TSTP Solution File: LCL531+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL531+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 04:56:36 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL531+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 22:06:48 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.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(is_a_theorem_type, type, (
% 0.19/0.41 is_a_theorem: $i > $o)).
% 0.19/0.41 tff(implies_type, type, (
% 0.19/0.41 implies: ( $i * $i ) > $i)).
% 0.19/0.41 tff(not_type, type, (
% 0.19/0.41 not: $i > $i)).
% 0.19/0.41 tff(and_type, type, (
% 0.19/0.41 and: ( $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_X_3_type, type, (
% 0.19/0.41 tptp_fun_X_3: $i)).
% 0.19/0.41 tff(op_implies_and_type, type, (
% 0.19/0.41 op_implies_and: $o)).
% 0.19/0.41 tff(implies_2_type, type, (
% 0.19/0.41 implies_2: $o)).
% 0.19/0.41 tff(and_3_type, type, (
% 0.19/0.41 and_3: $o)).
% 0.19/0.41 tff(necessarily_type, type, (
% 0.19/0.41 necessarily: $i > $i)).
% 0.19/0.41 tff(strict_implies_type, type, (
% 0.19/0.41 strict_implies: ( $i * $i ) > $i)).
% 0.19/0.41 tff(op_strict_implies_type, type, (
% 0.19/0.41 op_strict_implies: $o)).
% 0.19/0.41 tff(axiom_m4_type, type, (
% 0.19/0.41 axiom_m4: $o)).
% 0.19/0.41 tff(necessitation_type, type, (
% 0.19/0.41 necessitation: $o)).
% 0.19/0.41 tff(modus_ponens_type, type, (
% 0.19/0.41 modus_ponens: $o)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (($false | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 ((~$true) <=> $false),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(6,axiom,(op_implies_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_op_implies_and')).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (op_implies_and <=> $true),
% 0.19/0.41 inference(iff_true,[status(thm)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 ((~op_implies_and) <=> (~$true)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[7])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 ((~op_implies_and) <=> $false),
% 0.19/0.41 inference(transitivity,[status(thm)],[8, 5])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (((~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)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[9])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (((~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))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[10, 4])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (((~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)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 ((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)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(14,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')).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.19/0.41 tff(19,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(X!3, and(X!3, X!3)) = not(and(X!3, not(and(X!3, X!3)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (implies(X!3, and(X!3, X!3)) = not(and(X!3, not(and(X!3, X!3))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(X!3, implies(X!3, and(X!3, X!3))) = not(and(X!3, not(implies(X!3, and(X!3, X!3))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (implies(X!3, implies(X!3, and(X!3, X!3))) = not(and(X!3, not(implies(X!3, and(X!3, X!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (implies(implies(X!3, implies(X!3, and(X!3, X!3))), implies(X!3, and(X!3, X!3))) = implies(not(and(X!3, not(implies(X!3, and(X!3, X!3))))), not(and(X!3, not(and(X!3, X!3)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[24, 22])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (is_a_theorem(implies(implies(X!3, implies(X!3, and(X!3, X!3))), implies(X!3, and(X!3, X!3)))) <=> is_a_theorem(implies(not(and(X!3, not(implies(X!3, and(X!3, X!3))))), not(and(X!3, not(and(X!3, X!3))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))) <=> is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(31,axiom,(implies_2), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_implies_2')).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (implies_2 <=> $true),
% 0.19/0.41 inference(iff_true,[status(thm)],[31])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 ((implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 ((implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[33, 30])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 ((implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))) <=> (implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(36,axiom,(implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','implies_2')).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 35])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.19/0.41 tff(41,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[40])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[41, 28])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))) | is_a_theorem(implies(implies(X!3, implies(X!3, and(X!3, X!3))), implies(X!3, and(X!3, X!3))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (is_a_theorem(implies(implies(X!3, implies(X!3, and(X!3, X!3))), implies(X!3, and(X!3, X!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (is_a_theorem(implies(not(and(X!3, not(implies(X!3, and(X!3, X!3))))), not(and(X!3, not(and(X!3, X!3))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 26])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (not(and(X!3, not(implies(X!3, and(X!3, X!3))))) = implies(X!3, implies(X!3, and(X!3, X!3)))),
% 0.19/0.42 inference(symmetry,[status(thm)],[24])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (is_a_theorem(not(and(X!3, not(implies(X!3, and(X!3, X!3)))))) <=> is_a_theorem(implies(X!3, implies(X!3, and(X!3, X!3))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (is_a_theorem(implies(X!3, implies(X!3, and(X!3, X!3)))) <=> is_a_theorem(not(and(X!3, not(implies(X!3, and(X!3, X!3))))))),
% 0.19/0.42 inference(symmetry,[status(thm)],[47])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(X, implies(Y, and(X, Y)))) <=> is_a_theorem(implies(X, implies(Y, and(X, Y)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(53,axiom,(and_3), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_and_3')).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (and_3 <=> $true),
% 0.19/0.42 inference(iff_true,[status(thm)],[53])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 ((and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 ((and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[55, 52])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 ((and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) <=> (and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(58,axiom,(and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','and_3')).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[59, 57])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.19/0.42 tff(63,plain,(
% 0.19/0.42 ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[62])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[63, 50])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) | is_a_theorem(implies(X!3, implies(X!3, and(X!3, X!3))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (is_a_theorem(implies(X!3, implies(X!3, and(X!3, X!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (is_a_theorem(not(and(X!3, not(implies(X!3, and(X!3, X!3))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[66, 48])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (not(and(X!3, not(and(X!3, X!3)))) = implies(X!3, and(X!3, X!3))),
% 0.19/0.42 inference(symmetry,[status(thm)],[22])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (is_a_theorem(not(and(X!3, not(and(X!3, X!3))))) <=> is_a_theorem(implies(X!3, and(X!3, X!3)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (is_a_theorem(implies(X!3, and(X!3, X!3))) <=> is_a_theorem(not(and(X!3, not(and(X!3, X!3)))))),
% 0.19/0.42 inference(symmetry,[status(thm)],[69])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 ((~is_a_theorem(implies(X!3, and(X!3, X!3)))) <=> (~is_a_theorem(not(and(X!3, not(and(X!3, X!3))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[70])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : refl((strict_implies(X, Y) = necessarily(implies(X, Y))) <=> (strict_implies(X, Y) = necessarily(implies(X, Y))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))) <=> ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))) <=> ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (($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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(76,axiom,(op_strict_implies), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_0_op_strict_implies')).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (op_strict_implies <=> $true),
% 0.19/0.42 inference(iff_true,[status(thm)],[76])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~op_strict_implies) <=> (~$true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 ((~op_strict_implies) <=> $false),
% 0.19/0.42 inference(transitivity,[status(thm)],[78, 5])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (((~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))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (((~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)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[80, 75])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (((~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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 ((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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(84,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')).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[87, 81])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[88, 74])).
% 0.19/0.42 tff(90,plain,(
% 0.19/0.42 ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[89])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[90, 73])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) | (strict_implies(X!3, and(X!3, X!3)) = necessarily(implies(X!3, and(X!3, X!3))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (strict_implies(X!3, and(X!3, X!3)) = necessarily(implies(X!3, and(X!3, X!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (necessarily(implies(X!3, and(X!3, X!3))) = strict_implies(X!3, and(X!3, X!3))),
% 0.19/0.42 inference(symmetry,[status(thm)],[93])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (is_a_theorem(necessarily(implies(X!3, and(X!3, X!3)))) <=> is_a_theorem(strict_implies(X!3, and(X!3, X!3)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (is_a_theorem(strict_implies(X!3, and(X!3, X!3))) <=> is_a_theorem(necessarily(implies(X!3, and(X!3, X!3))))),
% 0.19/0.42 inference(symmetry,[status(thm)],[95])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 ((~is_a_theorem(strict_implies(X!3, and(X!3, X!3)))) <=> (~is_a_theorem(necessarily(implies(X!3, and(X!3, X!3)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[96])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 ((~![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))) <=> (~![X: $i] : is_a_theorem(strict_implies(X, and(X, X))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (($false <=> ![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))) <=> (~![X: $i] : is_a_theorem(strict_implies(X, and(X, X))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(100,axiom,(~axiom_m4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_0_axiom_m4')).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (axiom_m4 <=> $false),
% 0.19/0.42 inference(iff_false,[status(thm)],[100])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 ((axiom_m4 <=> ![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))) <=> ($false <=> ![X: $i] : is_a_theorem(strict_implies(X, and(X, X))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 ((axiom_m4 <=> ![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))) <=> (~![X: $i] : is_a_theorem(strict_implies(X, and(X, X))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[102, 99])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((axiom_m4 <=> ![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))) <=> (axiom_m4 <=> ![X: $i] : is_a_theorem(strict_implies(X, and(X, X))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(105,axiom,(axiom_m4 <=> ![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax','axiom_m4')).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (axiom_m4 <=> ![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (axiom_m4 <=> ![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[106, 104])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (axiom_m4 <=> ![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[107, 104])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (~![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[108, 103])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (~![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[109, 98])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (~![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[110, 98])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (~![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[111, 98])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (~![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[112, 98])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (~![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[113, 98])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (~![X: $i] : is_a_theorem(strict_implies(X, and(X, X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[114, 98])).
% 0.19/0.42 tff(116,plain,(
% 0.19/0.42 ~is_a_theorem(strict_implies(X!3, and(X!3, X!3)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[115])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (~is_a_theorem(necessarily(implies(X!3, and(X!3, X!3))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[116, 97])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (^[X: $i] : refl((is_a_theorem(necessarily(X)) | (~is_a_theorem(X))) <=> (is_a_theorem(necessarily(X)) | (~is_a_theorem(X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X))) <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X))) <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (($true <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))) <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(122,axiom,(necessitation), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax','km5_necessitation')).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (necessitation <=> $true),
% 0.19/0.42 inference(iff_true,[status(thm)],[122])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 ((necessitation <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))) <=> ($true <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[123])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 ((necessitation <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))) <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[124, 121])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 ((necessitation <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))) <=> (necessitation <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 ((necessitation <=> ![X: $i] : (is_a_theorem(X) => is_a_theorem(necessarily(X)))) <=> (necessitation <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(128,axiom,(necessitation <=> ![X: $i] : (is_a_theorem(X) => is_a_theorem(necessarily(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax','necessitation')).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (necessitation <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (necessitation <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[129, 126])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 (necessitation <=> ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[131, 125])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[132, 120])).
% 0.19/0.42 tff(134,plain,(
% 0.19/0.42 ![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[133])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[134, 119])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (((~![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))) | (is_a_theorem(necessarily(implies(X!3, and(X!3, X!3)))) | (~is_a_theorem(implies(X!3, and(X!3, X!3)))))) <=> ((~![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))) | is_a_theorem(necessarily(implies(X!3, and(X!3, X!3)))) | (~is_a_theorem(implies(X!3, and(X!3, X!3)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 ((~![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))) | (is_a_theorem(necessarily(implies(X!3, and(X!3, X!3)))) | (~is_a_theorem(implies(X!3, and(X!3, X!3)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 ((~![X: $i] : (is_a_theorem(necessarily(X)) | (~is_a_theorem(X)))) | is_a_theorem(necessarily(implies(X!3, and(X!3, X!3)))) | (~is_a_theorem(implies(X!3, and(X!3, X!3))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (is_a_theorem(necessarily(implies(X!3, and(X!3, X!3)))) | (~is_a_theorem(implies(X!3, and(X!3, X!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[138, 135])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (~is_a_theorem(implies(X!3, and(X!3, X!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[139, 117])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 (~is_a_theorem(not(and(X!3, not(and(X!3, X!3)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[140, 71])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[142])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (^[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))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[144])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 (($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)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(148,axiom,(modus_ponens), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_modus_ponens')).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (modus_ponens <=> $true),
% 0.19/0.42 inference(iff_true,[status(thm)],[148])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 ((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))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[149])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 ((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)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[150, 147])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 ((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))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 ((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))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(154,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')).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[155, 152])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[156, 151])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[157, 146])).
% 0.19/0.43 tff(159,plain,(
% 0.19/0.43 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[158])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[159, 145])).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[160, 143])).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(X!3, not(and(X!3, X!3))))) | (~is_a_theorem(not(and(X!3, not(implies(X!3, and(X!3, X!3))))))) | (~is_a_theorem(implies(not(and(X!3, not(implies(X!3, and(X!3, X!3))))), not(and(X!3, not(and(X!3, X!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!3, not(and(X!3, X!3))))) | (~is_a_theorem(not(and(X!3, not(implies(X!3, and(X!3, X!3))))))) | (~is_a_theorem(implies(not(and(X!3, not(implies(X!3, and(X!3, X!3))))), not(and(X!3, not(and(X!3, X!3))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(163,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(X!3, not(and(X!3, X!3))))) | (~is_a_theorem(not(and(X!3, not(implies(X!3, and(X!3, X!3))))))) | (~is_a_theorem(implies(not(and(X!3, not(implies(X!3, and(X!3, X!3))))), not(and(X!3, not(and(X!3, X!3))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(164,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(X!3, not(and(X!3, X!3))))) | (~is_a_theorem(not(and(X!3, not(implies(X!3, and(X!3, X!3))))))) | (~is_a_theorem(implies(not(and(X!3, not(implies(X!3, and(X!3, X!3))))), not(and(X!3, not(and(X!3, X!3)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 (is_a_theorem(not(and(X!3, not(and(X!3, X!3))))) | (~is_a_theorem(not(and(X!3, not(implies(X!3, and(X!3, X!3))))))) | (~is_a_theorem(implies(not(and(X!3, not(implies(X!3, and(X!3, X!3))))), not(and(X!3, not(and(X!3, X!3)))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[164, 161])).
% 0.19/0.43 tff(166,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[165, 141, 67, 45])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------