TSTP Solution File: LCL483+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL483+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 04:56:27 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL483+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 21:58:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(is_a_theorem_type, type, (
% 0.20/0.40 is_a_theorem: $i > $o)).
% 0.20/0.40 tff(implies_type, type, (
% 0.20/0.40 implies: ( $i * $i ) > $i)).
% 0.20/0.40 tff(or_type, type, (
% 0.20/0.40 or: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.40 tptp_fun_Y_0: $i)).
% 0.20/0.40 tff(not_type, type, (
% 0.20/0.40 not: $i > $i)).
% 0.20/0.40 tff(tptp_fun_X_1_type, type, (
% 0.20/0.40 tptp_fun_X_1: $i)).
% 0.20/0.40 tff(op_implies_or_type, type, (
% 0.20/0.40 op_implies_or: $o)).
% 0.20/0.40 tff(and_type, type, (
% 0.20/0.40 and: ( $i * $i ) > $i)).
% 0.20/0.40 tff(op_implies_and_type, type, (
% 0.20/0.40 op_implies_and: $o)).
% 0.20/0.40 tff(op_or_type, type, (
% 0.20/0.40 op_or: $o)).
% 0.20/0.40 tff(modus_tollens_type, type, (
% 0.20/0.40 modus_tollens: $o)).
% 0.20/0.40 tff(r3_type, type, (
% 0.20/0.40 r3: $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 ((~$true) <=> $false),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(6,axiom,(op_implies_or), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_implies_or')).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (op_implies_or <=> $true),
% 0.20/0.40 inference(iff_true,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 ((~op_implies_or) <=> (~$true)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[7])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 ((~op_implies_or) <=> $false),
% 0.20/0.40 inference(transitivity,[status(thm)],[8, 5])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.40 inference(transitivity,[status(thm)],[10, 4])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 ((op_implies_or => ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(14,axiom,(op_implies_or => ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_implies_or')).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.20/0.40 tff(19,plain,(
% 0.20/0.40 ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.40 inference(skolemize,[status(sab)],[18])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(X!1, Y!0) = or(not(X!1), Y!0))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (implies(X!1, Y!0) = or(not(X!1), Y!0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (or(not(X!1), Y!0) = implies(X!1, Y!0)),
% 0.20/0.40 inference(symmetry,[status(thm)],[22])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (($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))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(28,axiom,(op_implies_and), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hilbert_op_implies_and')).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (op_implies_and <=> $true),
% 0.20/0.40 inference(iff_true,[status(thm)],[28])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 ((~op_implies_and) <=> (~$true)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ((~op_implies_and) <=> $false),
% 0.20/0.40 inference(transitivity,[status(thm)],[30, 5])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (((~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)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (((~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))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[32, 27])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (((~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)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((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)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 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')).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[39, 26])).
% 0.20/0.40 tff(41,plain,(
% 0.20/0.40 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[40])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[41, 25])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(Y!0), not(X!1)) = not(and(not(Y!0), not(not(X!1)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (implies(not(Y!0), not(X!1)) = not(and(not(Y!0), not(not(X!1))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (not(and(not(Y!0), not(not(X!1)))) = implies(not(Y!0), not(X!1))),
% 0.20/0.40 inference(symmetry,[status(thm)],[44])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : refl((or(X, Y) = not(and(not(X), not(Y)))) <=> (or(X, Y) = not(and(not(X), not(Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (($false | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(50,axiom,(op_or), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hilbert_op_or')).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (op_or <=> $true),
% 0.20/0.40 inference(iff_true,[status(thm)],[50])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 ((~op_or) <=> (~$true)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 ((~op_or) <=> $false),
% 0.20/0.40 inference(transitivity,[status(thm)],[52, 5])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) <=> ($false | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[54, 49])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) <=> ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 ((op_or => ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) <=> ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(58,axiom,(op_or => ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_or')).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[59, 56])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[61, 48])).
% 0.20/0.40 tff(63,plain,(
% 0.20/0.40 ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[62])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[63, 47])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(Y!0, not(X!1)) = not(and(not(Y!0), not(not(X!1)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (or(Y!0, not(X!1)) = not(and(not(Y!0), not(not(X!1))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (or(Y!0, not(X!1)) = implies(not(Y!0), not(X!1))),
% 0.20/0.40 inference(transitivity,[status(thm)],[66, 45])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (implies(or(Y!0, not(X!1)), or(not(X!1), Y!0)) = implies(implies(not(Y!0), not(X!1)), implies(X!1, Y!0))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[67, 23])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (is_a_theorem(implies(or(Y!0, not(X!1)), or(not(X!1), Y!0))) <=> is_a_theorem(implies(implies(not(Y!0), not(X!1)), implies(X!1, Y!0)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (is_a_theorem(implies(implies(not(Y!0), not(X!1)), implies(X!1, Y!0))) <=> is_a_theorem(implies(or(Y!0, not(X!1)), or(not(X!1), Y!0)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[69])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((~is_a_theorem(implies(implies(not(Y!0), not(X!1)), implies(X!1, Y!0)))) <=> (~is_a_theorem(implies(or(Y!0, not(X!1)), or(not(X!1), Y!0))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[70])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(74,axiom,(~modus_tollens), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hilbert_modus_tollens')).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (modus_tollens <=> $false),
% 0.20/0.40 inference(iff_false,[status(thm)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 ((modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) <=> ($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 ((modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[76, 73])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 ((modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))) <=> (modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(79,axiom,(modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','modus_tollens')).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (modus_tollens <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[80, 78])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[83, 72])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[84, 72])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[85, 72])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[86, 72])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (~![X: $i, Y: $i] : is_a_theorem(implies(implies(not(Y), not(X)), implies(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[87, 72])).
% 0.20/0.41 tff(89,plain,(
% 0.20/0.41 ~is_a_theorem(implies(implies(not(Y!0), not(X!1)), implies(X!1, Y!0)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[88])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (~is_a_theorem(implies(or(Y!0, not(X!1)), or(not(X!1), Y!0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 71])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (^[P: $i, Q: $i] : refl(is_a_theorem(implies(or(P, Q), or(Q, P))) <=> is_a_theorem(implies(or(P, Q), or(Q, P))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(95,axiom,(r3), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_r3')).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (r3 <=> $true),
% 0.20/0.41 inference(iff_true,[status(thm)],[95])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> ($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 ((r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[97, 94])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 ((r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(100,axiom,(r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','r3')).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[101, 99])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[103, 93])).
% 0.20/0.41 tff(105,plain,(
% 0.20/0.41 ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[104])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[105, 92])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(Y!0, not(X!1)), or(not(X!1), Y!0)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (is_a_theorem(implies(or(Y!0, not(X!1)), or(not(X!1), Y!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[108, 90])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------