TSTP Solution File: LCL539+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL539+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 04:56:38 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL539+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 22:11:01 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(is_a_theorem_type, type, (
% 0.20/0.46 is_a_theorem: $i > $o)).
% 0.20/0.46 tff(implies_type, type, (
% 0.20/0.46 implies: ( $i * $i ) > $i)).
% 0.20/0.46 tff(and_type, type, (
% 0.20/0.46 and: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_X_4_type, type, (
% 0.20/0.46 tptp_fun_X_4: $i)).
% 0.20/0.46 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.46 tptp_fun_Y_3: $i)).
% 0.20/0.46 tff(not_type, type, (
% 0.20/0.46 not: $i > $i)).
% 0.20/0.46 tff(equiv_type, type, (
% 0.20/0.46 equiv: ( $i * $i ) > $i)).
% 0.20/0.46 tff(op_equiv_type, type, (
% 0.20/0.46 op_equiv: $o)).
% 0.20/0.46 tff(op_implies_and_type, type, (
% 0.20/0.46 op_implies_and: $o)).
% 0.20/0.46 tff(necessarily_type, type, (
% 0.20/0.46 necessarily: $i > $i)).
% 0.20/0.46 tff(strict_implies_type, type, (
% 0.20/0.46 strict_implies: ( $i * $i ) > $i)).
% 0.20/0.46 tff(op_strict_implies_type, type, (
% 0.20/0.46 op_strict_implies: $o)).
% 0.20/0.46 tff(and_1_type, type, (
% 0.20/0.46 and_1: $o)).
% 0.20/0.46 tff(strict_equiv_type, type, (
% 0.20/0.46 strict_equiv: ( $i * $i ) > $i)).
% 0.20/0.46 tff(op_strict_equiv_type, type, (
% 0.20/0.46 op_strict_equiv: $o)).
% 0.20/0.46 tff(substitution_strict_equiv_type, type, (
% 0.20/0.46 substitution_strict_equiv: $o)).
% 0.20/0.46 tff(modus_ponens_type, type, (
% 0.20/0.46 modus_ponens: $o)).
% 0.20/0.46 tff(axiom_M_type, type, (
% 0.20/0.46 axiom_M: $o)).
% 0.20/0.46 tff(equivalence_3_type, type, (
% 0.20/0.46 equivalence_3: $o)).
% 0.20/0.46 tff(and_2_type, type, (
% 0.20/0.46 and_2: $o)).
% 0.20/0.46 tff(substitution_of_equivalents_type, type, (
% 0.20/0.46 substitution_of_equivalents: $o)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (($false | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 ((~$true) <=> $false),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(6,axiom,(op_equiv), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_op_equiv')).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (op_equiv <=> $true),
% 0.20/0.46 inference(iff_true,[status(thm)],[6])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 ((~op_equiv) <=> (~$true)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[7])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 ((~op_equiv) <=> $false),
% 0.20/0.46 inference(transitivity,[status(thm)],[8, 5])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (((~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))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (((~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)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[10, 4])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (((~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))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 ((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))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(14,axiom,(op_equiv => ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_equiv')).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.20/0.47 tff(19,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[18])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(X!4, Y!3) = and(implies(X!4, Y!3), implies(Y!3, X!4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 (equiv(X!4, Y!3) = and(implies(X!4, Y!3), implies(Y!3, X!4))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (and(implies(X!4, Y!3), implies(Y!3, X!4)) = equiv(X!4, Y!3)),
% 0.20/0.47 inference(symmetry,[status(thm)],[22])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (($false | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(28,axiom,(op_implies_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_op_implies_and')).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (op_implies_and <=> $true),
% 0.20/0.47 inference(iff_true,[status(thm)],[28])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 ((~op_implies_and) <=> (~$true)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 ((~op_implies_and) <=> $false),
% 0.20/0.47 inference(transitivity,[status(thm)],[30, 5])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ($false | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[32, 27])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 ((op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(36,axiom,(op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_implies_and')).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[39, 26])).
% 0.20/0.47 tff(41,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[40])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[41, 25])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(Y!3, X!4) = not(and(Y!3, not(X!4))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 (implies(Y!3, X!4) = not(and(Y!3, not(X!4)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (not(and(Y!3, not(X!4))) = implies(Y!3, X!4)),
% 0.20/0.47 inference(symmetry,[status(thm)],[44])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (implies(not(and(Y!3, not(X!4))), and(implies(X!4, Y!3), implies(Y!3, X!4))) = implies(implies(Y!3, X!4), equiv(X!4, Y!3))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[45, 23])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (is_a_theorem(implies(not(and(Y!3, not(X!4))), and(implies(X!4, Y!3), implies(Y!3, X!4)))) <=> is_a_theorem(implies(implies(Y!3, X!4), equiv(X!4, Y!3)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (is_a_theorem(implies(implies(Y!3, X!4), equiv(X!4, Y!3))) <=> is_a_theorem(implies(not(and(Y!3, not(X!4))), and(implies(X!4, Y!3), implies(Y!3, X!4))))),
% 0.20/0.47 inference(symmetry,[status(thm)],[47])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (^[X: $i, Y: $i] : refl((strict_implies(X, Y) = necessarily(implies(X, Y))) <=> (strict_implies(X, Y) = necessarily(implies(X, Y))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))) <=> ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))) <=> ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (($false | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) <=> ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(53,axiom,(op_strict_implies), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_0_op_strict_implies')).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (op_strict_implies <=> $true),
% 0.20/0.47 inference(iff_true,[status(thm)],[53])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 ((~op_strict_implies) <=> (~$true)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[54])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 ((~op_strict_implies) <=> $false),
% 0.20/0.47 inference(transitivity,[status(thm)],[55, 5])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) <=> ($false | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) <=> ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[57, 52])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) <=> ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 ((op_strict_implies => ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) <=> ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(61,axiom,(op_strict_implies => ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax','op_strict_implies')).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[64, 58])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[65, 51])).
% 0.20/0.47 tff(67,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[66])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[67, 50])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) | (strict_implies(X!4, Y!3) = necessarily(implies(X!4, Y!3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (strict_implies(X!4, Y!3) = necessarily(implies(X!4, Y!3))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), strict_implies(X!4, Y!3)) = implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(X!4, Y!3)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[70])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), strict_implies(X!4, Y!3))) <=> is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(X!4, Y!3))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(and(X, Y), X)) <=> is_a_theorem(implies(and(X, Y), X)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(77,axiom,(and_1), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_and_1')).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 (and_1 <=> $true),
% 0.20/0.47 inference(iff_true,[status(thm)],[77])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 ((and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[78])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 ((and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.20/0.47 inference(transitivity,[status(thm)],[79, 76])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 ((and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(82,axiom,(and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','and_1')).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[83, 81])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.20/0.47 tff(87,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.20/0.47 inference(skolemize,[status(sab)],[86])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[87, 74])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) | is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), strict_implies(X!4, Y!3)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), strict_implies(X!4, Y!3)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(X!4, Y!3))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[90, 72])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 (^[X: $i, Y: $i] : refl((strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X))) <=> (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X))) <=> ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X))) <=> ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (($false | ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))) <=> ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(96,axiom,(op_strict_equiv), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_0_op_strict_equiv')).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (op_strict_equiv <=> $true),
% 0.20/0.47 inference(iff_true,[status(thm)],[96])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 ((~op_strict_equiv) <=> (~$true)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 ((~op_strict_equiv) <=> $false),
% 0.20/0.47 inference(transitivity,[status(thm)],[98, 5])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (((~op_strict_equiv) | ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))) <=> ($false | ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (((~op_strict_equiv) | ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))) <=> ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[100, 95])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 (((~op_strict_equiv) | ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))) <=> ((~op_strict_equiv) | ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 ((op_strict_equiv => ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))) <=> ((~op_strict_equiv) | ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(104,axiom,(op_strict_equiv => ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax','op_strict_equiv')).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 ((~op_strict_equiv) | ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 ((~op_strict_equiv) | ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[105, 102])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 ((~op_strict_equiv) | ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[107, 101])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[108, 94])).
% 0.20/0.47 tff(110,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[109])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[110, 93])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : (strict_equiv(X, Y) = and(strict_implies(X, Y), strict_implies(Y, X)))) | (strict_equiv(X!4, Y!3) = and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (strict_equiv(X!4, Y!3) = and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)) = strict_equiv(X!4, Y!3)),
% 0.20/0.47 inference(symmetry,[status(thm)],[113])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4))) <=> is_a_theorem(strict_equiv(X!4, Y!3))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[114])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (is_a_theorem(strict_equiv(X!4, Y!3)) <=> is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[115])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))) <=> (~![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (($false <=> ![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))) <=> (~![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(119,axiom,(~substitution_strict_equiv), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_0_substitution_strict_equiv')).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (substitution_strict_equiv <=> $false),
% 0.20/0.47 inference(iff_false,[status(thm)],[119])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 ((substitution_strict_equiv <=> ![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))) <=> ($false <=> ![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 ((substitution_strict_equiv <=> ![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))) <=> (~![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[121, 118])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 ((substitution_strict_equiv <=> ![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))) <=> (substitution_strict_equiv <=> ![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 ((substitution_strict_equiv <=> ![X: $i, Y: $i] : (is_a_theorem(strict_equiv(X, Y)) => (X = Y))) <=> (substitution_strict_equiv <=> ![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(125,axiom,(substitution_strict_equiv <=> ![X: $i, Y: $i] : (is_a_theorem(strict_equiv(X, Y)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax','substitution_strict_equiv')).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (substitution_strict_equiv <=> ![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 (substitution_strict_equiv <=> ![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[126, 123])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (substitution_strict_equiv <=> ![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[128, 122])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[129, 117])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[130, 117])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[131, 117])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[132, 117])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[133, 117])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~is_a_theorem(strict_equiv(X, Y))) | (X = Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[134, 117])).
% 0.20/0.47 tff(136,plain,(
% 0.20/0.47 ~((~is_a_theorem(strict_equiv(X!4, Y!3))) | (X!4 = Y!3))),
% 0.20/0.47 inference(skolemize,[status(sab)],[135])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (is_a_theorem(strict_equiv(X!4, Y!3))),
% 0.20/0.47 inference(or_elim,[status(thm)],[136])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 (is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[137, 116])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (($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)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(145,axiom,(modus_ponens), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_modus_ponens')).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (modus_ponens <=> $true),
% 0.20/0.47 inference(iff_true,[status(thm)],[145])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 ((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))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 ((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)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[147, 144])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 ((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))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 ((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))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(151,axiom,(modus_ponens <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(implies(X, Y))) => is_a_theorem(Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','modus_ponens')).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[152, 149])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[153, 148])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[154, 143])).
% 0.20/0.48 tff(156,plain,(
% 0.20/0.48 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[155])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[156, 142])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[157, 140])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(necessarily(implies(X!4, Y!3))) | (~is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))) | (~is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(X!4, Y!3))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(necessarily(implies(X!4, Y!3))) | (~is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))) | (~is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(X!4, Y!3))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(necessarily(implies(X!4, Y!3))) | (~is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))) | (~is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(X!4, Y!3))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(necessarily(implies(X!4, Y!3))) | (~is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))) | (~is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(X!4, Y!3)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 (is_a_theorem(necessarily(implies(X!4, Y!3))) | (~is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))) | (~is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(X!4, Y!3)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[161, 158])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (is_a_theorem(necessarily(implies(X!4, Y!3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[162, 138, 91])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(X!4, Y!3) = not(and(X!4, not(Y!3))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 (implies(X!4, Y!3) = not(and(X!4, not(Y!3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[164, 42])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 (implies(necessarily(implies(X!4, Y!3)), implies(X!4, Y!3)) = implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[165])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 (is_a_theorem(implies(necessarily(implies(X!4, Y!3)), implies(X!4, Y!3))) <=> is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[166])).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 (^[X: $i] : refl(is_a_theorem(implies(necessarily(X), X)) <=> is_a_theorem(implies(necessarily(X), X)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (![X: $i] : is_a_theorem(implies(necessarily(X), X)) <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 (![X: $i] : is_a_theorem(implies(necessarily(X), X)) <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (($true <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))) <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(172,axiom,(axiom_M), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax','km4b_axiom_M')).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (axiom_M <=> $true),
% 0.20/0.48 inference(iff_true,[status(thm)],[172])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 ((axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))) <=> ($true <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 ((axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))) <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.20/0.48 inference(transitivity,[status(thm)],[174, 171])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 ((axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))) <=> (axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(177,axiom,(axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax','axiom_M')).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 (axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 (axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[178, 176])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 (axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[179, 176])).
% 0.20/0.48 tff(181,plain,
% 0.20/0.48 (![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[180, 175])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 (![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[181, 170])).
% 0.20/0.48 tff(183,plain,(
% 0.20/0.48 ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.20/0.48 inference(skolemize,[status(sab)],[182])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 (![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[183, 169])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 ((~![X: $i] : is_a_theorem(implies(necessarily(X), X))) | is_a_theorem(implies(necessarily(implies(X!4, Y!3)), implies(X!4, Y!3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 (is_a_theorem(implies(necessarily(implies(X!4, Y!3)), implies(X!4, Y!3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.20/0.48 tff(187,plain,
% 0.20/0.48 (is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[186, 167])).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(necessarily(implies(X!4, Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(necessarily(implies(X!4, Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(189,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(necessarily(implies(X!4, Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(necessarily(implies(X!4, Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 (is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(necessarily(implies(X!4, Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[190, 158])).
% 0.20/0.48 tff(192,plain,
% 0.20/0.48 (is_a_theorem(not(and(X!4, not(Y!3))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[191, 187, 163])).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 (not(and(X!4, not(Y!3))) = implies(X!4, Y!3)),
% 0.20/0.48 inference(symmetry,[status(thm)],[165])).
% 0.20/0.48 tff(194,plain,
% 0.20/0.48 (implies(not(and(X!4, not(Y!3))), implies(implies(Y!3, X!4), equiv(X!4, Y!3))) = implies(implies(X!4, Y!3), implies(implies(Y!3, X!4), equiv(X!4, Y!3)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[193])).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (is_a_theorem(implies(not(and(X!4, not(Y!3))), implies(implies(Y!3, X!4), equiv(X!4, Y!3)))) <=> is_a_theorem(implies(implies(X!4, Y!3), implies(implies(Y!3, X!4), equiv(X!4, Y!3))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[194])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 (is_a_theorem(implies(implies(X!4, Y!3), implies(implies(Y!3, X!4), equiv(X!4, Y!3)))) <=> is_a_theorem(implies(not(and(X!4, not(Y!3))), implies(implies(Y!3, X!4), equiv(X!4, Y!3))))),
% 0.20/0.48 inference(symmetry,[status(thm)],[195])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y)))) <=> is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[197])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(200,plain,
% 0.20/0.48 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(201,axiom,(equivalence_3), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_equivalence_3')).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 (equivalence_3 <=> $true),
% 0.20/0.48 inference(iff_true,[status(thm)],[201])).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 ((equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[202])).
% 0.20/0.48 tff(204,plain,
% 0.20/0.48 ((equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[203, 200])).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 ((equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))) <=> (equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(206,axiom,(equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','equivalence_3')).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 (equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.20/0.48 tff(208,plain,
% 0.20/0.48 (equivalence_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[207, 205])).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.20/0.48 tff(210,plain,
% 0.20/0.48 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[209, 199])).
% 0.20/0.48 tff(211,plain,(
% 0.20/0.48 ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[210])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[211, 198])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, X), equiv(X, Y))))) | is_a_theorem(implies(implies(X!4, Y!3), implies(implies(Y!3, X!4), equiv(X!4, Y!3))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 (is_a_theorem(implies(implies(X!4, Y!3), implies(implies(Y!3, X!4), equiv(X!4, Y!3))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 (is_a_theorem(implies(not(and(X!4, not(Y!3))), implies(implies(Y!3, X!4), equiv(X!4, Y!3))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[214, 196])).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(implies(Y!3, X!4), equiv(X!4, Y!3))) | (~is_a_theorem(not(and(X!4, not(Y!3))))) | (~is_a_theorem(implies(not(and(X!4, not(Y!3))), implies(implies(Y!3, X!4), equiv(X!4, Y!3))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(implies(Y!3, X!4), equiv(X!4, Y!3))) | (~is_a_theorem(not(and(X!4, not(Y!3))))) | (~is_a_theorem(implies(not(and(X!4, not(Y!3))), implies(implies(Y!3, X!4), equiv(X!4, Y!3))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(217,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(implies(Y!3, X!4), equiv(X!4, Y!3))) | (~is_a_theorem(not(and(X!4, not(Y!3))))) | (~is_a_theorem(implies(not(and(X!4, not(Y!3))), implies(implies(Y!3, X!4), equiv(X!4, Y!3))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(218,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(implies(Y!3, X!4), equiv(X!4, Y!3))) | (~is_a_theorem(not(and(X!4, not(Y!3))))) | (~is_a_theorem(implies(not(and(X!4, not(Y!3))), implies(implies(Y!3, X!4), equiv(X!4, Y!3)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.20/0.48 tff(219,plain,
% 0.20/0.48 (is_a_theorem(implies(implies(Y!3, X!4), equiv(X!4, Y!3))) | (~is_a_theorem(not(and(X!4, not(Y!3))))) | (~is_a_theorem(implies(not(and(X!4, not(Y!3))), implies(implies(Y!3, X!4), equiv(X!4, Y!3)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[218, 158])).
% 0.20/0.48 tff(220,plain,
% 0.20/0.48 (is_a_theorem(implies(implies(Y!3, X!4), equiv(X!4, Y!3)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[219, 215, 192])).
% 0.20/0.48 tff(221,plain,
% 0.20/0.48 (is_a_theorem(implies(not(and(Y!3, not(X!4))), and(implies(X!4, Y!3), implies(Y!3, X!4))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[220, 48])).
% 0.20/0.48 tff(222,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) | (strict_implies(Y!3, X!4) = necessarily(implies(Y!3, X!4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(223,plain,
% 0.20/0.48 (strict_implies(Y!3, X!4) = necessarily(implies(Y!3, X!4))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[222, 68])).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 (implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), strict_implies(Y!3, X!4)) = implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(Y!3, X!4)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[223])).
% 0.20/0.48 tff(225,plain,
% 0.20/0.48 (is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), strict_implies(Y!3, X!4))) <=> is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(Y!3, X!4))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[224])).
% 0.20/0.48 tff(226,plain,
% 0.20/0.48 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(and(X, Y), Y)) <=> is_a_theorem(implies(and(X, Y), Y)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(227,plain,
% 0.20/0.48 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[226])).
% 0.20/0.48 tff(228,plain,
% 0.20/0.48 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(229,plain,
% 0.20/0.48 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(230,axiom,(and_2), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_and_2')).
% 0.20/0.48 tff(231,plain,
% 0.20/0.48 (and_2 <=> $true),
% 0.20/0.48 inference(iff_true,[status(thm)],[230])).
% 0.20/0.48 tff(232,plain,
% 0.20/0.48 ((and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[231])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 ((and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.48 inference(transitivity,[status(thm)],[232, 229])).
% 0.20/0.48 tff(234,plain,
% 0.20/0.48 ((and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> (and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(235,axiom,(and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','and_2')).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 (and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.48 tff(237,plain,
% 0.20/0.48 (and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[236, 234])).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[237, 233])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[238, 228])).
% 0.20/0.48 tff(240,plain,(
% 0.20/0.48 ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.48 inference(skolemize,[status(sab)],[239])).
% 0.20/0.48 tff(241,plain,
% 0.20/0.48 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[240, 227])).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) | is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), strict_implies(Y!3, X!4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 (is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), strict_implies(Y!3, X!4)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 (is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(Y!3, X!4))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[243, 225])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(necessarily(implies(Y!3, X!4))) | (~is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))) | (~is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(Y!3, X!4))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(necessarily(implies(Y!3, X!4))) | (~is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))) | (~is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(Y!3, X!4))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(necessarily(implies(Y!3, X!4))) | (~is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))) | (~is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(Y!3, X!4))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(necessarily(implies(Y!3, X!4))) | (~is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))) | (~is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(Y!3, X!4)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 (is_a_theorem(necessarily(implies(Y!3, X!4))) | (~is_a_theorem(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)))) | (~is_a_theorem(implies(and(strict_implies(X!4, Y!3), strict_implies(Y!3, X!4)), necessarily(implies(Y!3, X!4)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[247, 158])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 (is_a_theorem(necessarily(implies(Y!3, X!4)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[248, 138, 244])).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 (implies(necessarily(implies(Y!3, X!4)), implies(Y!3, X!4)) = implies(necessarily(implies(Y!3, X!4)), not(and(Y!3, not(X!4))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.48 tff(251,plain,
% 0.20/0.48 (is_a_theorem(implies(necessarily(implies(Y!3, X!4)), implies(Y!3, X!4))) <=> is_a_theorem(implies(necessarily(implies(Y!3, X!4)), not(and(Y!3, not(X!4)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[250])).
% 0.20/0.48 tff(252,plain,
% 0.20/0.48 ((~![X: $i] : is_a_theorem(implies(necessarily(X), X))) | is_a_theorem(implies(necessarily(implies(Y!3, X!4)), implies(Y!3, X!4)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(253,plain,
% 0.20/0.48 (is_a_theorem(implies(necessarily(implies(Y!3, X!4)), implies(Y!3, X!4)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[252, 184])).
% 0.20/0.48 tff(254,plain,
% 0.20/0.48 (is_a_theorem(implies(necessarily(implies(Y!3, X!4)), not(and(Y!3, not(X!4)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[253, 251])).
% 0.20/0.48 tff(255,plain,
% 0.20/0.48 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(Y!3, not(X!4)))) | (~is_a_theorem(necessarily(implies(Y!3, X!4)))) | (~is_a_theorem(implies(necessarily(implies(Y!3, X!4)), not(and(Y!3, not(X!4)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(Y!3, not(X!4)))) | (~is_a_theorem(necessarily(implies(Y!3, X!4)))) | (~is_a_theorem(implies(necessarily(implies(Y!3, X!4)), not(and(Y!3, not(X!4)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(256,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(Y!3, not(X!4)))) | (~is_a_theorem(necessarily(implies(Y!3, X!4)))) | (~is_a_theorem(implies(necessarily(implies(Y!3, X!4)), not(and(Y!3, not(X!4)))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(Y!3, not(X!4)))) | (~is_a_theorem(necessarily(implies(Y!3, X!4)))) | (~is_a_theorem(implies(necessarily(implies(Y!3, X!4)), not(and(Y!3, not(X!4))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.20/0.48 tff(258,plain,
% 0.20/0.48 (is_a_theorem(not(and(Y!3, not(X!4)))) | (~is_a_theorem(necessarily(implies(Y!3, X!4)))) | (~is_a_theorem(implies(necessarily(implies(Y!3, X!4)), not(and(Y!3, not(X!4))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[257, 158])).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 (is_a_theorem(not(and(Y!3, not(X!4))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[258, 254, 249])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 (is_a_theorem(and(implies(X!4, Y!3), implies(Y!3, X!4))) <=> is_a_theorem(equiv(X!4, Y!3))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.48 tff(261,plain,
% 0.20/0.48 (is_a_theorem(equiv(X!4, Y!3)) <=> is_a_theorem(and(implies(X!4, Y!3), implies(Y!3, X!4)))),
% 0.20/0.48 inference(symmetry,[status(thm)],[260])).
% 0.20/0.48 tff(262,plain,
% 0.20/0.48 ((~is_a_theorem(equiv(X!4, Y!3))) <=> (~is_a_theorem(and(implies(X!4, Y!3), implies(Y!3, X!4))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[261])).
% 0.20/0.48 tff(263,plain,
% 0.20/0.48 (~(X!4 = Y!3)),
% 0.20/0.48 inference(or_elim,[status(thm)],[136])).
% 0.20/0.48 tff(264,plain,
% 0.20/0.48 (^[X: $i, Y: $i] : refl(((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ((~is_a_theorem(equiv(X, Y))) | (X = Y)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(265,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[264])).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(267,plain,
% 0.20/0.48 (($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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(268,axiom,(substitution_of_equivalents), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','substitution_of_equivalents')).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 (substitution_of_equivalents <=> $true),
% 0.20/0.48 inference(iff_true,[status(thm)],[268])).
% 0.20/0.48 tff(270,plain,
% 0.20/0.48 ((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)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[269])).
% 0.20/0.48 tff(271,plain,
% 0.20/0.48 ((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))),
% 0.20/0.48 inference(transitivity,[status(thm)],[270, 267])).
% 0.20/0.48 tff(272,plain,
% 0.20/0.48 ((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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(273,plain,
% 0.20/0.48 ((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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(274,axiom,(substitution_of_equivalents <=> ![X: $i, Y: $i] : (is_a_theorem(equiv(X, Y)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','substitution_of_equivalents')).
% 0.20/0.48 tff(275,plain,
% 0.20/0.48 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.20/0.48 tff(276,plain,
% 0.20/0.48 (substitution_of_equivalents <=> ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[275, 272])).
% 0.20/0.48 tff(277,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[276, 271])).
% 0.20/0.48 tff(278,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[277, 266])).
% 0.20/0.48 tff(279,plain,(
% 0.20/0.48 ![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 0.20/0.48 inference(skolemize,[status(sab)],[278])).
% 0.20/0.48 tff(280,plain,
% 0.20/0.48 (![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[279, 265])).
% 0.20/0.48 tff(281,plain,
% 0.20/0.48 (((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(X!4, Y!3))) | (X!4 = Y!3))) <=> ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(X!4, Y!3))) | (X!4 = Y!3))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(282,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | ((~is_a_theorem(equiv(X!4, Y!3))) | (X!4 = Y!3))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(283,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : ((~is_a_theorem(equiv(X, Y))) | (X = Y))) | (~is_a_theorem(equiv(X!4, Y!3))) | (X!4 = Y!3)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.20/0.48 tff(284,plain,
% 0.20/0.48 (~is_a_theorem(equiv(X!4, Y!3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[283, 280, 263])).
% 0.20/0.48 tff(285,plain,
% 0.20/0.48 (~is_a_theorem(and(implies(X!4, Y!3), implies(Y!3, X!4)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[284, 262])).
% 0.20/0.49 tff(286,plain,
% 0.20/0.49 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(and(implies(X!4, Y!3), implies(Y!3, X!4))) | (~is_a_theorem(not(and(Y!3, not(X!4))))) | (~is_a_theorem(implies(not(and(Y!3, not(X!4))), and(implies(X!4, Y!3), implies(Y!3, X!4))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(and(implies(X!4, Y!3), implies(Y!3, X!4))) | (~is_a_theorem(not(and(Y!3, not(X!4))))) | (~is_a_theorem(implies(not(and(Y!3, not(X!4))), and(implies(X!4, Y!3), implies(Y!3, X!4))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(287,plain,
% 0.20/0.49 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(and(implies(X!4, Y!3), implies(Y!3, X!4))) | (~is_a_theorem(not(and(Y!3, not(X!4))))) | (~is_a_theorem(implies(not(and(Y!3, not(X!4))), and(implies(X!4, Y!3), implies(Y!3, X!4))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(288,plain,
% 0.20/0.49 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(and(implies(X!4, Y!3), implies(Y!3, X!4))) | (~is_a_theorem(not(and(Y!3, not(X!4))))) | (~is_a_theorem(implies(not(and(Y!3, not(X!4))), and(implies(X!4, Y!3), implies(Y!3, X!4)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.20/0.49 tff(289,plain,
% 0.20/0.49 (is_a_theorem(and(implies(X!4, Y!3), implies(Y!3, X!4))) | (~is_a_theorem(not(and(Y!3, not(X!4))))) | (~is_a_theorem(implies(not(and(Y!3, not(X!4))), and(implies(X!4, Y!3), implies(Y!3, X!4)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[288, 158])).
% 0.20/0.49 tff(290,plain,
% 0.20/0.49 (~is_a_theorem(implies(not(and(Y!3, not(X!4))), and(implies(X!4, Y!3), implies(Y!3, X!4))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[289, 285, 259])).
% 0.20/0.49 tff(291,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[290, 221])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------