TSTP Solution File: LCL486+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL486+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL486+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n019.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
% 0.14/0.34 % DateTime : Thu Sep 1 21:53:20 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(is_a_theorem_type, type, (
% 0.21/0.43 is_a_theorem: $i > $o)).
% 0.21/0.43 tff(implies_type, type, (
% 0.21/0.43 implies: ( $i * $i ) > $i)).
% 0.21/0.43 tff(or_type, type, (
% 0.21/0.43 or: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_Z_0_type, type, (
% 0.21/0.43 tptp_fun_Z_0: $i)).
% 0.21/0.43 tff(not_type, type, (
% 0.21/0.43 not: $i > $i)).
% 0.21/0.43 tff(tptp_fun_X_2_type, type, (
% 0.21/0.43 tptp_fun_X_2: $i)).
% 0.21/0.43 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.43 tptp_fun_Y_1: $i)).
% 0.21/0.43 tff(op_implies_or_type, type, (
% 0.21/0.43 op_implies_or: $o)).
% 0.21/0.43 tff(r4_type, type, (
% 0.21/0.43 r4: $o)).
% 0.21/0.43 tff(implies_3_type, type, (
% 0.21/0.43 implies_3: $o)).
% 0.21/0.43 tff(modus_ponens_type, type, (
% 0.21/0.43 modus_ponens: $o)).
% 0.21/0.43 tff(r5_type, type, (
% 0.21/0.43 r5: $o)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 (^[X: $i, Y: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (($false | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) <=> ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 ((~$true) <=> $false),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(6,axiom,(op_implies_or), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_op_implies_or')).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (op_implies_or <=> $true),
% 0.21/0.43 inference(iff_true,[status(thm)],[6])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 ((~op_implies_or) <=> (~$true)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[7])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 ((~op_implies_or) <=> $false),
% 0.21/0.43 inference(transitivity,[status(thm)],[8, 5])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (((~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)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[9])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (((~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))),
% 0.21/0.43 inference(transitivity,[status(thm)],[10, 4])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (((~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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 ((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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 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')).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 ((~op_implies_or) | ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.21/0.43 tff(19,plain,(
% 0.21/0.43 ![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.21/0.43 inference(skolemize,[status(sab)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(Y!1, Z!0) = or(not(Y!1), Z!0))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (implies(Y!1, Z!0) = or(not(Y!1), Z!0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (or(not(Y!1), Z!0) = implies(Y!1, Z!0)),
% 0.21/0.43 inference(symmetry,[status(thm)],[22])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (not(or(not(Y!1), Z!0)) = not(implies(Y!1, Z!0))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (or(not(or(not(Y!1), Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))) = or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[24])).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(Y!1), Z!0), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))) = or(not(or(not(Y!1), Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 (implies(or(not(Y!1), Z!0), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))) = or(not(or(not(Y!1), Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[26, 20])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(X!2, Y!1) = or(not(X!2), Y!1))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (implies(X!2, Y!1) = or(not(X!2), Y!1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[28, 20])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (or(not(X!2), Y!1) = implies(X!2, Y!1)),
% 0.21/0.44 inference(symmetry,[status(thm)],[29])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (not(or(not(X!2), Y!1)) = not(implies(X!2, Y!1))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[30])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (or(not(or(not(X!2), Y!1)), or(not(X!2), Z!0)) = or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[31])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(X!2), Y!1), or(not(X!2), Z!0)) = or(not(or(not(X!2), Y!1)), or(not(X!2), Z!0)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 (implies(or(not(X!2), Y!1), or(not(X!2), Z!0)) = or(not(or(not(X!2), Y!1)), or(not(X!2), Z!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[33, 20])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (implies(or(not(X!2), Y!1), or(not(X!2), Z!0)) = or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))),
% 0.21/0.44 inference(transitivity,[status(thm)],[34, 32])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (implies(implies(Y!1, Z!0), implies(or(not(X!2), Y!1), or(not(X!2), Z!0))) = implies(or(not(Y!1), Z!0), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[22, 35])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (implies(implies(Y!1, Z!0), implies(or(not(X!2), Y!1), or(not(X!2), Z!0))) = or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[36, 27, 25])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (is_a_theorem(implies(implies(Y!1, Z!0), implies(or(not(X!2), Y!1), or(not(X!2), Z!0)))) <=> is_a_theorem(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (is_a_theorem(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0)))) <=> is_a_theorem(implies(implies(Y!1, Z!0), implies(or(not(X!2), Y!1), or(not(X!2), Z!0))))),
% 0.21/0.44 inference(symmetry,[status(thm)],[38])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 ((~is_a_theorem(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))))) <=> (~is_a_theorem(implies(implies(Y!1, Z!0), implies(or(not(X!2), Y!1), or(not(X!2), Z!0)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(implies(Y!1, Z!0), implies(X!2, Z!0)) = or(not(implies(Y!1, Z!0)), implies(X!2, Z!0)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (implies(implies(Y!1, Z!0), implies(X!2, Z!0)) = or(not(implies(Y!1, Z!0)), implies(X!2, Z!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[41, 20])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (or(not(implies(Y!1, Z!0)), implies(X!2, Z!0)) = implies(implies(Y!1, Z!0), implies(X!2, Z!0))),
% 0.21/0.44 inference(symmetry,[status(thm)],[42])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(X!2, Z!0) = or(not(X!2), Z!0))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (implies(X!2, Z!0) = or(not(X!2), Z!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[44, 20])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (or(not(X!2), Z!0) = implies(X!2, Z!0)),
% 0.21/0.44 inference(symmetry,[status(thm)],[45])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (or(not(implies(Y!1, Z!0)), or(not(X!2), Z!0)) = or(not(implies(Y!1, Z!0)), implies(X!2, Z!0))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[46])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (or(not(implies(Y!1, Z!0)), or(not(X!2), Z!0)) = implies(implies(Y!1, Z!0), implies(X!2, Z!0))),
% 0.21/0.44 inference(transitivity,[status(thm)],[47, 43])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 (or(not(implies(X!2, Y!1)), or(not(implies(Y!1, Z!0)), or(not(X!2), Z!0))) = or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[48])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), or(not(implies(Y!1, Z!0)), or(not(X!2), Z!0)))) = implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[49])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (is_a_theorem(implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), or(not(implies(Y!1, Z!0)), or(not(X!2), Z!0))))) <=> is_a_theorem(implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[50])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (^[P: $i, Q: $i, R: $i] : refl(is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))) <=> is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (($true <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(56,axiom,(r4), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r4')).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (r4 <=> $true),
% 0.21/0.44 inference(iff_true,[status(thm)],[56])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 ((r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) <=> ($true <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[57])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 ((r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[58, 55])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 ((r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) <=> (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(61,axiom,(r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','r4')).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (r4 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[62, 60])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.21/0.44 tff(66,plain,(
% 0.21/0.44 ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[65])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[66, 53])).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(or(P, or(Q, R)), or(Q, or(P, R))))) | is_a_theorem(implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), or(not(implies(Y!1, Z!0)), or(not(X!2), Z!0)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (is_a_theorem(implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), or(not(implies(Y!1, Z!0)), or(not(X!2), Z!0)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (is_a_theorem(implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[69, 51])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 ((~![X: $i, Y: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(implies(X!2, Y!1), implies(implies(Y!1, Z!0), implies(X!2, Z!0))) = or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (implies(implies(X!2, Y!1), implies(implies(Y!1, Z!0), implies(X!2, Z!0))) = or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[71, 20])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0))) = implies(implies(X!2, Y!1), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))),
% 0.21/0.45 inference(symmetry,[status(thm)],[72])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (is_a_theorem(or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))) <=> is_a_theorem(implies(implies(X!2, Y!1), implies(implies(Y!1, Z!0), implies(X!2, Z!0))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[73])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (is_a_theorem(implies(implies(X!2, Y!1), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))) <=> is_a_theorem(or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0))))),
% 0.21/0.45 inference(symmetry,[status(thm)],[74])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 ((~is_a_theorem(implies(implies(X!2, Y!1), implies(implies(Y!1, Z!0), implies(X!2, Z!0))))) <=> (~is_a_theorem(or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (($false <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(79,axiom,(~implies_3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hilbert_implies_3')).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (implies_3 <=> $false),
% 0.21/0.45 inference(iff_false,[status(thm)],[79])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 ((implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) <=> ($false <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[80])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 ((implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[81, 78])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 ((implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))) <=> (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(84,axiom,(implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','implies_3')).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (implies_3 <=> ![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[85, 83])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[88, 77])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[89, 77])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[90, 77])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[91, 77])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (~![X: $i, Y: $i, Z: $i] : is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[92, 77])).
% 0.21/0.45 tff(94,plain,(
% 0.21/0.45 ~is_a_theorem(implies(implies(X!2, Y!1), implies(implies(Y!1, Z!0), implies(X!2, Z!0))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[93])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (~is_a_theorem(or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[94, 76])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 (^[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))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 (($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)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(102,axiom,(modus_ponens), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_modus_ponens')).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 (modus_ponens <=> $true),
% 0.21/0.45 inference(iff_true,[status(thm)],[102])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 ((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))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 ((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)))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[104, 101])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 ((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))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 ((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))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(108,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')).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[109, 106])).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[110, 105])).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[111, 100])).
% 0.21/0.45 tff(113,plain,(
% 0.21/0.45 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[112])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[113, 99])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[114, 97])).
% 0.21/0.45 tff(116,plain,
% 0.21/0.45 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))) | (~is_a_theorem(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))))) | (~is_a_theorem(implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))) | (~is_a_theorem(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))))) | (~is_a_theorem(implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))) | (~is_a_theorem(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))))) | (~is_a_theorem(implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))) | (~is_a_theorem(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))))) | (~is_a_theorem(implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (is_a_theorem(or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0)))) | (~is_a_theorem(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))))) | (~is_a_theorem(implies(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))), or(not(implies(X!2, Y!1)), implies(implies(Y!1, Z!0), implies(X!2, Z!0))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.21/0.45 tff(120,plain,
% 0.21/0.45 (~is_a_theorem(or(not(implies(Y!1, Z!0)), or(not(implies(X!2, Y!1)), or(not(X!2), Z!0))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[119, 95, 70])).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 (~is_a_theorem(implies(implies(Y!1, Z!0), implies(or(not(X!2), Y!1), or(not(X!2), Z!0))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[120, 40])).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 (^[P: $i, Q: $i, R: $i] : refl(is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))) <=> is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 (($true <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(126,axiom,(r5), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r5')).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 (r5 <=> $true),
% 0.21/0.45 inference(iff_true,[status(thm)],[126])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 ((r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))) <=> ($true <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 ((r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))) <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[128, 125])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 ((r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))) <=> (r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(131,axiom,(r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','r5')).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 (r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.46 tff(133,plain,
% 0.21/0.46 (r5 <=> ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[132, 130])).
% 0.21/0.46 tff(134,plain,
% 0.21/0.46 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.21/0.46 tff(135,plain,
% 0.21/0.46 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[134, 124])).
% 0.21/0.46 tff(136,plain,(
% 0.21/0.46 ![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[135])).
% 0.21/0.46 tff(137,plain,
% 0.21/0.46 (![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[136, 123])).
% 0.21/0.46 tff(138,plain,
% 0.21/0.46 ((~![P: $i, Q: $i, R: $i] : is_a_theorem(implies(implies(Q, R), implies(or(P, Q), or(P, R))))) | is_a_theorem(implies(implies(Y!1, Z!0), implies(or(not(X!2), Y!1), or(not(X!2), Z!0))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(139,plain,
% 0.21/0.46 (is_a_theorem(implies(implies(Y!1, Z!0), implies(or(not(X!2), Y!1), or(not(X!2), Z!0))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.21/0.46 tff(140,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[139, 121])).
% 0.21/0.46 % SZS output end Proof
%------------------------------------------------------------------------------