TSTP Solution File: LCL452+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL452+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 04:56:21 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL452+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Sep 1 21:18:48 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(is_a_theorem_type, type, (
% 0.14/0.40 is_a_theorem: $i > $o)).
% 0.14/0.40 tff(implies_type, type, (
% 0.14/0.40 implies: ( $i * $i ) > $i)).
% 0.14/0.40 tff(or_type, type, (
% 0.14/0.40 or: ( $i * $i ) > $i)).
% 0.14/0.40 tff(tptp_fun_Q_2_type, type, (
% 0.14/0.40 tptp_fun_Q_2: $i)).
% 0.14/0.40 tff(tptp_fun_P_3_type, type, (
% 0.14/0.40 tptp_fun_P_3: $i)).
% 0.14/0.40 tff(not_type, type, (
% 0.14/0.40 not: $i > $i)).
% 0.14/0.40 tff(and_type, type, (
% 0.14/0.40 and: ( $i * $i ) > $i)).
% 0.14/0.40 tff(op_implies_and_type, type, (
% 0.14/0.40 op_implies_and: $o)).
% 0.14/0.40 tff(op_or_type, type, (
% 0.14/0.40 op_or: $o)).
% 0.14/0.40 tff(cn2_type, type, (
% 0.14/0.40 cn2: $o)).
% 0.14/0.40 tff(or_1_type, type, (
% 0.14/0.40 or_1: $o)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (($false | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 ((~$true) <=> $false),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(6,axiom,(op_implies_and), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_op_implies_and')).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (op_implies_and <=> $true),
% 0.14/0.40 inference(iff_true,[status(thm)],[6])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 ((~op_implies_and) <=> (~$true)),
% 0.14/0.40 inference(monotonicity,[status(thm)],[7])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 ((~op_implies_and) <=> $false),
% 0.14/0.40 inference(transitivity,[status(thm)],[8, 5])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (((~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)))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[9])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (((~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))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[10, 4])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (((~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)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 ((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)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(14,axiom,(op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax','op_implies_and')).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.14/0.40 tff(19,plain,(
% 0.14/0.40 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[18])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(not(P!3), Q!2) = not(and(not(P!3), not(Q!2))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 (implies(not(P!3), Q!2) = not(and(not(P!3), not(Q!2)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (not(and(not(P!3), not(Q!2))) = implies(not(P!3), Q!2)),
% 0.14/0.40 inference(symmetry,[status(thm)],[22])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (^[X: $i, Y: $i] : refl((or(X, Y) = not(and(not(X), not(Y)))) <=> (or(X, Y) = not(and(not(X), not(Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y)))) <=> ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (($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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(28,axiom,(op_or), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_op_or')).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (op_or <=> $true),
% 0.21/0.41 inference(iff_true,[status(thm)],[28])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 ((~op_or) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 ((~op_or) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[30, 5])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (((~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)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[31])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (((~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))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[32, 27])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (((~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)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 ((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)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 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')).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 ((~op_or) | ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[39, 26])).
% 0.21/0.41 tff(41,plain,(
% 0.21/0.41 ![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[40])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[41, 25])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : (or(X, Y) = not(and(not(X), not(Y))))) | (or(P!3, Q!2) = not(and(not(P!3), not(Q!2))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (or(P!3, Q!2) = not(and(not(P!3), not(Q!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (or(P!3, Q!2) = implies(not(P!3), Q!2)),
% 0.21/0.41 inference(transitivity,[status(thm)],[44, 23])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (implies(P!3, or(P!3, Q!2)) = implies(P!3, implies(not(P!3), Q!2))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[45])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (is_a_theorem(implies(P!3, or(P!3, Q!2))) <=> is_a_theorem(implies(P!3, implies(not(P!3), Q!2)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[46])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (is_a_theorem(implies(P!3, implies(not(P!3), Q!2))) <=> is_a_theorem(implies(P!3, or(P!3, Q!2)))),
% 0.21/0.41 inference(symmetry,[status(thm)],[47])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 ((~is_a_theorem(implies(P!3, implies(not(P!3), Q!2)))) <=> (~is_a_theorem(implies(P!3, or(P!3, Q!2))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[48])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 ((~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (($false <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(52,axiom,(~cn2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','luka_cn2')).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (cn2 <=> $false),
% 0.21/0.41 inference(iff_false,[status(thm)],[52])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 ((cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))) <=> ($false <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 ((cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[54, 51])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 ((cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))) <=> (cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(57,axiom,(cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','cn2')).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (cn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[58, 56])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[61, 50])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[62, 50])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[63, 50])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[64, 50])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (~![P: $i, Q: $i] : is_a_theorem(implies(P, implies(not(P), Q)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[65, 50])).
% 0.21/0.41 tff(67,plain,(
% 0.21/0.41 ~is_a_theorem(implies(P!3, implies(not(P!3), Q!2)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[66])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (~is_a_theorem(implies(P!3, or(P!3, Q!2)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[67, 49])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(X, or(X, Y))) <=> is_a_theorem(implies(X, or(X, Y))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(73,axiom,(or_1), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_or_1')).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (or_1 <=> $true),
% 0.21/0.41 inference(iff_true,[status(thm)],[73])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 ((or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 ((or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[75, 72])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 ((or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) <=> (or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(78,axiom,(or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','or_1')).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 (or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[79, 77])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.21/0.41 tff(83,plain,(
% 0.21/0.41 ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[82])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[83, 70])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) | is_a_theorem(implies(P!3, or(P!3, Q!2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (is_a_theorem(implies(P!3, or(P!3, Q!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[86, 68])).
% 0.21/0.41 % SZS output end Proof
%------------------------------------------------------------------------------