TSTP Solution File: LCL506+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL506+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 04:56:33 EDT 2022
% Result : Theorem 0.17s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL506+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.32 % Computer : n029.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Thu Sep 1 22:07:14 EDT 2022
% 0.17/0.32 % CPUTime :
% 0.17/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.17/0.33 Usage: tptp [options] [-file:]file
% 0.17/0.33 -h, -? prints this message.
% 0.17/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.17/0.33 -m, -model generate model.
% 0.17/0.33 -p, -proof generate proof.
% 0.17/0.33 -c, -core generate unsat core of named formulas.
% 0.17/0.33 -st, -statistics display statistics.
% 0.17/0.33 -t:timeout set timeout (in second).
% 0.17/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.17/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.17/0.33 -<param>:<value> configuration parameter and value.
% 0.17/0.33 -o:<output-file> file to place output in.
% 0.17/0.37 % SZS status Theorem
% 0.17/0.37 % SZS output start Proof
% 0.17/0.37 tff(is_a_theorem_type, type, (
% 0.17/0.37 is_a_theorem: $i > $o)).
% 0.17/0.37 tff(implies_type, type, (
% 0.17/0.37 implies: ( $i * $i ) > $i)).
% 0.17/0.37 tff(and_type, type, (
% 0.17/0.37 and: ( $i * $i ) > $i)).
% 0.17/0.37 tff(kn2_type, type, (
% 0.17/0.37 kn2: $o)).
% 0.17/0.37 tff(tptp_fun_X_3_type, type, (
% 0.17/0.37 tptp_fun_X_3: $i)).
% 0.17/0.37 tff(tptp_fun_Y_2_type, type, (
% 0.17/0.37 tptp_fun_Y_2: $i)).
% 0.17/0.37 tff(and_1_type, type, (
% 0.17/0.37 and_1: $o)).
% 0.17/0.37 tff(1,plain,
% 0.17/0.37 (^[P: $i, Q: $i] : refl(is_a_theorem(implies(and(P, Q), P)) <=> is_a_theorem(implies(and(P, Q), P)))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(2,plain,
% 0.17/0.37 (![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)) <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.37 tff(3,plain,
% 0.17/0.37 (![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P)) <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(4,plain,
% 0.17/0.37 (($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))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(5,axiom,(kn2), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax','rosser_kn2')).
% 0.17/0.37 tff(6,plain,
% 0.17/0.37 (kn2 <=> $true),
% 0.17/0.37 inference(iff_true,[status(thm)],[5])).
% 0.17/0.37 tff(7,plain,
% 0.17/0.37 ((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)))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[6])).
% 0.17/0.37 tff(8,plain,
% 0.17/0.37 ((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))),
% 0.17/0.37 inference(transitivity,[status(thm)],[7, 4])).
% 0.17/0.37 tff(9,plain,
% 0.17/0.37 ((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)))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(10,axiom,(kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','kn2')).
% 0.17/0.37 tff(11,plain,
% 0.17/0.37 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.17/0.37 tff(12,plain,
% 0.17/0.37 (kn2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[11, 9])).
% 0.17/0.37 tff(13,plain,
% 0.17/0.37 (![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.17/0.37 tff(14,plain,
% 0.17/0.37 (![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.17/0.37 tff(15,plain,(
% 0.17/0.37 ![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.37 inference(skolemize,[status(sab)],[14])).
% 0.17/0.37 tff(16,plain,
% 0.17/0.37 (![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.17/0.37 tff(17,plain,
% 0.17/0.37 ((~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(18,plain,
% 0.17/0.37 (($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(19,axiom,(~and_1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hilbert_and_1')).
% 0.17/0.37 tff(20,plain,
% 0.17/0.37 (and_1 <=> $false),
% 0.17/0.37 inference(iff_false,[status(thm)],[19])).
% 0.17/0.37 tff(21,plain,
% 0.17/0.37 ((and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))) <=> ($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X)))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[20])).
% 0.17/0.37 tff(22,plain,
% 0.17/0.37 ((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)))),
% 0.17/0.37 inference(transitivity,[status(thm)],[21, 18])).
% 0.17/0.37 tff(23,plain,
% 0.17/0.37 ((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)))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(24,axiom,(and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','and_1')).
% 0.17/0.37 tff(25,plain,
% 0.17/0.38 (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.17/0.38 tff(26,plain,
% 0.17/0.38 (and_1 <=> ![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.17/0.38 tff(27,plain,
% 0.17/0.38 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.17/0.38 tff(28,plain,
% 0.17/0.38 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.17/0.38 tff(29,plain,
% 0.17/0.38 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[28, 17])).
% 0.17/0.38 tff(30,plain,
% 0.17/0.38 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[29, 17])).
% 0.17/0.38 tff(31,plain,
% 0.17/0.38 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[30, 17])).
% 0.17/0.38 tff(32,plain,
% 0.17/0.38 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[31, 17])).
% 0.17/0.38 tff(33,plain,
% 0.17/0.38 (~![X: $i, Y: $i] : is_a_theorem(implies(and(X, Y), X))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[32, 17])).
% 0.17/0.38 tff(34,plain,(
% 0.17/0.38 ~is_a_theorem(implies(and(X!3, Y!2), X!3))),
% 0.17/0.38 inference(skolemize,[status(sab)],[33])).
% 0.17/0.38 tff(35,plain,
% 0.17/0.38 ((~![P: $i, Q: $i] : is_a_theorem(implies(and(P, Q), P))) | is_a_theorem(implies(and(X!3, Y!2), X!3))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(36,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[35, 34, 16])).
% 0.17/0.38 % SZS output end Proof
%------------------------------------------------------------------------------