TSTP Solution File: LCL460+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL460+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 04:56:24 EDT 2022
% Result : Theorem 0.17s 0.39s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL460+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 21:40:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.17/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.17/0.34 Usage: tptp [options] [-file:]file
% 0.17/0.34 -h, -? prints this message.
% 0.17/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.17/0.34 -m, -model generate model.
% 0.17/0.34 -p, -proof generate proof.
% 0.17/0.34 -c, -core generate unsat core of named formulas.
% 0.17/0.34 -st, -statistics display statistics.
% 0.17/0.34 -t:timeout set timeout (in second).
% 0.17/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.17/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.17/0.34 -<param>:<value> configuration parameter and value.
% 0.17/0.34 -o:<output-file> file to place output in.
% 0.17/0.39 % SZS status Theorem
% 0.17/0.39 % SZS output start Proof
% 0.17/0.39 tff(is_a_theorem_type, type, (
% 0.17/0.39 is_a_theorem: $i > $o)).
% 0.17/0.39 tff(implies_type, type, (
% 0.17/0.39 implies: ( $i * $i ) > $i)).
% 0.17/0.39 tff(tptp_fun_P_3_type, type, (
% 0.17/0.39 tptp_fun_P_3: $i)).
% 0.17/0.39 tff(and_type, type, (
% 0.17/0.39 and: ( $i * $i ) > $i)).
% 0.17/0.39 tff(tptp_fun_Q_2_type, type, (
% 0.17/0.39 tptp_fun_Q_2: $i)).
% 0.17/0.39 tff(kn2_type, type, (
% 0.17/0.39 kn2: $o)).
% 0.17/0.39 tff(and_1_type, type, (
% 0.17/0.39 and_1: $o)).
% 0.17/0.39 tff(1,plain,
% 0.17/0.39 ((~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(2,plain,
% 0.17/0.39 (($false <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(3,axiom,(~kn2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rosser_kn2')).
% 0.17/0.39 tff(4,plain,
% 0.17/0.39 (kn2 <=> $false),
% 0.17/0.39 inference(iff_false,[status(thm)],[3])).
% 0.17/0.39 tff(5,plain,
% 0.17/0.39 ((kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) <=> ($false <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[4])).
% 0.17/0.39 tff(6,plain,
% 0.17/0.39 ((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)))),
% 0.17/0.39 inference(transitivity,[status(thm)],[5, 2])).
% 0.17/0.39 tff(7,plain,
% 0.17/0.39 ((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)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(8,axiom,(kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','kn2')).
% 0.17/0.39 tff(9,plain,
% 0.17/0.39 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.17/0.39 tff(10,plain,
% 0.17/0.39 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[9, 7])).
% 0.17/0.39 tff(11,plain,
% 0.17/0.39 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.17/0.39 tff(12,plain,
% 0.17/0.39 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.17/0.39 tff(13,plain,
% 0.17/0.39 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.17/0.39 tff(14,plain,
% 0.17/0.39 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[13, 1])).
% 0.17/0.39 tff(15,plain,
% 0.17/0.39 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[14, 1])).
% 0.17/0.39 tff(16,plain,
% 0.17/0.39 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[15, 1])).
% 0.17/0.39 tff(17,plain,
% 0.17/0.39 (~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[16, 1])).
% 0.17/0.39 tff(18,plain,(
% 0.17/0.39 ~is_a_theorem(implies(and(P!3, Q!2), P!3))),
% 0.17/0.39 inference(skolemize,[status(sab)],[17])).
% 0.17/0.39 tff(19,plain,
% 0.17/0.39 (^[X: $i, Y: $i] : refl(is_a_theorem(implies(and(X, Y), X)) <=> is_a_theorem(implies(and(X, Y), X)))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(20,plain,
% 0.17/0.39 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.17/0.39 tff(21,plain,
% 0.17/0.39 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(22,plain,
% 0.17/0.39 (($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(23,axiom,(and_1), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax','hilbert_and_1')).
% 0.17/0.39 tff(24,plain,
% 0.17/0.39 (and_1 <=> $true),
% 0.17/0.39 inference(iff_true,[status(thm)],[23])).
% 0.17/0.39 tff(25,plain,
% 0.17/0.39 ((and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> ($true <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.17/0.39 tff(26,plain,
% 0.17/0.39 ((and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.39 inference(transitivity,[status(thm)],[25, 22])).
% 0.17/0.39 tff(27,plain,
% 0.17/0.39 ((and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(28,axiom,(and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax','and_1')).
% 0.17/0.39 tff(29,plain,
% 0.17/0.39 (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.17/0.39 tff(30,plain,
% 0.17/0.39 (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.17/0.39 tff(31,plain,
% 0.17/0.39 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.17/0.39 tff(32,plain,
% 0.17/0.39 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.17/0.39 tff(33,plain,(
% 0.17/0.39 ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.39 inference(skolemize,[status(sab)],[32])).
% 0.17/0.39 tff(34,plain,
% 0.17/0.39 (![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[33, 20])).
% 0.17/0.39 tff(35,plain,
% 0.17/0.39 ((~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) | is_a_theorem(implies(and(P!3, Q!2), P!3))),
% 0.17/0.39 inference(quant_inst,[status(thm)],[])).
% 0.17/0.39 tff(36,plain,
% 0.17/0.39 ($false),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[35, 34, 18])).
% 0.17/0.39 % SZS output end Proof
%------------------------------------------------------------------------------