TSTP Solution File: LCL491+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LCL491+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n026.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 04:56:29 EDT 2022

% Result   : Theorem 0.19s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : LCL491+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Sep  1 22:05:37 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.19/0.39  % SZS status Theorem
% 0.19/0.39  % SZS output start Proof
% 0.19/0.39  tff(is_a_theorem_type, type, (
% 0.19/0.39     is_a_theorem: $i > $o)).
% 0.19/0.39  tff(implies_type, type, (
% 0.19/0.39     implies: ( $i * $i ) > $i)).
% 0.19/0.39  tff(or_type, type, (
% 0.19/0.39     or: ( $i * $i ) > $i)).
% 0.19/0.39  tff(r2_type, type, (
% 0.19/0.39     r2: $o)).
% 0.19/0.39  tff(tptp_fun_Y_0_type, type, (
% 0.19/0.39     tptp_fun_Y_0: $i)).
% 0.19/0.39  tff(tptp_fun_X_1_type, type, (
% 0.19/0.39     tptp_fun_X_1: $i)).
% 0.19/0.39  tff(or_2_type, type, (
% 0.19/0.39     or_2: $o)).
% 0.19/0.39  tff(1,plain,
% 0.19/0.39      (^[P: $i, Q: $i] : refl(is_a_theorem(implies(Q, or(P, Q))) <=> is_a_theorem(implies(Q, or(P, Q))))),
% 0.19/0.39      inference(bind,[status(th)],[])).
% 0.19/0.39  tff(2,plain,
% 0.19/0.39      (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.19/0.39      inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39  tff(3,plain,
% 0.19/0.39      (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(4,plain,
% 0.19/0.39      (($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(5,axiom,(r2), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax','principia_r2')).
% 0.19/0.39  tff(6,plain,
% 0.19/0.39      (r2 <=> $true),
% 0.19/0.39      inference(iff_true,[status(thm)],[5])).
% 0.19/0.39  tff(7,plain,
% 0.19/0.39      ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ($true <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 0.19/0.39      inference(monotonicity,[status(thm)],[6])).
% 0.19/0.39  tff(8,plain,
% 0.19/0.39      ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.19/0.39      inference(transitivity,[status(thm)],[7, 4])).
% 0.19/0.39  tff(9,plain,
% 0.19/0.39      ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(10,axiom,(r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','r2')).
% 0.19/0.39  tff(11,plain,
% 0.19/0.39      (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.39  tff(12,plain,
% 0.19/0.39      (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[11, 9])).
% 0.19/0.39  tff(13,plain,
% 0.19/0.39      (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.39  tff(14,plain,
% 0.19/0.39      (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[13, 3])).
% 0.19/0.39  tff(15,plain,(
% 0.19/0.39      ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.19/0.39      inference(skolemize,[status(sab)],[14])).
% 0.19/0.39  tff(16,plain,
% 0.19/0.39      (![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[15, 2])).
% 0.19/0.39  tff(17,plain,
% 0.19/0.39      ((~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(18,plain,
% 0.19/0.39      (($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(19,axiom,(~or_2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hilbert_or_2')).
% 0.19/0.39  tff(20,plain,
% 0.19/0.39      (or_2 <=> $false),
% 0.19/0.39      inference(iff_false,[status(thm)],[19])).
% 0.19/0.39  tff(21,plain,
% 0.19/0.39      ((or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> ($false <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 0.19/0.39      inference(monotonicity,[status(thm)],[20])).
% 0.19/0.39  tff(22,plain,
% 0.19/0.39      ((or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> (~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 0.19/0.39      inference(transitivity,[status(thm)],[21, 18])).
% 0.19/0.39  tff(23,plain,
% 0.19/0.39      ((or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(24,axiom,(or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','or_2')).
% 0.19/0.39  tff(25,plain,
% 0.19/0.39      (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.40  tff(26,plain,
% 0.19/0.40      (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[25, 23])).
% 0.19/0.40  tff(27,plain,
% 0.19/0.40      (~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.40  tff(28,plain,
% 0.19/0.40      (~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[27, 17])).
% 0.19/0.40  tff(29,plain,
% 0.19/0.40      (~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[28, 17])).
% 0.19/0.40  tff(30,plain,
% 0.19/0.40      (~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[29, 17])).
% 0.19/0.40  tff(31,plain,
% 0.19/0.40      (~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[30, 17])).
% 0.19/0.40  tff(32,plain,
% 0.19/0.40      (~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[31, 17])).
% 0.19/0.40  tff(33,plain,
% 0.19/0.40      (~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.19/0.40      inference(modus_ponens,[status(thm)],[32, 17])).
% 0.19/0.40  tff(34,plain,(
% 0.19/0.40      ~is_a_theorem(implies(Y!0, or(X!1, Y!0)))),
% 0.19/0.40      inference(skolemize,[status(sab)],[33])).
% 0.19/0.40  tff(35,plain,
% 0.19/0.40      ((~![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) | is_a_theorem(implies(Y!0, or(X!1, Y!0)))),
% 0.19/0.40      inference(quant_inst,[status(thm)],[])).
% 0.19/0.40  tff(36,plain,
% 0.19/0.40      ($false),
% 0.19/0.40      inference(unit_resolution,[status(thm)],[35, 34, 16])).
% 0.19/0.40  % SZS output end Proof
%------------------------------------------------------------------------------