TSTP Solution File: LCL499+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL499+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 04:56:31 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL499+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 21:55:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(is_a_theorem_type, type, (
% 0.12/0.40 is_a_theorem: $i > $o)).
% 0.12/0.40 tff(implies_type, type, (
% 0.12/0.40 implies: ( $i * $i ) > $i)).
% 0.12/0.40 tff(or_type, type, (
% 0.12/0.40 or: ( $i * $i ) > $i)).
% 0.12/0.40 tff(and_type, type, (
% 0.12/0.40 and: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_P_0_type, type, (
% 0.12/0.40 tptp_fun_P_0: $i)).
% 0.12/0.40 tff(not_type, type, (
% 0.12/0.40 not: $i > $i)).
% 0.12/0.40 tff(op_and_type, type, (
% 0.12/0.40 op_and: $o)).
% 0.12/0.40 tff(r3_type, type, (
% 0.12/0.40 r3: $o)).
% 0.12/0.40 tff(op_implies_or_type, type, (
% 0.12/0.40 op_implies_or: $o)).
% 0.12/0.40 tff(kn1_type, type, (
% 0.12/0.40 kn1: $o)).
% 0.12/0.40 tff(r1_type, type, (
% 0.12/0.40 r1: $o)).
% 0.12/0.40 tff(modus_ponens_type, type, (
% 0.12/0.40 modus_ponens: $o)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[X: $i, Y: $i] : refl((and(X, Y) = not(or(not(X), not(Y)))) <=> (and(X, Y) = not(or(not(X), not(Y)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (($false | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 ((~$true) <=> $false),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(6,axiom,(op_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_and')).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (op_and <=> $true),
% 0.12/0.40 inference(iff_true,[status(thm)],[6])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 ((~op_and) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[7])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 ((~op_and) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[8, 5])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ($false | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[9])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[10, 4])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 ((op_and => ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) <=> ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(14,axiom,(op_and => ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_and')).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.12/0.40 tff(19,plain,(
% 0.12/0.40 ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[18])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(P!0, P!0) = not(or(not(P!0), not(P!0))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (and(P!0, P!0) = not(or(not(P!0), not(P!0)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (not(or(not(P!0), not(P!0))) = and(P!0, P!0)),
% 0.12/0.40 inference(symmetry,[status(thm)],[22])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (or(not(P!0), not(or(not(P!0), not(P!0)))) = or(not(P!0), and(P!0, P!0))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[23])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), not(or(not(P!0), not(P!0))))) = implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), and(P!0, P!0)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[24])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (is_a_theorem(implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), not(or(not(P!0), not(P!0)))))) <=> is_a_theorem(implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), and(P!0, P!0))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[25])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (($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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(31,axiom,(r3), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_r3')).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (r3 <=> $true),
% 0.12/0.40 inference(iff_true,[status(thm)],[31])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 ((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))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 ((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)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[33, 30])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 ((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))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(36,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')).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[37, 35])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.12/0.40 tff(41,plain,(
% 0.12/0.40 ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[40])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[41, 28])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), not(or(not(P!0), not(P!0))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (is_a_theorem(implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), not(or(not(P!0), not(P!0))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (is_a_theorem(implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), and(P!0, P!0))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[44, 26])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (^[X: $i, Y: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(50,axiom,(op_implies_or), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_implies_or')).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (op_implies_or <=> $true),
% 0.12/0.40 inference(iff_true,[status(thm)],[50])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 ((~op_implies_or) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[51])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 ((~op_implies_or) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[52, 5])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (((~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)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[53])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (((~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))),
% 0.12/0.40 inference(transitivity,[status(thm)],[54, 49])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (((~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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 ((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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(58,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')).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[59, 56])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[61, 48])).
% 0.12/0.40 tff(63,plain,(
% 0.12/0.40 ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.12/0.40 inference(skolemize,[status(sab)],[62])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[63, 47])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(P!0, and(P!0, P!0)) = or(not(P!0), and(P!0, P!0)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (implies(P!0, and(P!0, P!0)) = or(not(P!0), and(P!0, P!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (or(not(P!0), and(P!0, P!0)) = implies(P!0, and(P!0, P!0))),
% 0.12/0.40 inference(symmetry,[status(thm)],[66])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (is_a_theorem(or(not(P!0), and(P!0, P!0))) <=> is_a_theorem(implies(P!0, and(P!0, P!0)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[67])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (is_a_theorem(implies(P!0, and(P!0, P!0))) <=> is_a_theorem(or(not(P!0), and(P!0, P!0)))),
% 0.12/0.40 inference(symmetry,[status(thm)],[68])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 ((~is_a_theorem(implies(P!0, and(P!0, P!0)))) <=> (~is_a_theorem(or(not(P!0), and(P!0, P!0))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[69])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 ((~![P: $i] : is_a_theorem(implies(P, and(P, P)))) <=> (~![P: $i] : is_a_theorem(implies(P, and(P, P))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 (($false <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))) <=> (~![P: $i] : is_a_theorem(implies(P, and(P, P))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(73,axiom,(~kn1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rosser_kn1')).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 (kn1 <=> $false),
% 0.12/0.40 inference(iff_false,[status(thm)],[73])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 ((kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))) <=> ($false <=> ![P: $i] : is_a_theorem(implies(P, and(P, P))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[74])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 ((kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))) <=> (~![P: $i] : is_a_theorem(implies(P, and(P, P))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[75, 72])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 ((kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))) <=> (kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(78,axiom,(kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','kn1')).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 (kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[79, 77])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[82, 71])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[83, 71])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[84, 71])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[85, 71])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[86, 71])).
% 0.12/0.40 tff(88,plain,(
% 0.12/0.40 ~is_a_theorem(implies(P!0, and(P!0, P!0)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[87])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (~is_a_theorem(or(not(P!0), and(P!0, P!0)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[88, 70])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(P!0), not(P!0)), not(P!0)) = or(not(or(not(P!0), not(P!0))), not(P!0)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 (implies(or(not(P!0), not(P!0)), not(P!0)) = or(not(or(not(P!0), not(P!0))), not(P!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[90, 64])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (is_a_theorem(implies(or(not(P!0), not(P!0)), not(P!0))) <=> is_a_theorem(or(not(or(not(P!0), not(P!0))), not(P!0)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[91])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 (^[P: $i] : refl(is_a_theorem(implies(or(P, P), P)) <=> is_a_theorem(implies(or(P, P), P)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 (![P: $i] : is_a_theorem(implies(or(P, P), P)) <=> ![P: $i] : is_a_theorem(implies(or(P, P), P))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[93])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 (![P: $i] : is_a_theorem(implies(or(P, P), P)) <=> ![P: $i] : is_a_theorem(implies(or(P, P), P))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 (($true <=> ![P: $i] : is_a_theorem(implies(or(P, P), P))) <=> ![P: $i] : is_a_theorem(implies(or(P, P), P))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(97,axiom,(r1), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_r1')).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 (r1 <=> $true),
% 0.12/0.40 inference(iff_true,[status(thm)],[97])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 ((r1 <=> ![P: $i] : is_a_theorem(implies(or(P, P), P))) <=> ($true <=> ![P: $i] : is_a_theorem(implies(or(P, P), P)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[98])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 ((r1 <=> ![P: $i] : is_a_theorem(implies(or(P, P), P))) <=> ![P: $i] : is_a_theorem(implies(or(P, P), P))),
% 0.12/0.40 inference(transitivity,[status(thm)],[99, 96])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 ((r1 <=> ![P: $i] : is_a_theorem(implies(or(P, P), P))) <=> (r1 <=> ![P: $i] : is_a_theorem(implies(or(P, P), P)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(102,axiom,(r1 <=> ![P: $i] : is_a_theorem(implies(or(P, P), P))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','r1')).
% 0.12/0.40 tff(103,plain,
% 0.12/0.40 (r1 <=> ![P: $i] : is_a_theorem(implies(or(P, P), P))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 (r1 <=> ![P: $i] : is_a_theorem(implies(or(P, P), P))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[103, 101])).
% 0.12/0.40 tff(105,plain,
% 0.20/0.40 (![P: $i] : is_a_theorem(implies(or(P, P), P))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 (![P: $i] : is_a_theorem(implies(or(P, P), P))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[105, 95])).
% 0.20/0.40 tff(107,plain,(
% 0.20/0.40 ![P: $i] : is_a_theorem(implies(or(P, P), P))),
% 0.20/0.40 inference(skolemize,[status(sab)],[106])).
% 0.20/0.40 tff(108,plain,
% 0.20/0.40 (![P: $i] : is_a_theorem(implies(or(P, P), P))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[107, 94])).
% 0.20/0.40 tff(109,plain,
% 0.20/0.40 ((~![P: $i] : is_a_theorem(implies(or(P, P), P))) | is_a_theorem(implies(or(not(P!0), not(P!0)), not(P!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(110,plain,
% 0.20/0.40 (is_a_theorem(implies(or(not(P!0), not(P!0)), not(P!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.20/0.40 tff(111,plain,
% 0.20/0.40 (is_a_theorem(or(not(or(not(P!0), not(P!0))), not(P!0)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[110, 92])).
% 0.20/0.40 tff(112,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : refl((is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))) <=> (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(113,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((is_a_theorem(X) & is_a_theorem(implies(X, Y))) <=> (~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))), ((~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))) <=> (~(~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))))), rewrite((~(~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))) <=> ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))), ((~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))) <=> ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))), ((is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))))), rewrite((is_a_theorem(Y) | ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))), ((is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(115,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.40 tff(116,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(117,plain,
% 0.20/0.40 (($true <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(118,axiom,(modus_ponens), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_modus_ponens')).
% 0.20/0.40 tff(119,plain,
% 0.20/0.40 (modus_ponens <=> $true),
% 0.20/0.40 inference(iff_true,[status(thm)],[118])).
% 0.20/0.40 tff(120,plain,
% 0.20/0.40 ((modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> ($true <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[119])).
% 0.20/0.40 tff(121,plain,
% 0.20/0.40 ((modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[120, 117])).
% 0.20/0.40 tff(122,plain,
% 0.20/0.40 ((modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 ((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))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(124,axiom,(modus_ponens <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(implies(X, Y))) => is_a_theorem(Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','modus_ponens')).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[125, 122])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[126, 121])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[127, 116])).
% 0.20/0.41 tff(129,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[128])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[129, 115])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[130, 113])).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(P!0), and(P!0, P!0))) | (~is_a_theorem(or(not(or(not(P!0), not(P!0))), not(P!0)))) | (~is_a_theorem(implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), and(P!0, P!0))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(P!0), and(P!0, P!0))) | (~is_a_theorem(or(not(or(not(P!0), not(P!0))), not(P!0)))) | (~is_a_theorem(implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), and(P!0, P!0))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(133,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(P!0), and(P!0, P!0))) | (~is_a_theorem(or(not(or(not(P!0), not(P!0))), not(P!0)))) | (~is_a_theorem(implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), and(P!0, P!0))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(134,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(P!0), and(P!0, P!0))) | (~is_a_theorem(or(not(or(not(P!0), not(P!0))), not(P!0)))) | (~is_a_theorem(implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), and(P!0, P!0)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 (is_a_theorem(or(not(P!0), and(P!0, P!0))) | (~is_a_theorem(or(not(or(not(P!0), not(P!0))), not(P!0)))) | (~is_a_theorem(implies(or(not(or(not(P!0), not(P!0))), not(P!0)), or(not(P!0), and(P!0, P!0)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[134, 131])).
% 0.20/0.41 tff(136,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[135, 111, 89, 45])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------