TSTP Solution File: LCL512+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL512+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 04:56:34 EDT 2022
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : LCL512+1 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n029.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu Sep 1 22:09:14 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(is_a_theorem_type, type, (
% 0.11/0.36 is_a_theorem: $i > $o)).
% 0.11/0.36 tff(implies_type, type, (
% 0.11/0.36 implies: ( $i * $i ) > $i)).
% 0.11/0.36 tff(not_type, type, (
% 0.11/0.36 not: $i > $i)).
% 0.11/0.36 tff(and_type, type, (
% 0.11/0.36 and: ( $i * $i ) > $i)).
% 0.11/0.36 tff(tptp_fun_Y_2_type, type, (
% 0.11/0.36 tptp_fun_Y_2: $i)).
% 0.11/0.36 tff(tptp_fun_X_3_type, type, (
% 0.11/0.36 tptp_fun_X_3: $i)).
% 0.11/0.36 tff(equiv_type, type, (
% 0.11/0.36 equiv: ( $i * $i ) > $i)).
% 0.11/0.36 tff(op_implies_and_type, type, (
% 0.11/0.36 op_implies_and: $o)).
% 0.11/0.36 tff(op_equiv_type, type, (
% 0.11/0.36 op_equiv: $o)).
% 0.11/0.36 tff(equivalence_1_type, type, (
% 0.11/0.36 equivalence_1: $o)).
% 0.11/0.36 tff(kn2_type, type, (
% 0.11/0.36 kn2: $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (($false | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 ((~$true) <=> $false),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(6,axiom,(op_implies_and), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax','rosser_op_implies_and')).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (op_implies_and <=> $true),
% 0.11/0.36 inference(iff_true,[status(thm)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 ((~op_implies_and) <=> (~$true)),
% 0.11/0.36 inference(monotonicity,[status(thm)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 ((~op_implies_and) <=> $false),
% 0.11/0.36 inference(transitivity,[status(thm)],[8, 5])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (((~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)))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[9])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (((~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))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[10, 4])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (((~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)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 ((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)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(14,axiom,(op_implies_and => ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_implies_and')).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.11/0.36 tff(19,plain,(
% 0.11/0.36 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[18])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(X!3, Y!2) = not(and(X!3, not(Y!2))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (implies(X!3, Y!2) = not(and(X!3, not(Y!2)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (not(and(X!3, not(Y!2))) = implies(X!3, Y!2)),
% 0.11/0.36 inference(symmetry,[status(thm)],[22])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (^[X: $i, Y: $i] : refl((equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (($false | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(28,axiom,(op_equiv), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax','rosser_op_equiv')).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (op_equiv <=> $true),
% 0.11/0.37 inference(iff_true,[status(thm)],[28])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ((~op_equiv) <=> (~$true)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[29])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 ((~op_equiv) <=> $false),
% 0.11/0.37 inference(transitivity,[status(thm)],[30, 5])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ($false | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[31])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[32, 27])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 ((op_equiv => ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) <=> ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(36,axiom,(op_equiv => ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax','op_equiv')).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 ((~op_equiv) | ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[39, 26])).
% 0.11/0.37 tff(41,plain,(
% 0.11/0.37 ![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[40])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[41, 25])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : (equiv(X, Y) = and(implies(X, Y), implies(Y, X)))) | (equiv(X!3, Y!2) = and(implies(X!3, Y!2), implies(Y!2, X!3)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (equiv(X!3, Y!2) = and(implies(X!3, Y!2), implies(Y!2, X!3))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (and(implies(X!3, Y!2), implies(Y!2, X!3)) = equiv(X!3, Y!2)),
% 0.11/0.37 inference(symmetry,[status(thm)],[44])).
% 0.11/0.37 tff(46,plain,
% 0.11/0.37 (and(not(and(X!3, not(Y!2))), implies(Y!2, X!3)) = and(implies(X!3, Y!2), implies(Y!2, X!3))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[23])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (and(not(and(X!3, not(Y!2))), implies(Y!2, X!3)) = equiv(X!3, Y!2)),
% 0.11/0.37 inference(transitivity,[status(thm)],[46, 45])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (implies(and(not(and(X!3, not(Y!2))), implies(Y!2, X!3)), not(and(X!3, not(Y!2)))) = implies(equiv(X!3, Y!2), implies(X!3, Y!2))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[47, 23])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 (is_a_theorem(implies(and(not(and(X!3, not(Y!2))), implies(Y!2, X!3)), not(and(X!3, not(Y!2))))) <=> is_a_theorem(implies(equiv(X!3, Y!2), implies(X!3, Y!2)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[48])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 (is_a_theorem(implies(equiv(X!3, Y!2), implies(X!3, Y!2))) <=> is_a_theorem(implies(and(not(and(X!3, not(Y!2))), implies(Y!2, X!3)), not(and(X!3, not(Y!2)))))),
% 0.11/0.37 inference(symmetry,[status(thm)],[49])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 ((~is_a_theorem(implies(equiv(X!3, Y!2), implies(X!3, Y!2)))) <=> (~is_a_theorem(implies(and(not(and(X!3, not(Y!2))), implies(Y!2, X!3)), not(and(X!3, not(Y!2))))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[50])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 (($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(54,axiom,(~equivalence_1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hilbert_equivalence_1')).
% 0.11/0.37 tff(55,plain,
% 0.11/0.37 (equivalence_1 <=> $false),
% 0.11/0.37 inference(iff_false,[status(thm)],[54])).
% 0.11/0.37 tff(56,plain,
% 0.11/0.37 ((equivalence_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))) <=> ($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[55])).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 ((equivalence_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[56, 53])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 ((equivalence_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))) <=> (equivalence_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(59,axiom,(equivalence_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','equivalence_1')).
% 0.11/0.37 tff(60,plain,
% 0.11/0.37 (equivalence_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.11/0.37 tff(61,plain,
% 0.11/0.37 (equivalence_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[60, 58])).
% 0.11/0.37 tff(62,plain,
% 0.11/0.37 (~![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.11/0.37 tff(63,plain,
% 0.11/0.37 (~![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.11/0.37 tff(64,plain,
% 0.11/0.37 (~![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[63, 52])).
% 0.11/0.37 tff(65,plain,
% 0.11/0.37 (~![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[64, 52])).
% 0.11/0.37 tff(66,plain,
% 0.11/0.37 (~![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[65, 52])).
% 0.11/0.37 tff(67,plain,
% 0.11/0.37 (~![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[66, 52])).
% 0.11/0.37 tff(68,plain,
% 0.11/0.37 (~![X: $i, Y: $i] : is_a_theorem(implies(equiv(X, Y), implies(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[67, 52])).
% 0.11/0.37 tff(69,plain,(
% 0.11/0.37 ~is_a_theorem(implies(equiv(X!3, Y!2), implies(X!3, Y!2)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[68])).
% 0.11/0.37 tff(70,plain,
% 0.11/0.37 (~is_a_theorem(implies(and(not(and(X!3, not(Y!2))), implies(Y!2, X!3)), not(and(X!3, not(Y!2)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[69, 51])).
% 0.11/0.37 tff(71,plain,
% 0.11/0.37 (^[P: $i, Q: $i] : refl(is_a_theorem(implies(and(P, Q), P)) <=> is_a_theorem(implies(and(P, Q), P)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(72,plain,
% 0.11/0.37 (![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)) <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[71])).
% 0.11/0.37 tff(73,plain,
% 0.11/0.37 (![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)) <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(74,plain,
% 0.11/0.37 (($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(75,axiom,(kn2), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax','rosser_kn2')).
% 0.11/0.37 tff(76,plain,
% 0.11/0.37 (kn2 <=> $true),
% 0.11/0.37 inference(iff_true,[status(thm)],[75])).
% 0.11/0.37 tff(77,plain,
% 0.11/0.37 ((kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> ($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[76])).
% 0.11/0.37 tff(78,plain,
% 0.11/0.37 ((kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.11/0.37 inference(transitivity,[status(thm)],[77, 74])).
% 0.11/0.37 tff(79,plain,
% 0.11/0.37 ((kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(80,axiom,(kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','kn2')).
% 0.11/0.37 tff(81,plain,
% 0.11/0.37 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.11/0.37 tff(82,plain,
% 0.11/0.37 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[81, 79])).
% 0.11/0.37 tff(83,plain,
% 0.11/0.37 (![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.11/0.37 tff(84,plain,
% 0.11/0.37 (![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.11/0.37 tff(85,plain,(
% 0.11/0.37 ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.11/0.37 inference(skolemize,[status(sab)],[84])).
% 0.11/0.37 tff(86,plain,
% 0.11/0.37 (![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[85, 72])).
% 0.11/0.37 tff(87,plain,
% 0.11/0.37 ((~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) | is_a_theorem(implies(and(not(and(X!3, not(Y!2))), implies(Y!2, X!3)), not(and(X!3, not(Y!2)))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(88,plain,
% 0.11/0.37 (is_a_theorem(implies(and(not(and(X!3, not(Y!2))), implies(Y!2, X!3)), not(and(X!3, not(Y!2)))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.11/0.37 tff(89,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[88, 70])).
% 0.11/0.37 % SZS output end Proof
%------------------------------------------------------------------------------