TSTP Solution File: LCL456+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL456+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 04:56:23 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL456+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % 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 21:36:25 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.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(is_a_theorem_type, type, (
% 0.19/0.40 is_a_theorem: $i > $o)).
% 0.19/0.40 tff(or_type, type, (
% 0.19/0.40 or: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_P_1_type, type, (
% 0.19/0.40 tptp_fun_P_1: $i)).
% 0.19/0.40 tff(tptp_fun_Q_0_type, type, (
% 0.19/0.40 tptp_fun_Q_0: $i)).
% 0.19/0.40 tff(not_type, type, (
% 0.19/0.40 not: $i > $i)).
% 0.19/0.40 tff(implies_type, type, (
% 0.19/0.40 implies: ( $i * $i ) > $i)).
% 0.19/0.40 tff(op_implies_or_type, type, (
% 0.19/0.40 op_implies_or: $o)).
% 0.19/0.40 tff(r3_type, type, (
% 0.19/0.40 r3: $o)).
% 0.19/0.40 tff(or_2_type, type, (
% 0.19/0.40 or_2: $o)).
% 0.19/0.40 tff(or_3_type, type, (
% 0.19/0.40 or_3: $o)).
% 0.19/0.40 tff(modus_ponens_type, type, (
% 0.19/0.40 modus_ponens: $o)).
% 0.19/0.40 tff(or_1_type, type, (
% 0.19/0.40 or_1: $o)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 ((~$true) <=> $false),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(6,axiom,(op_implies_or), file('/export/starexec/sandbox/benchmark/theBenchmark.p','principia_op_implies_or')).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (op_implies_or <=> $true),
% 0.19/0.40 inference(iff_true,[status(thm)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 ((~op_implies_or) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[7])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 ((~op_implies_or) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[8, 5])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (((~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)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[9])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (((~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))),
% 0.19/0.40 inference(transitivity,[status(thm)],[10, 4])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (((~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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 ((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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,axiom,(op_implies_or => ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_implies_or')).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.19/0.40 tff(19,plain,(
% 0.19/0.40 ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.19/0.40 inference(skolemize,[status(sab)],[18])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(P!1, Q!0), or(Q!0, P!1)) = or(not(or(P!1, Q!0)), or(Q!0, P!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (implies(or(P!1, Q!0), or(Q!0, P!1)) = or(not(or(P!1, Q!0)), or(Q!0, P!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (or(not(or(P!1, Q!0)), or(Q!0, P!1)) = implies(or(P!1, Q!0), or(Q!0, P!1))),
% 0.19/0.40 inference(symmetry,[status(thm)],[22])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (is_a_theorem(or(not(or(P!1, Q!0)), or(Q!0, P!1))) <=> is_a_theorem(implies(or(P!1, Q!0), or(Q!0, P!1)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[23])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (is_a_theorem(implies(or(P!1, Q!0), or(Q!0, P!1))) <=> is_a_theorem(or(not(or(P!1, Q!0)), or(Q!0, P!1)))),
% 0.19/0.40 inference(symmetry,[status(thm)],[24])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 ((~is_a_theorem(implies(or(P!1, Q!0), or(Q!0, P!1)))) <=> (~is_a_theorem(or(not(or(P!1, Q!0)), or(Q!0, P!1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 ((~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (($false <=> ![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(29,axiom,(~r3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','principia_r3')).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (r3 <=> $false),
% 0.19/0.40 inference(iff_false,[status(thm)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 ((r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))) <=> ($false <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 ((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))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[31, 28])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 ((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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(34,axiom,(r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','r3')).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (r3 <=> ![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 33])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 27])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 27])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 27])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 27])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (~![P: $i, Q: $i] : is_a_theorem(implies(or(P, Q), or(Q, P)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 27])).
% 0.19/0.40 tff(44,plain,(
% 0.19/0.40 ~is_a_theorem(implies(or(P!1, Q!0), or(Q!0, P!1)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[43])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (~is_a_theorem(or(not(or(P!1, Q!0)), or(Q!0, P!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 26])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1))) = implies(implies(Q!0, or(Q!0, P!1)), or(not(or(P!1, Q!0)), or(Q!0, P!1)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[22])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1)))) <=> is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), or(not(or(P!1, Q!0)), or(Q!0, P!1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(Y, or(X, Y))) <=> is_a_theorem(implies(Y, or(X, Y))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(52,axiom,(or_2), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_or_2')).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (or_2 <=> $true),
% 0.19/0.40 inference(iff_true,[status(thm)],[52])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 ((or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ((or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[54, 51])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ((or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(57,axiom,(or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','or_2')).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 56])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.19/0.41 tff(62,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[61])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 49])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) | is_a_theorem(implies(P!1, or(Q!0, P!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (is_a_theorem(implies(P!1, or(Q!0, P!1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (^[X: $i, Y: $i, Z: $i] : refl(is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))) <=> is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (($true <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(70,axiom,(or_3), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_or_3')).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (or_3 <=> $true),
% 0.19/0.41 inference(iff_true,[status(thm)],[70])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))) <=> ($true <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[71])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ((or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))) <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[72, 69])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 ((or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))) <=> (or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(75,axiom,(or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','or_3')).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (or_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 74])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.19/0.41 tff(80,plain,(
% 0.19/0.41 ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[79])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[80, 67])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Z), implies(implies(Y, Z), implies(or(X, Y), Z))))) | is_a_theorem(implies(implies(P!1, or(Q!0, P!1)), implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (is_a_theorem(implies(implies(P!1, or(Q!0, P!1)), implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((is_a_theorem(X) & is_a_theorem(implies(X, Y))) <=> (~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))), ((~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))) <=> (~(~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))))), rewrite((~(~((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))) <=> ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))), ((~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))) <=> ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y)))))), ((is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))))), rewrite((is_a_theorem(Y) | ((~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) <=> (is_a_theorem(Y) | (~is_a_theorem(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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (($true <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(90,axiom,(modus_ponens), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_modus_ponens')).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (modus_ponens <=> $true),
% 0.19/0.41 inference(iff_true,[status(thm)],[90])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 ((modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> ($true <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[91])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 ((modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[92, 89])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ((modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))) <=> (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ((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))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(96,axiom,(modus_ponens <=> ![X: $i, Y: $i] : ((is_a_theorem(X) & is_a_theorem(implies(X, Y))) => is_a_theorem(Y))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','modus_ponens')).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[97, 94])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[98, 93])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[99, 88])).
% 0.19/0.41 tff(101,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[100])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[101, 87])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[102, 85])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1)))) | (~is_a_theorem(implies(P!1, or(Q!0, P!1)))) | (~is_a_theorem(implies(implies(P!1, or(Q!0, P!1)), implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1)))) | (~is_a_theorem(implies(P!1, or(Q!0, P!1)))) | (~is_a_theorem(implies(implies(P!1, or(Q!0, P!1)), implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1)))) | (~is_a_theorem(implies(P!1, or(Q!0, P!1)))) | (~is_a_theorem(implies(implies(P!1, or(Q!0, P!1)), implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1)))) | (~is_a_theorem(implies(P!1, or(Q!0, P!1)))) | (~is_a_theorem(implies(implies(P!1, or(Q!0, P!1)), implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), implies(or(P!1, Q!0), or(Q!0, P!1))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[106, 103, 83, 65])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), or(not(or(P!1, Q!0)), or(Q!0, P!1))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[107, 47])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(X, or(X, Y))) <=> is_a_theorem(implies(X, or(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (($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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(113,axiom,(or_1), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_or_1')).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (or_1 <=> $true),
% 0.19/0.41 inference(iff_true,[status(thm)],[113])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 ((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))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[114])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 ((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)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[115, 112])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 ((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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(118,axiom,(or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','or_1')).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (or_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[119, 117])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.19/0.41 tff(123,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[122])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[123, 110])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : is_a_theorem(implies(X, or(X, Y)))) | is_a_theorem(implies(Q!0, or(Q!0, P!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (is_a_theorem(implies(Q!0, or(Q!0, P!1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(P!1, Q!0)), or(Q!0, P!1))) | (~is_a_theorem(implies(Q!0, or(Q!0, P!1)))) | (~is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), or(not(or(P!1, Q!0)), or(Q!0, P!1))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(or(P!1, Q!0)), or(Q!0, P!1))) | (~is_a_theorem(implies(Q!0, or(Q!0, P!1)))) | (~is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), or(not(or(P!1, Q!0)), or(Q!0, P!1))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(or(P!1, Q!0)), or(Q!0, P!1))) | (~is_a_theorem(implies(Q!0, or(Q!0, P!1)))) | (~is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), or(not(or(P!1, Q!0)), or(Q!0, P!1))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(or(P!1, Q!0)), or(Q!0, P!1))) | (~is_a_theorem(implies(Q!0, or(Q!0, P!1)))) | (~is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), or(not(or(P!1, Q!0)), or(Q!0, P!1)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (is_a_theorem(or(not(or(P!1, Q!0)), or(Q!0, P!1))) | (~is_a_theorem(implies(implies(Q!0, or(Q!0, P!1)), or(not(or(P!1, Q!0)), or(Q!0, P!1)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[129, 103, 126])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[130, 108, 45])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------