TSTP Solution File: LCL538+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL538+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 04:56:37 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL538+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 22:12:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(is_a_theorem_type, type, (
% 0.13/0.40 is_a_theorem: $i > $o)).
% 0.13/0.40 tff(implies_type, type, (
% 0.13/0.40 implies: ( $i * $i ) > $i)).
% 0.13/0.40 tff(not_type, type, (
% 0.13/0.40 not: $i > $i)).
% 0.13/0.40 tff(and_type, type, (
% 0.13/0.40 and: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.13/0.40 tptp_fun_Y_3: $i)).
% 0.13/0.40 tff(tptp_fun_X_4_type, type, (
% 0.13/0.40 tptp_fun_X_4: $i)).
% 0.13/0.40 tff(necessarily_type, type, (
% 0.13/0.40 necessarily: $i > $i)).
% 0.13/0.40 tff(op_implies_and_type, type, (
% 0.13/0.40 op_implies_and: $o)).
% 0.13/0.40 tff(axiom_M_type, type, (
% 0.13/0.40 axiom_M: $o)).
% 0.13/0.40 tff(strict_implies_type, type, (
% 0.13/0.40 strict_implies: ( $i * $i ) > $i)).
% 0.13/0.40 tff(op_strict_implies_type, type, (
% 0.13/0.40 op_strict_implies: $o)).
% 0.13/0.40 tff(modus_ponens_strict_implies_type, type, (
% 0.13/0.40 modus_ponens_strict_implies: $o)).
% 0.13/0.40 tff(modus_ponens_type, type, (
% 0.13/0.40 modus_ponens: $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (($false | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 ((~$true) <=> $false),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(6,axiom,(op_implies_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_op_implies_and')).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (op_implies_and <=> $true),
% 0.13/0.40 inference(iff_true,[status(thm)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~op_implies_and) <=> (~$true)),
% 0.13/0.40 inference(monotonicity,[status(thm)],[7])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 ((~op_implies_and) <=> $false),
% 0.13/0.40 inference(transitivity,[status(thm)],[8, 5])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (((~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)))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[9])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (((~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))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[10, 4])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (((~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)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 ((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)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 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')).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.13/0.40 tff(19,plain,(
% 0.13/0.40 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[18])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(X!4, Y!3) = not(and(X!4, not(Y!3))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (implies(X!4, Y!3) = not(and(X!4, not(Y!3)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 (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))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[22])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (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)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[23])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (^[X: $i] : refl(is_a_theorem(implies(necessarily(X), X)) <=> is_a_theorem(implies(necessarily(X), X)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (![X: $i] : is_a_theorem(implies(necessarily(X), X)) <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (![X: $i] : is_a_theorem(implies(necessarily(X), X)) <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (($true <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))) <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(29,axiom,(axiom_M), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax','km4b_axiom_M')).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (axiom_M <=> $true),
% 0.13/0.41 inference(iff_true,[status(thm)],[29])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 ((axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))) <=> ($true <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X)))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[30])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 ((axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))) <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.13/0.41 inference(transitivity,[status(thm)],[31, 28])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 ((axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))) <=> (axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(34,axiom,(axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax','axiom_M')).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[35, 33])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (axiom_M <=> ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 (![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[38, 27])).
% 0.13/0.41 tff(40,plain,(
% 0.13/0.41 ![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.13/0.41 inference(skolemize,[status(sab)],[39])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (![X: $i] : is_a_theorem(implies(necessarily(X), X))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[40, 26])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 ((~![X: $i] : is_a_theorem(implies(necessarily(X), X))) | is_a_theorem(implies(necessarily(implies(X!4, Y!3)), implies(X!4, Y!3)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (is_a_theorem(implies(necessarily(implies(X!4, Y!3)), implies(X!4, Y!3)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[43, 24])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (^[X: $i, Y: $i] : refl((strict_implies(X, Y) = necessarily(implies(X, Y))) <=> (strict_implies(X, Y) = necessarily(implies(X, Y))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))) <=> ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y))) <=> ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (($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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(49,axiom,(op_strict_implies), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_0_op_strict_implies')).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (op_strict_implies <=> $true),
% 0.13/0.41 inference(iff_true,[status(thm)],[49])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 ((~op_strict_implies) <=> (~$true)),
% 0.13/0.41 inference(monotonicity,[status(thm)],[50])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 ((~op_strict_implies) <=> $false),
% 0.13/0.41 inference(transitivity,[status(thm)],[51, 5])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (((~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))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[52])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 (((~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)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[53, 48])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (((~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))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 ((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))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(57,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')).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 ((~op_strict_implies) | ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[60, 54])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[61, 47])).
% 0.13/0.41 tff(63,plain,(
% 0.13/0.41 ![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[62])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[63, 46])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (strict_implies(X, Y) = necessarily(implies(X, Y)))) | (strict_implies(X!4, Y!3) = necessarily(implies(X!4, Y!3)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (strict_implies(X!4, Y!3) = necessarily(implies(X!4, Y!3))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 (necessarily(implies(X!4, Y!3)) = strict_implies(X!4, Y!3)),
% 0.13/0.41 inference(symmetry,[status(thm)],[66])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (is_a_theorem(necessarily(implies(X!4, Y!3))) <=> is_a_theorem(strict_implies(X!4, Y!3))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[67])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (is_a_theorem(strict_implies(X!4, Y!3)) <=> is_a_theorem(necessarily(implies(X!4, Y!3)))),
% 0.13/0.41 inference(symmetry,[status(thm)],[68])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))) <=> (~![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (($false <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))) <=> (~![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(72,axiom,(~modus_ponens_strict_implies), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_0_modus_ponens_strict_implies')).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (modus_ponens_strict_implies <=> $false),
% 0.13/0.41 inference(iff_false,[status(thm)],[72])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 ((modus_ponens_strict_implies <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))) <=> ($false <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[73])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 ((modus_ponens_strict_implies <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))) <=> (~![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[74, 71])).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 ((modus_ponens_strict_implies <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))) <=> (modus_ponens_strict_implies <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(77,plain,
% 0.13/0.41 ((modus_ponens_strict_implies <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(strict_implies(X, Y))) => is_a_theorem(Y))) <=> (modus_ponens_strict_implies <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(78,axiom,(modus_ponens_strict_implies <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(strict_implies(X, Y))) => is_a_theorem(Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax','modus_ponens_strict_implies')).
% 0.13/0.41 tff(79,plain,
% 0.13/0.41 (modus_ponens_strict_implies <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.13/0.41 tff(80,plain,
% 0.13/0.41 (modus_ponens_strict_implies <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.13/0.41 tff(81,plain,
% 0.13/0.41 (modus_ponens_strict_implies <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.13/0.41 tff(82,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[81, 75])).
% 0.13/0.41 tff(83,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[82, 70])).
% 0.13/0.41 tff(84,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[83, 70])).
% 0.13/0.41 tff(85,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[84, 70])).
% 0.13/0.41 tff(86,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[85, 70])).
% 0.13/0.41 tff(87,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[86, 70])).
% 0.13/0.41 tff(88,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(strict_implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[87, 70])).
% 0.13/0.41 tff(89,plain,(
% 0.13/0.41 ~(is_a_theorem(Y!3) | (~(is_a_theorem(X!4) & is_a_theorem(strict_implies(X!4, Y!3)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[88])).
% 0.13/0.41 tff(90,plain,
% 0.13/0.41 (is_a_theorem(X!4) & is_a_theorem(strict_implies(X!4, Y!3))),
% 0.13/0.41 inference(or_elim,[status(thm)],[89])).
% 0.13/0.41 tff(91,plain,
% 0.13/0.41 (is_a_theorem(strict_implies(X!4, Y!3))),
% 0.13/0.41 inference(and_elim,[status(thm)],[90])).
% 0.13/0.41 tff(92,plain,
% 0.13/0.41 (is_a_theorem(necessarily(implies(X!4, Y!3)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[91, 69])).
% 0.13/0.41 tff(93,plain,
% 0.13/0.41 (not(and(X!4, not(Y!3))) = implies(X!4, Y!3)),
% 0.13/0.41 inference(symmetry,[status(thm)],[22])).
% 0.13/0.41 tff(94,plain,
% 0.13/0.41 (is_a_theorem(not(and(X!4, not(Y!3)))) <=> is_a_theorem(implies(X!4, Y!3))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[93])).
% 0.13/0.41 tff(95,plain,
% 0.13/0.41 (is_a_theorem(implies(X!4, Y!3)) <=> is_a_theorem(not(and(X!4, not(Y!3))))),
% 0.13/0.41 inference(symmetry,[status(thm)],[94])).
% 0.13/0.41 tff(96,plain,
% 0.13/0.41 ((~is_a_theorem(implies(X!4, Y!3))) <=> (~is_a_theorem(not(and(X!4, not(Y!3)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[95])).
% 0.13/0.41 tff(97,plain,
% 0.13/0.41 (is_a_theorem(X!4)),
% 0.13/0.41 inference(and_elim,[status(thm)],[90])).
% 0.13/0.41 tff(98,plain,
% 0.13/0.41 (~is_a_theorem(Y!3)),
% 0.13/0.41 inference(or_elim,[status(thm)],[89])).
% 0.13/0.41 tff(99,plain,
% 0.13/0.41 (^[X: $i, Y: $i] : refl((is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X))) <=> (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(100,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[99])).
% 0.13/0.41 tff(101,plain,
% 0.13/0.41 (^[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(implies(X, Y))) | (~is_a_theorem(X)))), ((is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(102,plain,
% 0.13/0.41 (![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(implies(X, Y))) | (~is_a_theorem(X)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[101])).
% 0.13/0.41 tff(103,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(104,plain,
% 0.13/0.41 (($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)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(105,axiom,(modus_ponens), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_modus_ponens')).
% 0.13/0.41 tff(106,plain,
% 0.13/0.41 (modus_ponens <=> $true),
% 0.13/0.41 inference(iff_true,[status(thm)],[105])).
% 0.13/0.41 tff(107,plain,
% 0.13/0.41 ((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))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[106])).
% 0.13/0.41 tff(108,plain,
% 0.13/0.41 ((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)))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[107, 104])).
% 0.13/0.41 tff(109,plain,
% 0.13/0.41 ((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))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(110,plain,
% 0.13/0.41 ((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))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(111,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')).
% 0.13/0.41 tff(112,plain,
% 0.13/0.41 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.13/0.41 tff(113,plain,
% 0.13/0.41 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[112, 109])).
% 0.13/0.41 tff(114,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[113, 108])).
% 0.13/0.41 tff(115,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[114, 103])).
% 0.13/0.41 tff(116,plain,(
% 0.13/0.41 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[115])).
% 0.13/0.41 tff(117,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[116, 102])).
% 0.13/0.41 tff(118,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[117, 100])).
% 0.13/0.41 tff(119,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(Y!3) | (~is_a_theorem(implies(X!4, Y!3))) | (~is_a_theorem(X!4)))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(Y!3) | (~is_a_theorem(implies(X!4, Y!3))) | (~is_a_theorem(X!4)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(120,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(Y!3) | (~is_a_theorem(implies(X!4, Y!3))) | (~is_a_theorem(X!4)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(121,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | is_a_theorem(Y!3) | (~is_a_theorem(implies(X!4, Y!3))) | (~is_a_theorem(X!4))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.13/0.41 tff(122,plain,
% 0.13/0.41 (~is_a_theorem(implies(X!4, Y!3))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[121, 118, 98, 97])).
% 0.13/0.41 tff(123,plain,
% 0.13/0.41 (~is_a_theorem(not(and(X!4, not(Y!3))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[122, 96])).
% 0.13/0.41 tff(124,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(necessarily(implies(X!4, Y!3)))) | is_a_theorem(not(and(X!4, not(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(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(necessarily(implies(X!4, Y!3)))) | is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(125,plain,
% 0.13/0.41 ((is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))) | (~is_a_theorem(necessarily(implies(X!4, Y!3))))) <=> ((~is_a_theorem(necessarily(implies(X!4, Y!3)))) | is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(126,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))) | (~is_a_theorem(necessarily(implies(X!4, Y!3)))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | ((~is_a_theorem(necessarily(implies(X!4, Y!3)))) | is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))) | (~is_a_theorem(necessarily(implies(X!4, Y!3)))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(necessarily(implies(X!4, Y!3)))) | is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[126, 124])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3)))))) | (~is_a_theorem(necessarily(implies(X!4, Y!3)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(implies(X, Y))) | (~is_a_theorem(X)))) | (~is_a_theorem(necessarily(implies(X!4, Y!3)))) | is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 ((~is_a_theorem(necessarily(implies(X!4, Y!3)))) | is_a_theorem(not(and(X!4, not(Y!3)))) | (~is_a_theorem(implies(necessarily(implies(X!4, Y!3)), not(and(X!4, not(Y!3))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[129, 118])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[130, 123, 92, 44])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------