TSTP Solution File: LCL459+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL459+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 0.14s 0.37s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL459+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n022.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Sep 1 21:37:40 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.
% 0.14/0.37 % SZS status Theorem
% 0.14/0.37 % SZS output start Proof
% 0.14/0.37 tff(is_a_theorem_type, type, (
% 0.14/0.37 is_a_theorem: $i > $o)).
% 0.14/0.37 tff(not_type, type, (
% 0.14/0.37 not: $i > $i)).
% 0.14/0.37 tff(and_type, type, (
% 0.14/0.37 and: ( $i * $i ) > $i)).
% 0.14/0.37 tff(tptp_fun_P_2_type, type, (
% 0.14/0.37 tptp_fun_P_2: $i)).
% 0.14/0.37 tff(implies_type, type, (
% 0.14/0.37 implies: ( $i * $i ) > $i)).
% 0.14/0.37 tff(op_implies_and_type, type, (
% 0.14/0.37 op_implies_and: $o)).
% 0.14/0.37 tff(and_3_type, type, (
% 0.14/0.37 and_3: $o)).
% 0.14/0.37 tff(implies_2_type, type, (
% 0.14/0.37 implies_2: $o)).
% 0.14/0.37 tff(kn1_type, type, (
% 0.14/0.37 kn1: $o)).
% 0.14/0.37 tff(modus_ponens_type, type, (
% 0.14/0.37 modus_ponens: $o)).
% 0.14/0.37 tff(1,plain,
% 0.14/0.37 (^[X: $i, Y: $i] : refl((implies(X, Y) = not(and(X, not(Y)))) <=> (implies(X, Y) = not(and(X, not(Y)))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(2,plain,
% 0.14/0.37 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.37 tff(3,plain,
% 0.14/0.37 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y)))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(4,plain,
% 0.14/0.37 (($false | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) <=> ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(5,plain,
% 0.14/0.37 ((~$true) <=> $false),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(6,axiom,(op_implies_and), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_op_implies_and')).
% 0.14/0.37 tff(7,plain,
% 0.14/0.37 (op_implies_and <=> $true),
% 0.14/0.37 inference(iff_true,[status(thm)],[6])).
% 0.14/0.37 tff(8,plain,
% 0.14/0.37 ((~op_implies_and) <=> (~$true)),
% 0.14/0.37 inference(monotonicity,[status(thm)],[7])).
% 0.14/0.37 tff(9,plain,
% 0.14/0.37 ((~op_implies_and) <=> $false),
% 0.14/0.37 inference(transitivity,[status(thm)],[8, 5])).
% 0.14/0.37 tff(10,plain,
% 0.14/0.37 (((~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)))))),
% 0.14/0.37 inference(monotonicity,[status(thm)],[9])).
% 0.14/0.37 tff(11,plain,
% 0.14/0.37 (((~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))))),
% 0.14/0.37 inference(transitivity,[status(thm)],[10, 4])).
% 0.14/0.37 tff(12,plain,
% 0.14/0.37 (((~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)))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(13,plain,
% 0.14/0.37 ((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)))))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 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')).
% 0.14/0.37 tff(15,plain,
% 0.14/0.37 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.14/0.37 tff(16,plain,
% 0.14/0.37 ((~op_implies_and) | ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.14/0.37 tff(17,plain,
% 0.14/0.37 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.14/0.37 tff(18,plain,
% 0.14/0.37 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.14/0.37 tff(19,plain,(
% 0.14/0.37 ![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.37 inference(skolemize,[status(sab)],[18])).
% 0.14/0.37 tff(20,plain,
% 0.14/0.37 (![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.14/0.37 tff(21,plain,
% 0.14/0.37 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(P!2, not(and(P!2, not(and(P!2, P!2))))) = not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))))),
% 0.14/0.37 inference(quant_inst,[status(thm)],[])).
% 0.14/0.37 tff(22,plain,
% 0.14/0.37 (implies(P!2, not(and(P!2, not(and(P!2, P!2))))) = not(and(P!2, not(not(and(P!2, not(and(P!2, P!2)))))))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.14/0.37 tff(23,plain,
% 0.14/0.37 (not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))) = implies(P!2, not(and(P!2, not(and(P!2, P!2)))))),
% 0.14/0.38 inference(symmetry,[status(thm)],[22])).
% 0.14/0.38 tff(24,plain,
% 0.14/0.38 (is_a_theorem(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2)))))))) <=> is_a_theorem(implies(P!2, not(and(P!2, not(and(P!2, P!2))))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[23])).
% 0.14/0.38 tff(25,plain,
% 0.14/0.38 (is_a_theorem(implies(P!2, not(and(P!2, not(and(P!2, P!2)))))) <=> is_a_theorem(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))))),
% 0.14/0.38 inference(symmetry,[status(thm)],[24])).
% 0.14/0.38 tff(26,plain,
% 0.14/0.38 ((~![X: $i, Y: $i] : (implies(X, Y) = not(and(X, not(Y))))) | (implies(P!2, and(P!2, P!2)) = not(and(P!2, not(and(P!2, P!2)))))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(27,plain,
% 0.14/0.38 (implies(P!2, and(P!2, P!2)) = not(and(P!2, not(and(P!2, P!2))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[26, 20])).
% 0.14/0.38 tff(28,plain,
% 0.14/0.38 (implies(P!2, implies(P!2, and(P!2, P!2))) = implies(P!2, not(and(P!2, not(and(P!2, P!2)))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[27])).
% 0.14/0.38 tff(29,plain,
% 0.14/0.38 (is_a_theorem(implies(P!2, implies(P!2, and(P!2, P!2)))) <=> is_a_theorem(implies(P!2, not(and(P!2, not(and(P!2, P!2))))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[28])).
% 0.14/0.38 tff(30,plain,
% 0.14/0.38 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(X, implies(Y, and(X, Y)))) <=> is_a_theorem(implies(X, implies(Y, and(X, Y)))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(31,plain,
% 0.14/0.38 (![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.14/0.38 tff(32,plain,
% 0.14/0.38 (![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(33,plain,
% 0.14/0.38 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(34,axiom,(and_3), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_and_3')).
% 0.14/0.38 tff(35,plain,
% 0.14/0.38 (and_3 <=> $true),
% 0.14/0.38 inference(iff_true,[status(thm)],[34])).
% 0.14/0.38 tff(36,plain,
% 0.14/0.38 ((and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y)))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[35])).
% 0.14/0.38 tff(37,plain,
% 0.14/0.38 ((and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.14/0.38 inference(transitivity,[status(thm)],[36, 33])).
% 0.14/0.38 tff(38,plain,
% 0.14/0.38 ((and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) <=> (and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y)))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(39,axiom,(and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','and_3')).
% 0.14/0.38 tff(40,plain,
% 0.14/0.38 (and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.14/0.38 tff(41,plain,
% 0.14/0.38 (and_3 <=> ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[40, 38])).
% 0.14/0.38 tff(42,plain,
% 0.14/0.38 (![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.14/0.38 tff(43,plain,
% 0.14/0.38 (![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.14/0.38 tff(44,plain,(
% 0.14/0.38 ![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.14/0.38 inference(skolemize,[status(sab)],[43])).
% 0.14/0.38 tff(45,plain,
% 0.14/0.38 (![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[44, 31])).
% 0.14/0.38 tff(46,plain,
% 0.14/0.38 ((~![X: $i, Y: $i] : is_a_theorem(implies(X, implies(Y, and(X, Y))))) | is_a_theorem(implies(P!2, implies(P!2, and(P!2, P!2))))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(47,plain,
% 0.14/0.38 (is_a_theorem(implies(P!2, implies(P!2, and(P!2, P!2))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.14/0.38 tff(48,plain,
% 0.14/0.38 (is_a_theorem(implies(P!2, not(and(P!2, not(and(P!2, P!2))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[47, 29])).
% 0.14/0.38 tff(49,plain,
% 0.14/0.38 (is_a_theorem(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[48, 25])).
% 0.14/0.38 tff(50,plain,
% 0.14/0.38 (implies(P!2, implies(P!2, and(P!2, P!2))) = not(and(P!2, not(not(and(P!2, not(and(P!2, P!2)))))))),
% 0.14/0.38 inference(transitivity,[status(thm)],[28, 22])).
% 0.14/0.38 tff(51,plain,
% 0.14/0.38 (implies(implies(P!2, implies(P!2, and(P!2, P!2))), implies(P!2, and(P!2, P!2))) = implies(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))), not(and(P!2, not(and(P!2, P!2)))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[50, 27])).
% 0.14/0.38 tff(52,plain,
% 0.14/0.38 (is_a_theorem(implies(implies(P!2, implies(P!2, and(P!2, P!2))), implies(P!2, and(P!2, P!2)))) <=> is_a_theorem(implies(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))), not(and(P!2, not(and(P!2, P!2))))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[51])).
% 0.14/0.38 tff(53,plain,
% 0.14/0.38 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))) <=> is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(54,plain,
% 0.14/0.38 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.14/0.38 tff(55,plain,
% 0.14/0.38 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(56,plain,
% 0.14/0.38 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(57,axiom,(implies_2), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_implies_2')).
% 0.14/0.38 tff(58,plain,
% 0.14/0.38 (implies_2 <=> $true),
% 0.14/0.38 inference(iff_true,[status(thm)],[57])).
% 0.14/0.38 tff(59,plain,
% 0.14/0.38 ((implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[58])).
% 0.14/0.38 tff(60,plain,
% 0.14/0.38 ((implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.14/0.38 inference(transitivity,[status(thm)],[59, 56])).
% 0.14/0.38 tff(61,plain,
% 0.14/0.38 ((implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))) <=> (implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(62,axiom,(implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','implies_2')).
% 0.14/0.38 tff(63,plain,
% 0.14/0.38 (implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.14/0.38 tff(64,plain,
% 0.14/0.38 (implies_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[63, 61])).
% 0.14/0.38 tff(65,plain,
% 0.14/0.38 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.14/0.38 tff(66,plain,
% 0.14/0.38 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.14/0.38 tff(67,plain,(
% 0.14/0.38 ![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.14/0.38 inference(skolemize,[status(sab)],[66])).
% 0.14/0.38 tff(68,plain,
% 0.14/0.38 (![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[67, 54])).
% 0.14/0.38 tff(69,plain,
% 0.14/0.38 ((~![X: $i, Y: $i] : is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y)))) | is_a_theorem(implies(implies(P!2, implies(P!2, and(P!2, P!2))), implies(P!2, and(P!2, P!2))))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(70,plain,
% 0.14/0.38 (is_a_theorem(implies(implies(P!2, implies(P!2, and(P!2, P!2))), implies(P!2, and(P!2, P!2))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.14/0.38 tff(71,plain,
% 0.14/0.38 (is_a_theorem(implies(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))), not(and(P!2, not(and(P!2, P!2))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[70, 52])).
% 0.14/0.38 tff(72,plain,
% 0.14/0.38 (not(and(P!2, not(and(P!2, P!2)))) = implies(P!2, and(P!2, P!2))),
% 0.14/0.38 inference(symmetry,[status(thm)],[27])).
% 0.14/0.38 tff(73,plain,
% 0.14/0.38 (is_a_theorem(not(and(P!2, not(and(P!2, P!2))))) <=> is_a_theorem(implies(P!2, and(P!2, P!2)))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[72])).
% 0.14/0.38 tff(74,plain,
% 0.14/0.38 (is_a_theorem(implies(P!2, and(P!2, P!2))) <=> is_a_theorem(not(and(P!2, not(and(P!2, P!2)))))),
% 0.14/0.38 inference(symmetry,[status(thm)],[73])).
% 0.14/0.38 tff(75,plain,
% 0.14/0.38 ((~is_a_theorem(implies(P!2, and(P!2, P!2)))) <=> (~is_a_theorem(not(and(P!2, not(and(P!2, P!2))))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[74])).
% 0.14/0.38 tff(76,plain,
% 0.14/0.38 ((~![P: $i] : is_a_theorem(implies(P, and(P, P)))) <=> (~![P: $i] : is_a_theorem(implies(P, and(P, P))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(77,plain,
% 0.14/0.38 (($false <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))) <=> (~![P: $i] : is_a_theorem(implies(P, and(P, P))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(78,axiom,(~kn1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rosser_kn1')).
% 0.14/0.38 tff(79,plain,
% 0.14/0.38 (kn1 <=> $false),
% 0.14/0.38 inference(iff_false,[status(thm)],[78])).
% 0.14/0.38 tff(80,plain,
% 0.14/0.38 ((kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))) <=> ($false <=> ![P: $i] : is_a_theorem(implies(P, and(P, P))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[79])).
% 0.14/0.38 tff(81,plain,
% 0.14/0.38 ((kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))) <=> (~![P: $i] : is_a_theorem(implies(P, and(P, P))))),
% 0.14/0.38 inference(transitivity,[status(thm)],[80, 77])).
% 0.14/0.38 tff(82,plain,
% 0.14/0.38 ((kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))) <=> (kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(83,axiom,(kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','kn1')).
% 0.14/0.38 tff(84,plain,
% 0.14/0.38 (kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.14/0.38 tff(85,plain,
% 0.14/0.38 (kn1 <=> ![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[84, 82])).
% 0.14/0.38 tff(86,plain,
% 0.14/0.38 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.14/0.38 tff(87,plain,
% 0.14/0.38 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.14/0.38 tff(88,plain,
% 0.14/0.38 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[87, 76])).
% 0.14/0.38 tff(89,plain,
% 0.14/0.38 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[88, 76])).
% 0.14/0.38 tff(90,plain,
% 0.14/0.38 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[89, 76])).
% 0.14/0.38 tff(91,plain,
% 0.14/0.38 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[90, 76])).
% 0.14/0.38 tff(92,plain,
% 0.14/0.38 (~![P: $i] : is_a_theorem(implies(P, and(P, P)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[91, 76])).
% 0.14/0.38 tff(93,plain,(
% 0.14/0.38 ~is_a_theorem(implies(P!2, and(P!2, P!2)))),
% 0.14/0.38 inference(skolemize,[status(sab)],[92])).
% 0.14/0.38 tff(94,plain,
% 0.14/0.38 (~is_a_theorem(not(and(P!2, not(and(P!2, P!2)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[93, 75])).
% 0.14/0.38 tff(95,plain,
% 0.14/0.38 (^[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)))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(96,plain,
% 0.14/0.38 (![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))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[95])).
% 0.14/0.38 tff(97,plain,
% 0.14/0.38 (^[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))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(98,plain,
% 0.14/0.38 (![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))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[97])).
% 0.14/0.38 tff(99,plain,
% 0.14/0.38 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y))))) <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(100,plain,
% 0.14/0.38 (($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)))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(101,axiom,(modus_ponens), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_modus_ponens')).
% 0.14/0.38 tff(102,plain,
% 0.14/0.38 (modus_ponens <=> $true),
% 0.14/0.38 inference(iff_true,[status(thm)],[101])).
% 0.14/0.38 tff(103,plain,
% 0.14/0.38 ((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))))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[102])).
% 0.14/0.38 tff(104,plain,
% 0.14/0.38 ((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)))))),
% 0.14/0.38 inference(transitivity,[status(thm)],[103, 100])).
% 0.14/0.38 tff(105,plain,
% 0.14/0.38 ((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))))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(106,plain,
% 0.14/0.38 ((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))))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(107,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')).
% 0.14/0.38 tff(108,plain,
% 0.14/0.38 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.14/0.38 tff(109,plain,
% 0.14/0.38 (modus_ponens <=> ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[108, 105])).
% 0.14/0.38 tff(110,plain,
% 0.14/0.38 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[109, 104])).
% 0.14/0.38 tff(111,plain,
% 0.14/0.38 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[110, 99])).
% 0.14/0.38 tff(112,plain,(
% 0.14/0.38 ![X: $i, Y: $i] : (is_a_theorem(Y) | (~(is_a_theorem(X) & is_a_theorem(implies(X, Y)))))),
% 0.14/0.38 inference(skolemize,[status(sab)],[111])).
% 0.14/0.38 tff(113,plain,
% 0.14/0.38 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[112, 98])).
% 0.14/0.38 tff(114,plain,
% 0.14/0.38 (![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[113, 96])).
% 0.14/0.38 tff(115,plain,
% 0.14/0.38 (((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(P!2, not(and(P!2, P!2))))) | (~is_a_theorem(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))))) | (~is_a_theorem(implies(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))), not(and(P!2, not(and(P!2, P!2))))))))) <=> ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(P!2, not(and(P!2, P!2))))) | (~is_a_theorem(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))))) | (~is_a_theorem(implies(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))), not(and(P!2, not(and(P!2, P!2))))))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(116,plain,
% 0.14/0.38 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | (is_a_theorem(not(and(P!2, not(and(P!2, P!2))))) | (~is_a_theorem(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))))) | (~is_a_theorem(implies(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))), not(and(P!2, not(and(P!2, P!2))))))))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(117,plain,
% 0.14/0.38 ((~![X: $i, Y: $i] : (is_a_theorem(Y) | (~is_a_theorem(X)) | (~is_a_theorem(implies(X, Y))))) | is_a_theorem(not(and(P!2, not(and(P!2, P!2))))) | (~is_a_theorem(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))))) | (~is_a_theorem(implies(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))), not(and(P!2, not(and(P!2, P!2)))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.14/0.38 tff(118,plain,
% 0.14/0.38 ((~is_a_theorem(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))))) | (~is_a_theorem(implies(not(and(P!2, not(not(and(P!2, not(and(P!2, P!2))))))), not(and(P!2, not(and(P!2, P!2)))))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[117, 114, 94])).
% 0.14/0.38 tff(119,plain,
% 0.14/0.38 ($false),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[118, 71, 49])).
% 0.14/0.38 % SZS output end Proof
%------------------------------------------------------------------------------