TSTP Solution File: LCL488+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL488+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 04:56:28 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL488+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.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 21:51:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(is_a_theorem_type, type, (
% 0.20/0.42 is_a_theorem: $i > $o)).
% 0.20/0.42 tff(or_type, type, (
% 0.20/0.42 or: ( $i * $i ) > $i)).
% 0.20/0.42 tff(not_type, type, (
% 0.20/0.42 not: $i > $i)).
% 0.20/0.42 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.42 tptp_fun_Y_0: $i)).
% 0.20/0.42 tff(tptp_fun_X_1_type, type, (
% 0.20/0.42 tptp_fun_X_1: $i)).
% 0.20/0.42 tff(implies_type, type, (
% 0.20/0.42 implies: ( $i * $i ) > $i)).
% 0.20/0.42 tff(and_type, type, (
% 0.20/0.42 and: ( $i * $i ) > $i)).
% 0.20/0.42 tff(op_implies_and_type, type, (
% 0.20/0.42 op_implies_and: $o)).
% 0.20/0.42 tff(op_or_type, type, (
% 0.20/0.42 op_or: $o)).
% 0.20/0.42 tff(r2_type, type, (
% 0.20/0.42 r2: $o)).
% 0.20/0.42 tff(op_implies_or_type, type, (
% 0.20/0.42 op_implies_or: $o)).
% 0.20/0.42 tff(op_and_type, type, (
% 0.20/0.42 op_and: $o)).
% 0.20/0.42 tff(r3_type, type, (
% 0.20/0.42 r3: $o)).
% 0.20/0.42 tff(and_2_type, type, (
% 0.20/0.42 and_2: $o)).
% 0.20/0.42 tff(modus_ponens_type, type, (
% 0.20/0.42 modus_ponens: $o)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (($false | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 ((~$true) <=> $false),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(6,axiom,(op_implies_and), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hilbert_op_implies_and')).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (op_implies_and <=> $true),
% 0.20/0.43 inference(iff_true,[status(thm)],[6])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 ((~op_implies_and) <=> (~$true)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[7])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 ((~op_implies_and) <=> $false),
% 0.20/0.43 inference(transitivity,[status(thm)],[8, 5])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (((~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)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 (((~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))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[10, 4])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (((~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)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 ((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)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 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')).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.20/0.43 tff(19,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[18])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(Y!0), or(not(X!1), not(Y!0))) = not(and(not(Y!0), not(or(not(X!1), not(Y!0))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (implies(not(Y!0), or(not(X!1), not(Y!0))) = not(and(not(Y!0), not(or(not(X!1), not(Y!0)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (not(and(not(Y!0), not(or(not(X!1), not(Y!0))))) = implies(not(Y!0), or(not(X!1), not(Y!0)))),
% 0.20/0.43 inference(symmetry,[status(thm)],[22])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : refl((or(X, Y) = not(and(not(X), not(Y)))) <=> (or(X, Y) = not(and(not(X), not(Y)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (($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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(28,axiom,(op_or), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hilbert_op_or')).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (op_or <=> $true),
% 0.20/0.43 inference(iff_true,[status(thm)],[28])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 ((~op_or) <=> (~$true)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 ((~op_or) <=> $false),
% 0.20/0.43 inference(transitivity,[status(thm)],[30, 5])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (((~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)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (((~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))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[32, 27])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (((~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)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 ((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)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(36,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')).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[39, 26])).
% 0.20/0.43 tff(41,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[40])).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[41, 25])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(Y!0, or(not(X!1), not(Y!0))) = not(and(not(Y!0), not(or(not(X!1), not(Y!0))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (or(Y!0, or(not(X!1), not(Y!0))) = not(and(not(Y!0), not(or(not(X!1), not(Y!0)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 (or(Y!0, or(not(X!1), not(Y!0))) = implies(not(Y!0), or(not(X!1), not(Y!0)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[44, 23])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (is_a_theorem(or(Y!0, or(not(X!1), not(Y!0)))) <=> is_a_theorem(implies(not(Y!0), or(not(X!1), not(Y!0))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (is_a_theorem(implies(not(Y!0), or(not(X!1), not(Y!0)))) <=> is_a_theorem(or(Y!0, or(not(X!1), not(Y!0))))),
% 0.20/0.43 inference(symmetry,[status(thm)],[46])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (^[P: $i, Q: $i] : refl(is_a_theorem(implies(Q, or(P, Q))) <=> is_a_theorem(implies(Q, or(P, Q))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(52,axiom,(r2), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_r2')).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (r2 <=> $true),
% 0.20/0.43 inference(iff_true,[status(thm)],[52])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[54, 51])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(57,axiom,(r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','r2')).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[58, 56])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.20/0.43 tff(62,plain,(
% 0.20/0.43 ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[61])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[62, 49])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 ((~![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) | is_a_theorem(implies(not(Y!0), or(not(X!1), not(Y!0))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (is_a_theorem(implies(not(Y!0), or(not(X!1), not(Y!0))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (is_a_theorem(or(Y!0, or(not(X!1), not(Y!0))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[65, 47])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(71,axiom,(op_implies_or), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_implies_or')).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (op_implies_or <=> $true),
% 0.20/0.43 inference(iff_true,[status(thm)],[71])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 ((~op_implies_or) <=> (~$true)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 ((~op_implies_or) <=> $false),
% 0.20/0.43 inference(transitivity,[status(thm)],[73, 5])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (((~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)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (((~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))),
% 0.20/0.43 inference(transitivity,[status(thm)],[75, 70])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (((~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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 ((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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(79,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')).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[80, 77])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[81, 76])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[82, 69])).
% 0.20/0.43 tff(84,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.43 inference(skolemize,[status(sab)],[83])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[84, 68])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(and(X!1, Y!0), Y!0) = or(not(and(X!1, Y!0)), Y!0))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (implies(and(X!1, Y!0), Y!0) = or(not(and(X!1, Y!0)), Y!0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(and(X!1, Y!0), Y!0) = not(and(and(X!1, Y!0), not(Y!0))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (implies(and(X!1, Y!0), Y!0) = not(and(and(X!1, Y!0), not(Y!0)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[88, 20])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (not(and(and(X!1, Y!0), not(Y!0))) = implies(and(X!1, Y!0), Y!0)),
% 0.20/0.43 inference(symmetry,[status(thm)],[89])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : refl((and(X, Y) = not(or(not(X), not(Y)))) <=> (and(X, Y) = not(or(not(X), not(Y)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (($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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(95,axiom,(op_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_op_and')).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (op_and <=> $true),
% 0.20/0.43 inference(iff_true,[status(thm)],[95])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 ((~op_and) <=> (~$true)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((~op_and) <=> $false),
% 0.20/0.43 inference(transitivity,[status(thm)],[97, 5])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (((~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)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[98])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (((~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))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[99, 94])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (((~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)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 ((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)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(103,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')).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((~op_and) | ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[104, 101])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[105, 100])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[106, 93])).
% 0.20/0.43 tff(108,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[107])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[108, 92])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : (and(X, Y) = not(or(not(X), not(Y))))) | (and(X!1, Y!0) = not(or(not(X!1), not(Y!0))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (and(X!1, Y!0) = not(or(not(X!1), not(Y!0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (and(and(X!1, Y!0), not(Y!0)) = and(not(or(not(X!1), not(Y!0))), not(Y!0))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (and(not(or(not(X!1), not(Y!0))), not(Y!0)) = and(and(X!1, Y!0), not(Y!0))),
% 0.20/0.44 inference(symmetry,[status(thm)],[112])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (not(and(not(or(not(X!1), not(Y!0))), not(Y!0))) = not(and(and(X!1, Y!0), not(Y!0)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[113])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(or(not(X!1), not(Y!0)), Y!0) = not(and(not(or(not(X!1), not(Y!0))), not(Y!0))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (or(or(not(X!1), not(Y!0)), Y!0) = not(and(not(or(not(X!1), not(Y!0))), not(Y!0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[115, 42])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (or(or(not(X!1), not(Y!0)), Y!0) = or(not(and(X!1, Y!0)), Y!0)),
% 0.20/0.44 inference(transitivity,[status(thm)],[116, 114, 90, 87])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (implies(or(Y!0, or(not(X!1), not(Y!0))), or(or(not(X!1), not(Y!0)), Y!0)) = implies(or(Y!0, or(not(X!1), not(Y!0))), or(not(and(X!1, Y!0)), Y!0))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (is_a_theorem(implies(or(Y!0, or(not(X!1), not(Y!0))), or(or(not(X!1), not(Y!0)), Y!0))) <=> is_a_theorem(implies(or(Y!0, or(not(X!1), not(Y!0))), or(not(and(X!1, Y!0)), Y!0)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[118])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (($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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(124,axiom,(r3), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_r3')).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (r3 <=> $true),
% 0.20/0.44 inference(iff_true,[status(thm)],[124])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 ((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))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[125])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 ((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)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[126, 123])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 ((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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(129,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')).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[130, 128])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[132, 122])).
% 0.20/0.44 tff(134,plain,(
% 0.20/0.44 ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[133])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 (![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[134, 121])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) | is_a_theorem(implies(or(Y!0, or(not(X!1), not(Y!0))), or(or(not(X!1), not(Y!0)), Y!0)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 (is_a_theorem(implies(or(Y!0, or(not(X!1), not(Y!0))), or(or(not(X!1), not(Y!0)), Y!0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (is_a_theorem(implies(or(Y!0, or(not(X!1), not(Y!0))), or(not(and(X!1, Y!0)), Y!0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[137, 119])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 (or(not(and(X!1, Y!0)), Y!0) = implies(and(X!1, Y!0), Y!0)),
% 0.20/0.44 inference(symmetry,[status(thm)],[87])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 (is_a_theorem(or(not(and(X!1, Y!0)), Y!0)) <=> is_a_theorem(implies(and(X!1, Y!0), Y!0))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (is_a_theorem(implies(and(X!1, Y!0), Y!0)) <=> is_a_theorem(or(not(and(X!1, Y!0)), Y!0))),
% 0.20/0.44 inference(symmetry,[status(thm)],[140])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 ((~is_a_theorem(implies(and(X!1, Y!0), Y!0))) <=> (~is_a_theorem(or(not(and(X!1, Y!0)), Y!0)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 (($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(145,axiom,(~and_2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hilbert_and_2')).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 (and_2 <=> $false),
% 0.20/0.44 inference(iff_false,[status(thm)],[145])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 ((and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> ($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 ((and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[147, 144])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 ((and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))) <=> (and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(150,axiom,(and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','and_2')).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (and_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[151, 149])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[153, 143])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[154, 143])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[155, 143])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[156, 143])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[157, 143])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[158, 143])).
% 0.20/0.44 tff(160,plain,(
% 0.20/0.44 ~is_a_theorem(implies(and(X!1, Y!0), Y!0))),
% 0.20/0.44 inference(skolemize,[status(sab)],[159])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (~is_a_theorem(or(not(and(X!1, Y!0)), Y!0))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[160, 142])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 (^[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))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 (($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)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(168,axiom,(modus_ponens), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax','principia_modus_ponens')).
% 0.20/0.44 tff(169,plain,
% 0.20/0.44 (modus_ponens <=> $true),
% 0.20/0.44 inference(iff_true,[status(thm)],[168])).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 ((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))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[169])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 ((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)))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[170, 167])).
% 0.20/0.45 tff(172,plain,
% 0.20/0.45 ((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))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(173,plain,
% 0.20/0.45 ((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))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(174,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')).
% 0.20/0.45 tff(175,plain,
% 0.20/0.45 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.45 tff(176,plain,
% 0.20/0.45 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[175, 172])).
% 0.20/0.45 tff(177,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[176, 171])).
% 0.20/0.45 tff(178,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[177, 166])).
% 0.20/0.45 tff(179,plain,(
% 0.20/0.45 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[178])).
% 0.20/0.45 tff(180,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[179, 165])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[180, 163])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(and(X!1, Y!0)), Y!0)) | (~is_a_theorem(or(Y!0, or(not(X!1), not(Y!0))))) | (~is_a_theorem(implies(or(Y!0, or(not(X!1), not(Y!0))), or(not(and(X!1, Y!0)), Y!0)))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(and(X!1, Y!0)), Y!0)) | (~is_a_theorem(or(Y!0, or(not(X!1), not(Y!0))))) | (~is_a_theorem(implies(or(Y!0, or(not(X!1), not(Y!0))), or(not(and(X!1, Y!0)), Y!0)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(183,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(and(X!1, Y!0)), Y!0)) | (~is_a_theorem(or(Y!0, or(not(X!1), not(Y!0))))) | (~is_a_theorem(implies(or(Y!0, or(not(X!1), not(Y!0))), or(not(and(X!1, Y!0)), Y!0)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(184,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(and(X!1, Y!0)), Y!0)) | (~is_a_theorem(or(Y!0, or(not(X!1), not(Y!0))))) | (~is_a_theorem(implies(or(Y!0, or(not(X!1), not(Y!0))), or(not(and(X!1, Y!0)), Y!0))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.45 tff(185,plain,
% 0.20/0.45 ((~is_a_theorem(or(Y!0, or(not(X!1), not(Y!0))))) | (~is_a_theorem(implies(or(Y!0, or(not(X!1), not(Y!0))), or(not(and(X!1, Y!0)), Y!0))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[184, 181, 161])).
% 0.20/0.45 tff(186,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[185, 138, 66])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------