((~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)))),
% 16.46/10.68 inference(transitivity,[status(thm)],[62, 57])).
% 16.46/10.68 tff(64,plain,
% 16.46/10.68 (((~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))))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(65,plain,
% 16.46/10.68 ((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))))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(66,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')).
% 16.46/10.68 tff(67,plain,
% 16.46/10.68 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[66, 65])).
% 16.46/10.68 tff(68,plain,
% 16.46/10.68 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[67, 64])).
% 16.46/10.68 tff(69,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[68, 63])).
% 16.46/10.68 tff(70,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[69, 56])).
% 16.46/10.68 tff(71,plain,(
% 16.46/10.68 ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 16.46/10.68 inference(skolemize,[status(sab)],[70])).
% 16.46/10.68 tff(72,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[71, 55])).
% 16.46/10.68 tff(73,plain,
% 16.46/10.68 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)) = and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))),
% 16.46/10.68 inference(quant_inst,[status(thm)],[])).
% 16.46/10.68 tff(74,plain,
% 16.46/10.68 (equiv(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)) = and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))),
% 16.46/10.68 inference(unit_resolution,[status(thm)],[73, 72])).
% 16.46/10.68 tff(75,plain,
% 16.46/10.68 (and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))) = equiv(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1))),
% 16.46/10.68 inference(symmetry,[status(thm)],[74])).
% 16.46/10.68 tff(76,plain,
% 16.46/10.68 (and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))) = equiv(not(and(not(Q!1), not(not(not(P!2))))), or(not(not(P!2)), Q!1))),
% 16.46/10.68 inference(transitivity,[status(thm)],[75, 53])).
% 16.46/10.68 tff(77,plain,
% 16.46/10.68 (is_a_theorem(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))) <=> is_a_theorem(equiv(not(and(not(Q!1), not(not(not(P!2))))), or(not(not(P!2)), Q!1)))),
% 16.46/10.68 inference(monotonicity,[status(thm)],[76])).
% 16.46/10.68 tff(78,plain,
% 16.46/10.68 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(not(P!2)), Q!1) = not(and(not(not(not(P!2))), not(Q!1))))),
% 16.46/10.68 inference(quant_inst,[status(thm)],[])).
% 16.46/10.68 tff(79,plain,
% 16.46/10.68 (or(not(not(P!2)), Q!1) = not(and(not(not(not(P!2))), not(Q!1)))),
% 16.46/10.68 inference(unit_resolution,[status(thm)],[78, 20])).
% 16.46/10.68 tff(80,plain,
% 16.46/10.68 (not(and(not(not(not(P!2))), not(Q!1))) = or(not(not(P!2)), Q!1)),
% 16.46/10.68 inference(symmetry,[status(thm)],[79])).
% 16.46/10.68 tff(81,plain,
% 16.46/10.68 (^[X: $i, Y: $i] : refl((and(X, Y) = not(or(not(X), not(Y)))) <=> (and(X, Y) = not(or(not(X), not(Y)))))),
% 16.46/10.68 inference(bind,[status(th)],[])).
% 16.46/10.68 tff(82,plain,
% 16.46/10.68 (![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))))),
% 16.46/10.68 inference(quant_intro,[status(thm)],[81])).
% 16.46/10.68 tff(83,plain,
% 16.46/10.68 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(84,plain,
% 16.46/10.68 (($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))))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(85,axiom,(op_and), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_op_and')).
% 16.46/10.68 tff(86,plain,
% 16.46/10.68 (op_and <=> $true),
% 16.46/10.68 inference(iff_true,[status(thm)],[85])).
% 16.46/10.68 tff(87,plain,
% 16.46/10.68 ((~op_and) <=> (~$true)),
% 16.46/10.68 inference(monotonicity,[status(thm)],[86])).
% 16.46/10.68 tff(88,plain,
% 16.46/10.68 ((~op_and) <=> $false),
% 16.46/10.68 inference(transitivity,[status(thm)],[87, 5])).
% 16.46/10.68 tff(89,plain,
% 16.46/10.68 (((~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)))))),
% 16.46/10.68 inference(monotonicity,[status(thm)],[88])).
% 16.46/10.68 tff(90,plain,
% 16.46/10.68 (((~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))))),
% 16.46/10.68 inference(transitivity,[status(thm)],[89, 84])).
% 16.46/10.68 tff(91,plain,
% 16.46/10.68 (((~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)))))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(92,plain,
% 16.46/10.68 ((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)))))),
% 16.46/10.68 inference(rewrite,[status(thm)],[])).
% 16.46/10.68 tff(93,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')).
% 16.46/10.68 tff(94,plain,
% 16.46/10.68 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[93, 92])).
% 16.46/10.68 tff(95,plain,
% 16.46/10.68 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 16.46/10.68 inference(modus_ponens,[status(thm)],[94, 91])).
% 16.46/10.69 tff(96,plain,
% 16.46/10.69 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 16.46/10.69 inference(modus_ponens,[status(thm)],[95, 90])).
% 16.46/10.69 tff(97,plain,
% 16.46/10.69 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 16.46/10.69 inference(modus_ponens,[status(thm)],[96, 83])).
% 16.46/10.69 tff(98,plain,(
% 16.46/10.69 ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 16.46/10.69 inference(skolemize,[status(sab)],[97])).
% 16.46/10.69 tff(99,plain,
% 16.46/10.69 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 16.46/10.69 inference(modus_ponens,[status(thm)],[98, 82])).
% 16.46/10.69 tff(100,plain,
% 16.46/10.69 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(not(P!2))), not(Q!1)) = not(or(not(not(not(not(P!2)))), not(not(Q!1)))))),
% 16.46/10.69 inference(quant_inst,[status(thm)],[])).
% 16.46/10.69 tff(101,plain,
% 16.46/10.69 (and(not(not(not(P!2))), not(Q!1)) = not(or(not(not(not(not(P!2)))), not(not(Q!1))))),
% 16.46/10.69 inference(unit_resolution,[status(thm)],[100, 99])).
% 16.46/10.69 tff(102,plain,
% 16.46/10.69 (not(or(not(not(not(not(P!2)))), not(not(Q!1)))) = and(not(not(not(P!2))), not(Q!1))),
% 16.46/10.69 inference(symmetry,[status(thm)],[101])).
% 16.46/10.69 tff(103,plain,
% 16.46/10.69 (not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))) = not(and(not(not(not(P!2))), not(Q!1)))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[102])).
% 16.46/10.69 tff(104,plain,
% 16.46/10.69 (not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))) = or(not(not(P!2)), Q!1)),
% 16.46/10.69 inference(transitivity,[status(thm)],[103, 80])).
% 16.46/10.69 tff(105,plain,
% 16.46/10.69 (not(not(and(not(Q!1), not(not(not(P!2)))))) = not(or(Q!1, not(not(P!2))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[51])).
% 16.46/10.69 tff(106,plain,
% 16.46/10.69 (or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))) = or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[105, 104])).
% 16.46/10.69 tff(107,plain,
% 16.46/10.69 (or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)) = or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))),
% 16.46/10.69 inference(symmetry,[status(thm)],[106])).
% 16.46/10.69 tff(108,plain,
% 16.46/10.69 (not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))) = not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[107])).
% 16.46/10.69 tff(109,plain,
% 16.46/10.69 (or(not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))) = or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[108])).
% 16.46/10.69 tff(110,plain,
% 16.46/10.69 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))) = or(not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))),
% 16.46/10.69 inference(quant_inst,[status(thm)],[])).
% 16.46/10.69 tff(111,plain,
% 16.46/10.69 (implies(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))) = or(not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))),
% 16.46/10.69 inference(unit_resolution,[status(thm)],[110, 45])).
% 16.46/10.69 tff(112,plain,
% 16.46/10.69 (implies(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))) = or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))),
% 16.46/10.69 inference(transitivity,[status(thm)],[111, 109])).
% 16.46/10.69 tff(113,plain,
% 16.46/10.69 (is_a_theorem(implies(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))) <=> is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[112])).
% 16.46/10.69 tff(114,plain,
% 16.46/10.69 (is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))) <=> is_a_theorem(implies(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))),
% 16.46/10.69 inference(symmetry,[status(thm)],[113])).
% 16.46/10.69 tff(115,plain,
% 16.46/10.69 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))) = not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))),
% 16.46/10.69 inference(quant_inst,[status(thm)],[])).
% 16.46/10.69 tff(116,plain,
% 16.46/10.69 (or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))) = not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.69 inference(unit_resolution,[status(thm)],[115, 20])).
% 16.46/10.69 tff(117,plain,
% 16.46/10.69 (not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))) = or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))),
% 16.46/10.69 inference(symmetry,[status(thm)],[116])).
% 16.46/10.69 tff(118,plain,
% 16.46/10.69 (implies(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))) = implies(or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[117])).
% 16.46/10.69 tff(119,plain,
% 16.46/10.69 (implies(or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))) = implies(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))),
% 16.46/10.69 inference(symmetry,[status(thm)],[118])).
% 16.46/10.69 tff(120,plain,
% 16.46/10.69 (is_a_theorem(implies(or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))) <=> is_a_theorem(implies(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[119])).
% 16.46/10.69 tff(121,plain,
% 16.46/10.69 (^[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))))),
% 16.46/10.69 inference(bind,[status(th)],[])).
% 16.46/10.69 tff(122,plain,
% 16.46/10.69 (![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)))),
% 16.46/10.69 inference(quant_intro,[status(thm)],[121])).
% 16.46/10.69 tff(123,plain,
% 16.46/10.69 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 16.46/10.69 inference(rewrite,[status(thm)],[])).
% 16.46/10.69 tff(124,plain,
% 16.46/10.69 (($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)))),
% 16.46/10.69 inference(rewrite,[status(thm)],[])).
% 16.46/10.69 tff(125,axiom,(r3), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r3')).
% 16.46/10.69 tff(126,plain,
% 16.46/10.69 (r3 <=> $true),
% 16.46/10.69 inference(iff_true,[status(thm)],[125])).
% 16.46/10.69 tff(127,plain,
% 16.46/10.69 ((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))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[126])).
% 16.46/10.69 tff(128,plain,
% 16.46/10.69 ((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)))),
% 16.46/10.69 inference(transitivity,[status(thm)],[127, 124])).
% 16.46/10.69 tff(129,plain,
% 16.46/10.69 ((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))))),
% 16.46/10.69 inference(rewrite,[status(thm)],[])).
% 16.46/10.69 tff(130,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')).
% 16.46/10.69 tff(131,plain,
% 16.46/10.69 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 16.46/10.69 inference(modus_ponens,[status(thm)],[130, 129])).
% 16.46/10.69 tff(132,plain,
% 16.46/10.69 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 16.46/10.69 inference(modus_ponens,[status(thm)],[131, 129])).
% 16.46/10.69 tff(133,plain,
% 16.46/10.69 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 16.46/10.69 inference(modus_ponens,[status(thm)],[132, 128])).
% 16.46/10.69 tff(134,plain,
% 16.46/10.69 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 16.46/10.69 inference(modus_ponens,[status(thm)],[133, 123])).
% 16.46/10.69 tff(135,plain,(
% 16.46/10.69 ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 16.46/10.69 inference(skolemize,[status(sab)],[134])).
% 16.46/10.69 tff(136,plain,
% 16.46/10.69 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 16.46/10.69 inference(modus_ponens,[status(thm)],[135, 122])).
% 16.46/10.69 tff(137,plain,
% 16.46/10.69 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))))),
% 16.46/10.69 inference(quant_inst,[status(thm)],[])).
% 16.46/10.69 tff(138,plain,
% 16.46/10.69 (is_a_theorem(implies(or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))))),
% 16.46/10.69 inference(unit_resolution,[status(thm)],[137, 136])).
% 16.46/10.69 tff(139,plain,
% 16.46/10.69 (is_a_theorem(implies(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))))),
% 16.46/10.69 inference(modus_ponens,[status(thm)],[138, 120])).
% 16.46/10.69 tff(140,plain,
% 16.46/10.69 (or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))) = or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[51])).
% 16.46/10.69 tff(141,plain,
% 16.46/10.69 (or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))) = or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))),
% 16.46/10.69 inference(symmetry,[status(thm)],[140])).
% 16.46/10.69 tff(142,plain,
% 16.46/10.69 (not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))) = not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[141])).
% 16.46/10.69 tff(143,plain,
% 16.46/10.69 (or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))) = or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[142])).
% 16.46/10.69 tff(144,plain,
% 16.46/10.69 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))) = or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.69 inference(quant_inst,[status(thm)],[])).
% 16.46/10.69 tff(145,plain,
% 16.46/10.69 (implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))) = or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))),
% 16.46/10.69 inference(unit_resolution,[status(thm)],[144, 45])).
% 16.46/10.69 tff(146,plain,
% 16.46/10.69 (implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) = implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[117])).
% 16.46/10.69 tff(147,plain,
% 16.46/10.69 (implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) = or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))),
% 16.46/10.69 inference(transitivity,[status(thm)],[146, 145, 143])).
% 16.46/10.69 tff(148,plain,
% 16.46/10.69 (is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))) <=> is_a_theorem(or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[147])).
% 16.46/10.69 tff(149,plain,
% 16.46/10.69 (is_a_theorem(or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))) <=> is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))))),
% 16.46/10.69 inference(symmetry,[status(thm)],[148])).
% 16.46/10.69 tff(150,plain,
% 16.46/10.69 (or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)))) = or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))),
% 16.46/10.69 inference(monotonicity,[status(thm)],[108])).
% 16.46/10.69 tff(151,plain,
% 16.46/10.69 (not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))) = not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)))),
% 16.46/10.69 inference(symmetry,[status(thm)],[108])).
% 16.46/10.70 tff(152,plain,
% 16.46/10.70 (not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))) = not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))),
% 16.46/10.70 inference(symmetry,[status(thm)],[142])).
% 16.46/10.70 tff(153,plain,
% 16.46/10.70 (or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))) = or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))))),
% 16.46/10.70 inference(monotonicity,[status(thm)],[152, 151])).
% 16.46/10.70 tff(154,plain,
% 16.46/10.70 (or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))) = or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))),
% 16.46/10.70 inference(transitivity,[status(thm)],[153, 150])).
% 16.46/10.70 tff(155,plain,
% 16.46/10.70 (or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))) = or(not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))), not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))))),
% 16.46/10.70 inference(monotonicity,[status(thm)],[151, 152])).
% 16.46/10.70 tff(156,plain,
% 16.46/10.70 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))) = not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))))),
% 16.46/10.70 inference(quant_inst,[status(thm)],[])).
% 16.46/10.70 tff(157,plain,
% 16.46/10.70 (or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))) = not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))),
% 16.46/10.70 inference(unit_resolution,[status(thm)],[156, 20])).
% 16.46/10.70 tff(158,plain,
% 16.46/10.70 (not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))) = or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))),
% 16.46/10.70 inference(symmetry,[status(thm)],[157])).
% 16.46/10.70 tff(159,plain,
% 16.46/10.70 (not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))) = or(not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))), not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))))),
% 16.46/10.70 inference(transitivity,[status(thm)],[158, 155])).
% 16.46/10.70 tff(160,plain,
% 16.46/10.70 (not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))) = not(or(not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))), not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))))),
% 16.46/10.70 inference(monotonicity,[status(thm)],[159])).
% 16.46/10.70 tff(161,plain,
% 16.46/10.70 (not(or(not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))), not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))))) = not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))))),
% 16.46/10.70 inference(symmetry,[status(thm)],[160])).
% 16.46/10.70 tff(162,plain,
% 16.46/10.70 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))) = not(or(not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))), not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))))))),
% 16.46/10.70 inference(quant_inst,[status(thm)],[])).
% 16.46/10.70 tff(163,plain,
% 16.46/10.70 (and(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))) = not(or(not(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))), not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))))),
% 16.46/10.70 inference(unit_resolution,[status(thm)],[162, 99])).
% 16.46/10.70 tff(164,plain,
% 16.46/10.70 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))) = or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))),
% 16.46/10.70 inference(quant_inst,[status(thm)],[])).
% 16.46/10.70 tff(165,plain,
% 16.46/10.70 (implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))) = or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))),
% 16.46/10.70 inference(unit_resolution,[status(thm)],[164, 45])).
% 16.46/10.70 tff(166,plain,
% 16.46/10.70 (or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))) = implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))),
% 16.46/10.70 inference(symmetry,[status(thm)],[165])).
% 16.46/10.70 tff(167,plain,
% 16.46/10.70 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)) = or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)))),
% 16.46/10.70 inference(quant_inst,[status(thm)],[])).
% 16.46/10.70 tff(168,plain,
% 16.46/10.70 (implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)) = or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))),
% 16.46/10.70 inference(unit_resolution,[status(thm)],[167, 45])).
% 16.46/10.70 tff(169,plain,
% 16.46/10.70 (or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)) = implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1))),
% 16.46/10.70 inference(symmetry,[status(thm)],[168])).
% 16.46/10.70 tff(170,plain,
% 16.46/10.70 (and(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))) = and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))),
% 16.46/10.70 inference(monotonicity,[status(thm)],[169, 166])).
% 16.46/10.70 tff(171,plain,
% 16.46/10.70 (and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))) = and(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))),
% 16.46/10.70 inference(symmetry,[status(thm)],[170])).
% 16.46/10.70 tff(172,plain,
% 16.46/10.70 (and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))) = not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))))),
% 16.46/10.70 inference(transitivity,[status(thm)],[171, 163, 161])).
% 16.46/10.70 tff(173,plain,
% 16.46/10.70 (or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))) = or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))),
% 16.46/10.70 inference(monotonicity,[status(thm)],[172, 154])).
% 16.46/10.70 tff(174,plain,
% 16.46/10.70 (implies(or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))) = implies(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.70 inference(monotonicity,[status(thm)],[173])).
% 16.46/10.70 tff(175,plain,
% 16.46/10.70 (is_a_theorem(implies(or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) <=> is_a_theorem(implies(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))),
% 16.46/10.70 inference(monotonicity,[status(thm)],[174])).
% 16.46/10.70 tff(176,plain,
% 16.46/10.70 (^[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)))))),
% 16.46/10.70 inference(bind,[status(th)],[])).
% 16.46/10.70 tff(177,plain,
% 16.46/10.70 (![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))))),
% 16.46/10.70 inference(quant_intro,[status(thm)],[176])).
% 16.46/10.70 tff(178,plain,
% 16.46/10.70 (![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: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 16.46/10.70 inference(rewrite,[status(thm)],[])).
% 16.46/10.70 tff(179,plain,
% 16.46/10.70 (($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))))),
% 16.46/10.70 inference(rewrite,[status(thm)],[])).
% 16.46/10.70 tff(180,axiom,(r4), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r4')).
% 16.46/10.70 tff(181,plain,
% 16.46/10.70 (r4 <=> $true),
% 16.46/10.70 inference(iff_true,[status(thm)],[180])).
% 16.46/10.70 tff(182,plain,
% 16.46/10.70 ((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)))))),
% 16.46/10.70 inference(monotonicity,[status(thm)],[181])).
% 16.46/10.70 tff(183,plain,
% 16.46/10.70 ((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))))),
% 16.46/10.70 inference(transitivity,[status(thm)],[182, 179])).
% 16.46/10.70 tff(184,plain,
% 16.46/10.70 ((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)))))),
% 16.46/10.70 inference(rewrite,[status(thm)],[])).
% 16.46/10.70 tff(185,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')).
% 16.46/10.70 tff(186,plain,
% 16.46/10.70 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 16.46/10.70 inference(modus_ponens,[status(thm)],[185, 184])).
% 16.46/10.70 tff(187,plain,
% 16.46/10.70 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 16.46/10.70 inference(modus_ponens,[status(thm)],[186, 184])).
% 16.46/10.70 tff(188,plain,
% 16.46/10.70 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 16.46/10.70 inference(modus_ponens,[status(thm)],[187, 183])).
% 16.46/10.70 tff(189,plain,
% 16.46/10.70 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 16.46/10.70 inference(modus_ponens,[status(thm)],[188, 178])).
% 16.46/10.70 tff(190,plain,(
% 16.46/10.70 ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 16.46/10.70 inference(skolemize,[status(sab)],[189])).
% 16.46/10.70 tff(191,plain,
% 16.46/10.70 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 16.46/10.70 inference(modus_ponens,[status(thm)],[190, 177])).
% 16.46/10.70 tff(192,plain,
% 16.46/10.70 ((~![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(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))),
% 16.46/10.70 inference(quant_inst,[status(thm)],[])).
% 16.46/10.70 tff(193,plain,
% 16.46/10.70 (is_a_theorem(implies(or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))),
% 16.46/10.70 inference(unit_resolution,[status(thm)],[192, 191])).
% 16.46/10.70 tff(194,plain,
% 16.46/10.70 (is_a_theorem(implies(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))),
% 16.46/10.70 inference(modus_ponens,[status(thm)],[193, 175])).
% 16.46/10.70 tff(195,plain,
% 16.46/10.70 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))) = or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.70 inference(quant_inst,[status(thm)],[])).
% 16.46/10.70 tff(196,plain,
% 16.46/10.70 (implies(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))) = or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))),
% 16.46/10.70 inference(unit_resolution,[status(thm)],[195, 45])).
% 16.46/10.70 tff(197,plain,
% 16.46/10.70 (or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))) = implies(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))),
% 16.46/10.70 inference(symmetry,[status(thm)],[196])).
% 16.46/10.70 tff(198,plain,
% 16.46/10.70 (is_a_theorem(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))) <=> is_a_theorem(implies(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.70 inference(monotonicity,[status(thm)],[197])).
% 16.46/10.70 tff(199,plain,
% 16.46/10.70 (is_a_theorem(implies(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))) <=> is_a_theorem(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.70 inference(symmetry,[status(thm)],[198])).
% 16.46/10.70 tff(200,plain,
% 16.46/10.70 (implies(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))) = implies(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))),
% 16.46/10.71 inference(monotonicity,[status(thm)],[157, 154])).
% 16.46/10.71 tff(201,plain,
% 16.46/10.71 (is_a_theorem(implies(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))) <=> is_a_theorem(implies(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.71 inference(monotonicity,[status(thm)],[200])).
% 16.46/10.71 tff(202,plain,
% 16.46/10.71 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.71 inference(quant_inst,[status(thm)],[])).
% 16.46/10.71 tff(203,plain,
% 16.46/10.71 (is_a_theorem(implies(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.71 inference(unit_resolution,[status(thm)],[202, 136])).
% 16.46/10.71 tff(204,plain,
% 16.46/10.71 (is_a_theorem(implies(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2)))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.71 inference(modus_ponens,[status(thm)],[203, 201])).
% 16.46/10.71 tff(205,plain,
% 16.46/10.71 (is_a_theorem(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.71 inference(modus_ponens,[status(thm)],[204, 199])).
% 16.46/10.71 tff(206,plain,
% 16.46/10.71 (^[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)))))),
% 16.46/10.71 inference(bind,[status(th)],[])).
% 16.46/10.71 tff(207,plain,
% 16.46/10.71 (![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))))),
% 16.46/10.71 inference(quant_intro,[status(thm)],[206])).
% 16.46/10.71 tff(208,plain,
% 16.46/10.71 (^[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))))))),
% 16.46/10.71 inference(bind,[status(th)],[])).
% 16.46/10.71 tff(209,plain,
% 16.46/10.71 (![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))))),
% 16.46/10.71 inference(quant_intro,[status(thm)],[208])).
% 16.46/10.71 tff(210,plain,
% 16.46/10.71 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 16.46/10.71 inference(rewrite,[status(thm)],[])).
% 16.46/10.71 tff(211,plain,
% 16.46/10.71 (($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)))))),
% 16.46/10.71 inference(rewrite,[status(thm)],[])).
% 16.46/10.71 tff(212,axiom,(modus_ponens), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_modus_ponens')).
% 16.46/10.71 tff(213,plain,
% 16.46/10.71 (modus_ponens <=> $true),
% 16.46/10.71 inference(iff_true,[status(thm)],[212])).
% 16.46/10.71 tff(214,plain,
% 16.46/10.71 ((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))))))),
% 16.46/10.71 inference(monotonicity,[status(thm)],[213])).
% 16.46/10.71 tff(215,plain,
% 16.46/10.71 ((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)))))),
% 16.46/10.71 inference(transitivity,[status(thm)],[214, 211])).
% 16.46/10.71 tff(216,plain,
% 16.46/10.71 ((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))))))),
% 16.46/10.71 inference(rewrite,[status(thm)],[])).
% 16.46/10.71 tff(217,plain,
% 16.46/10.71 ((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))))))),
% 16.46/10.71 inference(rewrite,[status(thm)],[])).
% 16.46/10.71 tff(218,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')).
% 16.46/10.71 tff(219,plain,
% 16.46/10.71 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 16.46/10.71 inference(modus_ponens,[status(thm)],[218, 217])).
% 16.46/10.71 tff(220,plain,
% 16.46/10.71 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 16.46/10.71 inference(modus_ponens,[status(thm)],[219, 216])).
% 16.46/10.71 tff(221,plain,
% 16.46/10.71 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 16.46/10.71 inference(modus_ponens,[status(thm)],[220, 215])).
% 16.46/10.71 tff(222,plain,
% 16.46/10.71 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 16.46/10.71 inference(modus_ponens,[status(thm)],[221, 210])).
% 16.46/10.71 tff(223,plain,(
% 16.46/10.71 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 16.46/10.71 inference(skolemize,[status(sab)],[222])).
% 16.46/10.71 tff(224,plain,
% 16.46/10.71 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 16.46/10.71 inference(modus_ponens,[status(thm)],[223, 209])).
% 16.46/10.71 tff(225,plain,
% 16.46/10.71 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 16.46/10.71 inference(modus_ponens,[status(thm)],[224, 207])).
% 16.46/10.71 tff(226,plain,
% 16.46/10.71 (((~![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(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))) | (~is_a_theorem(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))) | (~is_a_theorem(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))))),
% 16.46/10.71 inference(rewrite,[status(thm)],[])).
% 16.46/10.71 tff(227,plain,
% 16.46/10.71 ((~![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(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))) | (~is_a_theorem(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))))),
% 16.46/10.71 inference(quant_inst,[status(thm)],[])).
% 16.46/10.71 tff(228,plain,
% 16.46/10.71 ((~![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(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))) | (~is_a_theorem(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))))),
% 16.46/10.71 inference(modus_ponens,[status(thm)],[227, 226])).
% 16.46/10.71 tff(229,plain,
% 16.46/10.71 (is_a_theorem(or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))) | (~is_a_theorem(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(not(and(not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))), not(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))), or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))))),
% 16.46/10.71 inference(unit_resolution,[status(thm)],[228, 225])).
% 16.46/10.71 tff(230,plain,
% 16.46/10.71 (is_a_theorem(or(not(or(not(or(not(not(P!2)), Q!1)), not(and(not(Q!1), not(not(not(P!2))))))), or(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))), not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))),
% 16.46/10.71 inference(unit_resolution,[status(thm)],[229, 205, 194])).
% 16.46/10.71 tff(231,plain,
% 16.46/10.71 (is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))))),
% 16.46/10.71 inference(modus_ponens,[status(thm)],[230, 149])).
% 16.46/10.71 tff(232,plain,
% 16.46/10.71 (is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2))))) <=> is_a_theorem(implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))),
% 16.46/10.71 inference(monotonicity,[status(thm)],[166])).
% 16.46/10.71 tff(233,plain,
% 16.46/10.71 (is_a_theorem(implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))) <=> is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))),
% 16.46/10.71 inference(symmetry,[status(thm)],[232])).
% 16.46/10.71 tff(234,plain,
% 16.46/10.71 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))),
% 16.46/10.71 inference(quant_inst,[status(thm)],[])).
% 16.46/10.71 tff(235,plain,
% 16.46/10.71 (is_a_theorem(implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))),
% 16.46/10.71 inference(unit_resolution,[status(thm)],[234, 136])).
% 16.46/10.71 tff(236,plain,
% 16.46/10.71 (is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))),
% 16.46/10.71 inference(modus_ponens,[status(thm)],[235, 233])).
% 16.46/10.71 tff(237,plain,
% 16.46/10.71 (((~![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(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))) | is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))) | is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))))))),
% 16.46/10.71 inference(rewrite,[status(thm)],[])).
% 16.46/10.71 tff(238,plain,
% 16.46/10.71 ((is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))) | (~is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))))) <=> ((~is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))) | is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))))))),
% 16.46/10.72 inference(rewrite,[status(thm)],[])).
% 16.46/10.72 tff(239,plain,
% 16.46/10.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))) | (~is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))) | is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))))))),
% 16.46/10.72 inference(monotonicity,[status(thm)],[238])).
% 16.46/10.72 tff(240,plain,
% 16.46/10.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))) | (~is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))) | is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))))))),
% 16.46/10.72 inference(transitivity,[status(thm)],[239, 237])).
% 16.46/10.72 tff(241,plain,
% 16.46/10.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))) | (~is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))))))),
% 16.46/10.72 inference(quant_inst,[status(thm)],[])).
% 16.46/10.72 tff(242,plain,
% 16.46/10.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))))) | is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))))),
% 16.46/10.72 inference(modus_ponens,[status(thm)],[241, 240])).
% 16.46/10.72 tff(243,plain,
% 16.46/10.72 (is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))))))) | (~is_a_theorem(implies(or(not(or(not(not(P!2)), Q!1)), or(Q!1, not(not(P!2)))), not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))))),
% 16.46/10.72 inference(unit_resolution,[status(thm)],[242, 225, 236])).
% 16.46/10.72 tff(244,plain,
% 16.46/10.72 (is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))),
% 16.46/10.72 inference(unit_resolution,[status(thm)],[243, 231])).
% 16.46/10.72 tff(245,plain,
% 16.46/10.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))) | (~is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))) | (~is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))))))),
% 16.46/10.72 inference(rewrite,[status(thm)],[])).
% 16.46/10.72 tff(246,plain,
% 16.46/10.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))) | (~is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))))))),
% 16.46/10.72 inference(quant_inst,[status(thm)],[])).
% 16.46/10.72 tff(247,plain,
% 16.46/10.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))) | (~is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))))),
% 16.46/10.72 inference(modus_ponens,[status(thm)],[246, 245])).
% 16.46/10.72 tff(248,plain,
% 16.46/10.72 (is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))) | (~is_a_theorem(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))))) | (~is_a_theorem(implies(not(and(not(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))), not(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1)))))))))), or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))))),
% 16.52/10.72 inference(unit_resolution,[status(thm)],[247, 225])).
% 16.52/10.72 tff(249,plain,
% 16.52/10.72 (is_a_theorem(or(not(or(not(not(and(not(Q!1), not(not(not(P!2)))))), not(not(or(not(not(not(not(P!2)))), not(not(Q!1))))))), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))),
% 16.52/10.72 inference(unit_resolution,[status(thm)],[248, 244, 139])).
% 16.52/10.72 tff(250,plain,
% 16.52/10.72 (is_a_theorem(implies(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))),
% 16.52/10.72 inference(modus_ponens,[status(thm)],[249, 114])).
% 16.52/10.72 tff(251,plain,
% 16.52/10.72 (is_a_theorem(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1))) <=> is_a_theorem(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)))),
% 16.52/10.72 inference(monotonicity,[status(thm)],[169])).
% 16.52/10.72 tff(252,plain,
% 16.52/10.72 (is_a_theorem(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1))) <=> is_a_theorem(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)))),
% 16.52/10.72 inference(symmetry,[status(thm)],[251])).
% 16.52/10.72 tff(253,plain,
% 16.52/10.72 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)))),
% 16.52/10.72 inference(quant_inst,[status(thm)],[])).
% 16.52/10.72 tff(254,plain,
% 16.52/10.72 (is_a_theorem(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)))),
% 16.52/10.72 inference(unit_resolution,[status(thm)],[253, 136])).
% 16.52/10.72 tff(255,plain,
% 16.52/10.72 (is_a_theorem(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)))),
% 16.52/10.72 inference(modus_ponens,[status(thm)],[254, 252])).
% 16.52/10.72 tff(256,plain,
% 16.52/10.72 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))) | (~is_a_theorem(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)))) | (~is_a_theorem(implies(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))) | (~is_a_theorem(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)))) | (~is_a_theorem(implies(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))))),
% 16.52/10.72 inference(rewrite,[status(thm)],[])).
% 16.52/10.72 tff(257,plain,
% 16.52/10.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))) | (~is_a_theorem(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)))) | (~is_a_theorem(implies(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))))))),
% 16.52/10.72 inference(quant_inst,[status(thm)],[])).
% 16.52/10.72 tff(258,plain,
% 16.52/10.72 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))) | (~is_a_theorem(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)))) | (~is_a_theorem(implies(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))))),
% 16.52/10.72 inference(modus_ponens,[status(thm)],[257, 256])).
% 16.52/10.72 tff(259,plain,
% 16.52/10.72 (is_a_theorem(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2)))))) | (~is_a_theorem(implies(or(not(or(Q!1, not(not(P!2)))), or(not(not(P!2)), Q!1)), and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))))),
% 16.52/10.72 inference(unit_resolution,[status(thm)],[258, 225, 255])).
% 16.52/10.72 tff(260,plain,
% 16.52/10.72 (is_a_theorem(and(implies(or(Q!1, not(not(P!2))), or(not(not(P!2)), Q!1)), implies(or(not(not(P!2)), Q!1), or(Q!1, not(not(P!2))))))),
% 16.52/10.72 inference(unit_resolution,[status(thm)],[259, 250])).
% 16.52/10.72 tff(261,plain,
% 16.52/10.72 (is_a_theorem(equiv(not(and(not(Q!1), not(not(not(P!2))))), or(not(not(P!2)), Q!1)))),
% 16.52/10.72 inference(modus_ponens,[status(thm)],[260, 77])).
% 16.52/10.72 tff(262,plain,
% 16.52/10.72 (^[X: $i, Y: $i] : refl(((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 16.52/10.72 inference(bind,[status(th)],[])).
% 16.52/10.72 tff(263,plain,
% 16.52/10.72 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 16.52/10.72 inference(quant_intro,[status(thm)],[262])).
% 16.52/10.72 tff(264,plain,
% 16.52/10.72 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 16.52/10.72 inference(rewrite,[status(thm)],[])).
% 16.52/10.72 tff(265,plain,
% 16.52/10.72 (($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))),
% 16.52/10.72 inference(rewrite,[status(thm)],[])).
% 16.52/10.72 tff(266,axiom,(substitution_of_equivalents), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','substitution_of_equivalents')).
% 16.52/10.72 tff(267,plain,
% 16.52/10.72 (substitution_of_equivalents <=> $true),
% 16.52/10.72 inference(iff_true,[status(thm)],[266])).
% 16.52/10.72 tff(268,plain,
% 16.52/10.72 ((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)))),
% 16.52/10.72 inference(monotonicity,[status(thm)],[267])).
% 16.52/10.72 tff(269,plain,
% 16.52/10.72 ((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))),
% 16.52/10.72 inference(transitivity,[status(thm)],[268, 265])).
% 16.52/10.72 tff(270,plain,
% 16.52/10.72 ((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)))),
% 16.52/10.72 inference(rewrite,[status(thm)],[])).
% 16.52/10.72 tff(271,plain,
% 16.52/10.72 ((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)))),
% 16.52/10.72 inference(rewrite,[status(thm)],[])).
% 16.52/10.72 tff(272,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')).
% 16.52/10.72 tff(273,plain,
% 16.52/10.72 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 16.52/10.72 inference(modus_ponens,[status(thm)],[272, 271])).
% 16.52/10.72 tff(274,plain,
% 16.52/10.72 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 16.52/10.72 inference(modus_ponens,[status(thm)],[273, 270])).
% 16.52/10.72 tff(275,plain,
% 16.52/10.72 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 16.52/10.72 inference(modus_ponens,[status(thm)],[274, 269])).
% 16.52/10.72 tff(276,plain,
% 16.52/10.72 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 16.52/10.72 inference(modus_ponens,[status(thm)],[275, 264])).
% 16.52/10.72 tff(277,plain,(
% 16.52/10.72 ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 16.52/10.72 inference(skolemize,[status(sab)],[276])).
% 16.52/10.72 tff(278,plain,
% 16.52/10.72 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 16.52/10.72 inference(modus_ponens,[status(thm)],[277, 263])).
% 16.52/10.72 tff(279,plain,
% 16.52/10.72 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(and(not(Q!1), not(not(not(P!2))))), or(not(not(P!2)), Q!1)))) | (not(and(not(Q!1), not(not(not(P!2))))) = or(not(not(P!2)), Q!1)))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(and(not(Q!1), not(not(not(P!2))))), or(not(not(P!2)), Q!1)))) | (not(and(not(Q!1), not(not(not(P!2))))) = or(not(not(P!2)), Q!1)))),
% 16.52/10.73 inference(rewrite,[status(thm)],[])).
% 16.52/10.73 tff(280,plain,
% 16.52/10.73 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(not(and(not(Q!1), not(not(not(P!2))))), or(not(not(P!2)), Q!1)))) | (not(and(not(Q!1), not(not(not(P!2))))) = or(not(not(P!2)), Q!1)))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(281,plain,
% 16.52/10.73 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(not(and(not(Q!1), not(not(not(P!2))))), or(not(not(P!2)), Q!1)))) | (not(and(not(Q!1), not(not(not(P!2))))) = or(not(not(P!2)), Q!1))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[280, 279])).
% 16.52/10.73 tff(282,plain,
% 16.52/10.73 ((~is_a_theorem(equiv(not(and(not(Q!1), not(not(not(P!2))))), or(not(not(P!2)), Q!1)))) | (not(and(not(Q!1), not(not(not(P!2))))) = or(not(not(P!2)), Q!1))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[281, 278])).
% 16.52/10.73 tff(283,plain,
% 16.52/10.73 (not(and(not(Q!1), not(not(not(P!2))))) = or(not(not(P!2)), Q!1)),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[282, 261])).
% 16.52/10.73 tff(284,plain,
% 16.52/10.73 (or(Q!1, not(not(P!2))) = implies(not(P!2), Q!1)),
% 16.52/10.73 inference(transitivity,[status(thm)],[50, 283, 48])).
% 16.52/10.73 tff(285,plain,
% 16.52/10.73 (or(not(P!2), or(Q!1, not(not(P!2)))) = or(not(P!2), implies(not(P!2), Q!1))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[284])).
% 16.52/10.73 tff(286,plain,
% 16.52/10.73 (implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), or(Q!1, not(not(P!2))))) = implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), implies(not(P!2), Q!1)))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[285])).
% 16.52/10.73 tff(287,plain,
% 16.52/10.73 (is_a_theorem(implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), or(Q!1, not(not(P!2)))))) <=> is_a_theorem(implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), implies(not(P!2), Q!1))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[286])).
% 16.52/10.73 tff(288,plain,
% 16.52/10.73 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) | is_a_theorem(implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), or(Q!1, not(not(P!2))))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(289,plain,
% 16.52/10.73 (is_a_theorem(implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), or(Q!1, not(not(P!2))))))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[288, 191])).
% 16.52/10.73 tff(290,plain,
% 16.52/10.73 (is_a_theorem(implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), implies(not(P!2), Q!1))))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[289, 287])).
% 16.52/10.73 tff(291,plain,
% 16.52/10.73 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(P!2, implies(not(P!2), Q!1)) = or(not(P!2), implies(not(P!2), Q!1)))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(292,plain,
% 16.52/10.73 (implies(P!2, implies(not(P!2), Q!1)) = or(not(P!2), implies(not(P!2), Q!1))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[291, 45])).
% 16.52/10.73 tff(293,plain,
% 16.52/10.73 (or(not(P!2), implies(not(P!2), Q!1)) = implies(P!2, implies(not(P!2), Q!1))),
% 16.52/10.73 inference(symmetry,[status(thm)],[292])).
% 16.52/10.73 tff(294,plain,
% 16.52/10.73 (is_a_theorem(or(not(P!2), implies(not(P!2), Q!1))) <=> is_a_theorem(implies(P!2, implies(not(P!2), Q!1)))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[293])).
% 16.52/10.73 tff(295,plain,
% 16.52/10.73 (is_a_theorem(implies(P!2, implies(not(P!2), Q!1))) <=> is_a_theorem(or(not(P!2), implies(not(P!2), Q!1)))),
% 16.52/10.73 inference(symmetry,[status(thm)],[294])).
% 16.52/10.73 tff(296,plain,
% 16.52/10.73 ((~is_a_theorem(implies(P!2, implies(not(P!2), Q!1)))) <=> (~is_a_theorem(or(not(P!2), implies(not(P!2), Q!1))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[295])).
% 16.52/10.73 tff(297,plain,
% 16.52/10.73 ((~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q))))),
% 16.52/10.73 inference(rewrite,[status(thm)],[])).
% 16.52/10.73 tff(298,plain,
% 16.52/10.73 (($false <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q))))),
% 16.52/10.73 inference(rewrite,[status(thm)],[])).
% 16.52/10.73 tff(299,axiom,(~cn2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','luka_cn2')).
% 16.52/10.73 tff(300,plain,
% 16.52/10.73 (cn2 <=> $false),
% 16.52/10.73 inference(iff_false,[status(thm)],[299])).
% 16.52/10.73 tff(301,plain,
% 16.52/10.73 ((cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))) <=> ($false <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[300])).
% 16.52/10.73 tff(302,plain,
% 16.52/10.73 ((cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q))))),
% 16.52/10.73 inference(transitivity,[status(thm)],[301, 298])).
% 16.52/10.73 tff(303,plain,
% 16.52/10.73 ((cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))) <=> (cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q))))),
% 16.52/10.73 inference(rewrite,[status(thm)],[])).
% 16.52/10.73 tff(304,axiom,(cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','cn2')).
% 16.52/10.73 tff(305,plain,
% 16.52/10.73 (cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[304, 303])).
% 16.52/10.73 tff(306,plain,
% 16.52/10.73 (cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[305, 303])).
% 16.52/10.73 tff(307,plain,
% 16.52/10.73 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[306, 302])).
% 16.52/10.73 tff(308,plain,
% 16.52/10.73 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[307, 297])).
% 16.52/10.73 tff(309,plain,
% 16.52/10.73 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[308, 297])).
% 16.52/10.73 tff(310,plain,
% 16.52/10.73 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[309, 297])).
% 16.52/10.73 tff(311,plain,
% 16.52/10.73 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[310, 297])).
% 16.52/10.73 tff(312,plain,
% 16.52/10.73 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[311, 297])).
% 16.52/10.73 tff(313,plain,
% 16.52/10.73 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[312, 297])).
% 16.52/10.73 tff(314,plain,(
% 16.52/10.73 ~is_a_theorem(implies(P!2, implies(not(P!2), Q!1)))),
% 16.52/10.73 inference(skolemize,[status(sab)],[313])).
% 16.52/10.73 tff(315,plain,
% 16.52/10.73 (~is_a_theorem(or(not(P!2), implies(not(P!2), Q!1)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[314, 296])).
% 16.52/10.73 tff(316,plain,
% 16.52/10.73 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(P!2), implies(not(P!2), Q!1))) | (~is_a_theorem(or(Q!1, or(not(P!2), not(not(P!2)))))) | (~is_a_theorem(implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), implies(not(P!2), Q!1))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(P!2), implies(not(P!2), Q!1))) | (~is_a_theorem(or(Q!1, or(not(P!2), not(not(P!2)))))) | (~is_a_theorem(implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), implies(not(P!2), Q!1))))))),
% 16.52/10.73 inference(rewrite,[status(thm)],[])).
% 16.52/10.73 tff(317,plain,
% 16.52/10.73 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(P!2), implies(not(P!2), Q!1))) | (~is_a_theorem(or(Q!1, or(not(P!2), not(not(P!2)))))) | (~is_a_theorem(implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), implies(not(P!2), Q!1))))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(318,plain,
% 16.52/10.73 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(P!2), implies(not(P!2), Q!1))) | (~is_a_theorem(or(Q!1, or(not(P!2), not(not(P!2)))))) | (~is_a_theorem(implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), implies(not(P!2), Q!1)))))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[317, 316])).
% 16.52/10.73 tff(319,plain,
% 16.52/10.73 ((~is_a_theorem(or(Q!1, or(not(P!2), not(not(P!2)))))) | (~is_a_theorem(implies(or(Q!1, or(not(P!2), not(not(P!2)))), or(not(P!2), implies(not(P!2), Q!1)))))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[318, 225, 315])).
% 16.52/10.73 tff(320,plain,
% 16.52/10.73 (~is_a_theorem(or(Q!1, or(not(P!2), not(not(P!2)))))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[319, 290])).
% 16.52/10.73 tff(321,plain,
% 16.52/10.73 (~is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2)))))))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[320, 26])).
% 16.52/10.73 tff(322,plain,
% 16.52/10.73 (implies(or(not(P!2), not(not(P!2))), or(Q!1, or(not(P!2), not(not(P!2))))) = implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2)))))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[22])).
% 16.52/10.73 tff(323,plain,
% 16.52/10.73 (is_a_theorem(implies(or(not(P!2), not(not(P!2))), or(Q!1, or(not(P!2), not(not(P!2)))))) <=> is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[322])).
% 16.52/10.73 tff(324,plain,
% 16.52/10.73 (^[P: $i, Q: $i] : refl(is_a_theorem(implies(Q, or(P, Q))) <=> is_a_theorem(implies(Q, or(P, Q))))),
% 16.52/10.73 inference(bind,[status(th)],[])).
% 16.52/10.73 tff(325,plain,
% 16.52/10.73 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 16.52/10.73 inference(quant_intro,[status(thm)],[324])).
% 16.52/10.73 tff(326,plain,
% 16.52/10.73 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 16.52/10.73 inference(rewrite,[status(thm)],[])).
% 16.52/10.73 tff(327,plain,
% 16.52/10.73 (($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 16.52/10.73 inference(rewrite,[status(thm)],[])).
% 16.52/10.73 tff(328,axiom,(r2), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r2')).
% 16.52/10.73 tff(329,plain,
% 16.52/10.73 (r2 <=> $true),
% 16.52/10.73 inference(iff_true,[status(thm)],[328])).
% 16.52/10.73 tff(330,plain,
% 16.52/10.73 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[329])).
% 16.52/10.73 tff(331,plain,
% 16.52/10.73 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 16.52/10.73 inference(transitivity,[status(thm)],[330, 327])).
% 16.52/10.73 tff(332,plain,
% 16.52/10.73 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 16.52/10.73 inference(rewrite,[status(thm)],[])).
% 16.52/10.73 tff(333,axiom,(r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','r2')).
% 16.52/10.73 tff(334,plain,
% 16.52/10.73 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[333, 332])).
% 16.52/10.73 tff(335,plain,
% 16.52/10.73 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[334, 332])).
% 16.52/10.73 tff(336,plain,
% 16.52/10.73 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[335, 331])).
% 16.52/10.73 tff(337,plain,
% 16.52/10.73 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[336, 326])).
% 16.52/10.73 tff(338,plain,(
% 16.52/10.73 ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 16.52/10.73 inference(skolemize,[status(sab)],[337])).
% 16.52/10.73 tff(339,plain,
% 16.52/10.73 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[338, 325])).
% 16.52/10.73 tff(340,plain,
% 16.52/10.73 ((~![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) | is_a_theorem(implies(or(not(P!2), not(not(P!2))), or(Q!1, or(not(P!2), not(not(P!2))))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(341,plain,
% 16.52/10.73 (is_a_theorem(implies(or(not(P!2), not(not(P!2))), or(Q!1, or(not(P!2), not(not(P!2))))))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[340, 339])).
% 16.52/10.73 tff(342,plain,
% 16.52/10.73 (is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[341, 323])).
% 16.52/10.73 tff(343,plain,
% 16.52/10.73 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), or(not(not(P!2)), not(P!2))) = not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2))))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(344,plain,
% 16.52/10.73 (or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), or(not(not(P!2)), not(P!2))) = not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[343, 20])).
% 16.52/10.73 tff(345,plain,
% 16.52/10.73 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(not(Q!1), not(P!2)) = not(and(not(not(Q!1)), not(not(P!2)))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(346,plain,
% 16.52/10.73 (or(not(Q!1), not(P!2)) = not(and(not(not(Q!1)), not(not(P!2))))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[345, 20])).
% 16.52/10.73 tff(347,plain,
% 16.52/10.73 (not(and(not(not(Q!1)), not(not(P!2)))) = or(not(Q!1), not(P!2))),
% 16.52/10.73 inference(symmetry,[status(thm)],[346])).
% 16.52/10.73 tff(348,plain,
% 16.52/10.73 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(not(not(Q!1)), not(not(P!2))) = not(or(not(not(not(Q!1))), not(not(not(P!2))))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(349,plain,
% 16.52/10.73 (and(not(not(Q!1)), not(not(P!2))) = not(or(not(not(not(Q!1))), not(not(not(P!2)))))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[348, 99])).
% 16.52/10.73 tff(350,plain,
% 16.52/10.73 (not(or(not(not(not(Q!1))), not(not(not(P!2))))) = and(not(not(Q!1)), not(not(P!2)))),
% 16.52/10.73 inference(symmetry,[status(thm)],[349])).
% 16.52/10.73 tff(351,plain,
% 16.52/10.73 (not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))) = not(and(not(not(Q!1)), not(not(P!2))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[350])).
% 16.52/10.73 tff(352,plain,
% 16.52/10.73 (not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))) = or(not(Q!1), not(P!2))),
% 16.52/10.73 inference(transitivity,[status(thm)],[351, 347])).
% 16.52/10.73 tff(353,plain,
% 16.52/10.73 (or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))) = or(not(not(P!2)), or(not(Q!1), not(P!2)))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[352])).
% 16.52/10.73 tff(354,plain,
% 16.52/10.73 (or(not(not(P!2)), or(not(Q!1), not(P!2))) = or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))),
% 16.52/10.73 inference(symmetry,[status(thm)],[353])).
% 16.52/10.73 tff(355,plain,
% 16.52/10.73 (not(or(not(not(P!2)), or(not(Q!1), not(P!2)))) = not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[354])).
% 16.52/10.73 tff(356,plain,
% 16.52/10.73 (or(not(or(not(not(P!2)), or(not(Q!1), not(P!2)))), or(not(not(P!2)), not(P!2))) = or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), or(not(not(P!2)), not(P!2)))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[355])).
% 16.52/10.73 tff(357,plain,
% 16.52/10.73 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(P!2)), or(not(Q!1), not(P!2))), or(not(not(P!2)), not(P!2))) = or(not(or(not(not(P!2)), or(not(Q!1), not(P!2)))), or(not(not(P!2)), not(P!2))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(358,plain,
% 16.52/10.73 (implies(or(not(not(P!2)), or(not(Q!1), not(P!2))), or(not(not(P!2)), not(P!2))) = or(not(or(not(not(P!2)), or(not(Q!1), not(P!2)))), or(not(not(P!2)), not(P!2)))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[357, 45])).
% 16.52/10.73 tff(359,plain,
% 16.52/10.73 (implies(or(not(not(P!2)), or(not(Q!1), not(P!2))), or(not(not(P!2)), not(P!2))) = not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))),
% 16.52/10.73 inference(transitivity,[status(thm)],[358, 356, 344])).
% 16.52/10.73 tff(360,plain,
% 16.52/10.73 (is_a_theorem(implies(or(not(not(P!2)), or(not(Q!1), not(P!2))), or(not(not(P!2)), not(P!2)))) <=> is_a_theorem(not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2))))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[359])).
% 16.52/10.73 tff(361,plain,
% 16.52/10.73 (is_a_theorem(not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))) <=> is_a_theorem(implies(or(not(not(P!2)), or(not(Q!1), not(P!2))), or(not(not(P!2)), not(P!2))))),
% 16.52/10.73 inference(symmetry,[status(thm)],[360])).
% 16.52/10.73 tff(362,plain,
% 16.52/10.73 (implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), or(not(not(P!2)), not(P!2)))) = implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2))))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[344])).
% 16.52/10.73 tff(363,plain,
% 16.52/10.73 (is_a_theorem(implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), or(not(not(P!2)), not(P!2))))) <=> is_a_theorem(implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[362])).
% 16.52/10.73 tff(364,plain,
% 16.52/10.73 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) | is_a_theorem(implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), or(not(not(P!2)), not(P!2)))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(365,plain,
% 16.52/10.73 (is_a_theorem(implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), or(not(not(P!2)), not(P!2)))))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[364, 191])).
% 16.52/10.73 tff(366,plain,
% 16.52/10.73 (is_a_theorem(implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[365, 363])).
% 16.52/10.73 tff(367,plain,
% 16.52/10.73 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(P!2), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))) = or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(368,plain,
% 16.52/10.73 (implies(not(P!2), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))) = or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2)))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[367, 45])).
% 16.52/10.73 tff(369,plain,
% 16.52/10.73 (is_a_theorem(implies(not(P!2), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2)))) <=> is_a_theorem(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[368])).
% 16.52/10.73 tff(370,plain,
% 16.52/10.73 ((~![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) | is_a_theorem(implies(not(P!2), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(371,plain,
% 16.52/10.73 (is_a_theorem(implies(not(P!2), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[370, 339])).
% 16.52/10.73 tff(372,plain,
% 16.52/10.73 (is_a_theorem(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[371, 369])).
% 16.52/10.73 tff(373,plain,
% 16.52/10.73 (((~![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(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))) | (~is_a_theorem(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))))) | (~is_a_theorem(implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))) | (~is_a_theorem(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))))) | (~is_a_theorem(implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))))))),
% 16.52/10.73 inference(rewrite,[status(thm)],[])).
% 16.52/10.73 tff(374,plain,
% 16.52/10.73 ((~![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(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))) | (~is_a_theorem(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))))) | (~is_a_theorem(implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(375,plain,
% 16.52/10.73 ((~![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(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))) | (~is_a_theorem(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))))) | (~is_a_theorem(implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2))))))))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[374, 373])).
% 16.52/10.73 tff(376,plain,
% 16.52/10.73 (is_a_theorem(not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2)))))) | (~is_a_theorem(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))))) | (~is_a_theorem(implies(or(not(not(P!2)), or(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2)))))))), not(P!2))), not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2))))))))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[375, 225])).
% 16.52/10.73 tff(377,plain,
% 16.52/10.73 (is_a_theorem(not(and(not(not(or(not(not(P!2)), not(not(or(not(not(not(Q!1))), not(not(not(P!2))))))))), not(or(not(not(P!2)), not(P!2))))))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[376, 372, 366])).
% 16.52/10.73 tff(378,plain,
% 16.52/10.73 (is_a_theorem(implies(or(not(not(P!2)), or(not(Q!1), not(P!2))), or(not(not(P!2)), not(P!2))))),
% 16.52/10.73 inference(modus_ponens,[status(thm)],[377, 361])).
% 16.52/10.73 tff(379,plain,
% 16.52/10.73 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(P!2), or(not(Q!1), not(P!2))) = or(not(not(P!2)), or(not(Q!1), not(P!2))))),
% 16.52/10.73 inference(quant_inst,[status(thm)],[])).
% 16.52/10.73 tff(380,plain,
% 16.52/10.73 (implies(not(P!2), or(not(Q!1), not(P!2))) = or(not(not(P!2)), or(not(Q!1), not(P!2)))),
% 16.52/10.73 inference(unit_resolution,[status(thm)],[379, 45])).
% 16.52/10.73 tff(381,plain,
% 16.52/10.73 (or(not(not(P!2)), or(not(Q!1), not(P!2))) = implies(not(P!2), or(not(Q!1), not(P!2)))),
% 16.52/10.73 inference(symmetry,[status(thm)],[380])).
% 16.52/10.73 tff(382,plain,
% 16.52/10.73 (is_a_theorem(or(not(not(P!2)), or(not(Q!1), not(P!2)))) <=> is_a_theorem(implies(not(P!2), or(not(Q!1), not(P!2))))),
% 16.52/10.73 inference(monotonicity,[status(thm)],[381])).
% 16.52/10.73 tff(383,plain,
% 16.52/10.73 (is_a_theorem(implies(not(P!2), or(not(Q!1), not(P!2)))) <=> is_a_theorem(or(not(not(P!2)), or(not(Q!1), not(P!2))))),
% 16.52/10.74 inference(symmetry,[status(thm)],[382])).
% 16.52/10.74 tff(384,plain,
% 16.52/10.74 ((~![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) | is_a_theorem(implies(not(P!2), or(not(Q!1), not(P!2))))),
% 16.52/10.74 inference(quant_inst,[status(thm)],[])).
% 16.52/10.74 tff(385,plain,
% 16.52/10.74 (is_a_theorem(implies(not(P!2), or(not(Q!1), not(P!2))))),
% 16.52/10.74 inference(unit_resolution,[status(thm)],[384, 339])).
% 16.52/10.74 tff(386,plain,
% 16.52/10.74 (is_a_theorem(or(not(not(P!2)), or(not(Q!1), not(P!2))))),
% 16.52/10.74 inference(modus_ponens,[status(thm)],[385, 383])).
% 16.52/10.74 tff(387,plain,
% 16.52/10.74 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(not(P!2)), not(P!2))) | (~is_a_theorem(or(not(not(P!2)), or(not(Q!1), not(P!2))))) | (~is_a_theorem(implies(or(not(not(P!2)), or(not(Q!1), not(P!2))), or(not(not(P!2)), not(P!2))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(not(P!2)), not(P!2))) | (~is_a_theorem(or(not(not(P!2)), or(not(Q!1), not(P!2))))) | (~is_a_theorem(implies(or(not(not(P!2)), or(not(Q!1), not(P!2))), or(not(not(P!2)), not(P!2))))))),
% 16.52/10.74 inference(rewrite,[status(thm)],[])).
% 16.52/10.74 tff(388,plain,
% 16.52/10.74 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(not(P!2)), not(P!2))) | (~is_a_theorem(or(not(not(P!2)), or(not(Q!1), not(P!2))))) | (~is_a_theorem(implies(or(not(not(P!2)), or(not(Q!1), not(P!2))), or(not(not(P!2)), not(P!2))))))),
% 16.52/10.74 inference(quant_inst,[status(thm)],[])).
% 16.52/10.74 tff(389,plain,
% 16.52/10.74 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(not(P!2)), not(P!2))) | (~is_a_theorem(or(not(not(P!2)), or(not(Q!1), not(P!2))))) | (~is_a_theorem(implies(or(not(not(P!2)), or(not(Q!1), not(P!2))), or(not(not(P!2)), not(P!2)))))),
% 16.52/10.74 inference(modus_ponens,[status(thm)],[388, 387])).
% 16.52/10.74 tff(390,plain,
% 16.52/10.74 (is_a_theorem(or(not(not(P!2)), not(P!2))) | (~is_a_theorem(implies(or(not(not(P!2)), or(not(Q!1), not(P!2))), or(not(not(P!2)), not(P!2)))))),
% 16.52/10.74 inference(unit_resolution,[status(thm)],[389, 225, 386])).
% 16.52/10.74 tff(391,plain,
% 16.52/10.74 (is_a_theorem(or(not(not(P!2)), not(P!2)))),
% 16.52/10.74 inference(unit_resolution,[status(thm)],[390, 378])).
% 16.52/10.74 tff(392,plain,
% 16.52/10.74 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(not(P!2)), not(P!2)), or(not(P!2), not(not(P!2)))))),
% 16.52/10.74 inference(quant_inst,[status(thm)],[])).
% 16.52/10.74 tff(393,plain,
% 16.52/10.74 (is_a_theorem(implies(or(not(not(P!2)), not(P!2)), or(not(P!2), not(not(P!2)))))),
% 16.52/10.74 inference(unit_resolution,[status(thm)],[392, 136])).
% 16.52/10.74 tff(394,plain,
% 16.52/10.74 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(P!2), not(not(P!2)))) | (~is_a_theorem(or(not(not(P!2)), not(P!2)))) | (~is_a_theorem(implies(or(not(not(P!2)), not(P!2)), or(not(P!2), not(not(P!2)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(P!2), not(not(P!2)))) | (~is_a_theorem(or(not(not(P!2)), not(P!2)))) | (~is_a_theorem(implies(or(not(not(P!2)), not(P!2)), or(not(P!2), not(not(P!2)))))))),
% 16.52/10.74 inference(rewrite,[status(thm)],[])).
% 16.52/10.74 tff(395,plain,
% 16.52/10.74 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(P!2), not(not(P!2)))) | (~is_a_theorem(or(not(not(P!2)), not(P!2)))) | (~is_a_theorem(implies(or(not(not(P!2)), not(P!2)), or(not(P!2), not(not(P!2)))))))),
% 16.52/10.74 inference(quant_inst,[status(thm)],[])).
% 16.52/10.74 tff(396,plain,
% 16.52/10.74 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(P!2), not(not(P!2)))) | (~is_a_theorem(or(not(not(P!2)), not(P!2)))) | (~is_a_theorem(implies(or(not(not(P!2)), not(P!2)), or(not(P!2), not(not(P!2))))))),
% 16.52/10.74 inference(modus_ponens,[status(thm)],[395, 394])).
% 16.52/10.74 tff(397,plain,
% 16.52/10.74 (is_a_theorem(or(not(P!2), not(not(P!2)))) | (~is_a_theorem(or(not(not(P!2)), not(P!2))))),
% 16.57/10.76 inference(unit_resolution,[status(thm)],[396, 225, 393])).
% 16.57/10.76 tff(398,plain,
% 16.57/10.76 (is_a_theorem(or(not(P!2), not(not(P!2))))),
% 16.57/10.76 inference(unit_resolution,[status(thm)],[397, 391])).
% 16.57/10.76 tff(399,plain,
% 16.57/10.76 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(P!2), not(not(P!2))))) | is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(P!2), not(not(P!2))))) | is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))))))),
% 16.57/10.76 inference(rewrite,[status(thm)],[])).
% 16.57/10.76 tff(400,plain,
% 16.57/10.76 ((is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) | (~is_a_theorem(or(not(P!2), not(not(P!2))))) | (~is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2)))))))))) <=> ((~is_a_theorem(or(not(P!2), not(not(P!2))))) | is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))))))),
% 16.57/10.76 inference(rewrite,[status(thm)],[])).
% 16.57/10.76 tff(401,plain,
% 16.57/10.76 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) | (~is_a_theorem(or(not(P!2), not(not(P!2))))) | (~is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | ((~is_a_theorem(or(not(P!2), not(not(P!2))))) | is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2)))))))))))),
% 16.57/10.76 inference(monotonicity,[status(thm)],[400])).
% 16.57/10.76 tff(402,plain,
% 16.57/10.76 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) | (~is_a_theorem(or(not(P!2), not(not(P!2))))) | (~is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(P!2), not(not(P!2))))) | is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))))))),
% 16.57/10.76 inference(transitivity,[status(thm)],[401, 399])).
% 16.57/10.76 tff(403,plain,
% 16.57/10.76 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) | (~is_a_theorem(or(not(P!2), not(not(P!2))))) | (~is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))))))),
% 16.57/10.76 inference(quant_inst,[status(thm)],[])).
% 16.57/10.76 tff(404,plain,
% 16.57/10.76 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (~is_a_theorem(or(not(P!2), not(not(P!2))))) | is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2)))))))))),
% 16.57/10.76 inference(modus_ponens,[status(thm)],[403, 402])).
% 16.57/10.76 tff(405,plain,
% 16.57/10.76 (is_a_theorem(not(and(not(Q!1), not(or(not(P!2), not(not(P!2))))))) | (~is_a_theorem(implies(or(not(P!2), not(not(P!2))), not(and(not(Q!1), not(or(not(P!2), not(not(P!2)))))))))),
% 16.57/10.76 inference(unit_resolution,[status(thm)],[404, 225, 398])).
% 16.57/10.76 tff(406,plain,
% 16.57/10.76 ($false),
% 16.57/10.76 inference(unit_resolution,[status(thm)],[405, 342, 321])).
% 16.57/10.76 % SZS output end Proof
%------------------------------------------------------------------------------