TSTP Solution File: HWV010-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : HWV010-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n004.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 : Sat Sep 17 02:10:32 EDT 2022

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : HWV010-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n004.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 : Wed Aug 31 21:56:49 EDT 2022
% 0.13/0.33  % 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.
% 0.20/0.42  % SZS status Unsatisfiable
% 0.20/0.42  % SZS output start Proof
% 0.20/0.42  tff(n0_type, type, (
% 0.20/0.42     n0: $i)).
% 0.20/0.42  tff(int_level_type, type, (
% 0.20/0.42     int_level: $i > $i)).
% 0.20/0.42  tff(t_139_type, type, (
% 0.20/0.42     t_139: $i)).
% 0.20/0.42  tff(level_type, type, (
% 0.20/0.42     level: $i > $i)).
% 0.20/0.42  tff(p_Empty_type, type, (
% 0.20/0.42     p_Empty: $i > $o)).
% 0.20/0.42  tff(1,assumption,(~(level(t_139) = n0)), introduced(assumption)).
% 0.20/0.42  tff(2,plain,
% 0.20/0.42      ((p_Empty(t_139) | (level(t_139) = n0)) <=> (p_Empty(t_139) | (level(t_139) = n0))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(3,axiom,(p_Empty(t_139) | (level(t_139) = n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_2')).
% 0.20/0.42  tff(4,plain,
% 0.20/0.42      (p_Empty(t_139) | (level(t_139) = n0)),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.42  tff(5,plain,
% 0.20/0.42      (p_Empty(t_139)),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[4, 1])).
% 0.20/0.42  tff(6,plain,
% 0.20/0.42      (^[X_t_36: $i] : refl(((int_level(X_t_36) = n0) | (~p_Empty(X_t_36))) <=> ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(7,plain,
% 0.20/0.42      (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36))) <=> ![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[6])).
% 0.20/0.42  tff(8,plain,
% 0.20/0.42      (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36))) <=> ![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(9,axiom,(![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_25')).
% 0.20/0.42  tff(10,plain,
% 0.20/0.42      (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.42  tff(11,plain,(
% 0.20/0.42      ![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.20/0.42      inference(skolemize,[status(sab)],[10])).
% 0.20/0.42  tff(12,plain,
% 0.20/0.42      (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.42  tff(13,plain,
% 0.20/0.42      (((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | ((~p_Empty(t_139)) | (int_level(t_139) = n0))) <=> ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | (~p_Empty(t_139)) | (int_level(t_139) = n0))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(14,plain,
% 0.20/0.42      (((int_level(t_139) = n0) | (~p_Empty(t_139))) <=> ((~p_Empty(t_139)) | (int_level(t_139) = n0))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(15,plain,
% 0.20/0.42      (((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | ((int_level(t_139) = n0) | (~p_Empty(t_139)))) <=> ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | ((~p_Empty(t_139)) | (int_level(t_139) = n0)))),
% 0.20/0.42      inference(monotonicity,[status(thm)],[14])).
% 0.20/0.42  tff(16,plain,
% 0.20/0.42      (((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | ((int_level(t_139) = n0) | (~p_Empty(t_139)))) <=> ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | (~p_Empty(t_139)) | (int_level(t_139) = n0))),
% 0.20/0.42      inference(transitivity,[status(thm)],[15, 13])).
% 0.20/0.42  tff(17,plain,
% 0.20/0.42      ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | ((int_level(t_139) = n0) | (~p_Empty(t_139)))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(18,plain,
% 0.20/0.42      ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | (~p_Empty(t_139)) | (int_level(t_139) = n0)),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.42  tff(19,plain,
% 0.20/0.42      (int_level(t_139) = n0),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[18, 12, 5])).
% 0.20/0.42  tff(20,plain,
% 0.20/0.42      (^[X_t_32: $i] : refl((level(X_t_32) = int_level(X_t_32)) <=> (level(X_t_32) = int_level(X_t_32)))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(21,plain,
% 0.20/0.42      (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32)) <=> ![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[20])).
% 0.20/0.42  tff(22,plain,
% 0.20/0.42      (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32)) <=> ![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(23,axiom,(![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_21')).
% 0.20/0.42  tff(24,plain,
% 0.20/0.42      (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.42  tff(25,plain,(
% 0.20/0.42      ![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.42      inference(skolemize,[status(sab)],[24])).
% 0.20/0.42  tff(26,plain,
% 0.20/0.42      (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.42  tff(27,plain,
% 0.20/0.42      ((~![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))) | (level(t_139) = int_level(t_139))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(28,plain,
% 0.20/0.42      (level(t_139) = int_level(t_139)),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.42  tff(29,plain,
% 0.20/0.42      (level(t_139) = n0),
% 0.20/0.42      inference(transitivity,[status(thm)],[28, 19])).
% 0.20/0.42  tff(30,plain,
% 0.20/0.42      ($false),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[1, 29])).
% 0.20/0.42  tff(31,plain,(level(t_139) = n0), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42  tff(32,plain,
% 0.20/0.42      (int_level(t_139) = level(t_139)),
% 0.20/0.42      inference(symmetry,[status(thm)],[28])).
% 0.20/0.42  tff(33,plain,
% 0.20/0.42      (int_level(t_139) = n0),
% 0.20/0.42      inference(transitivity,[status(thm)],[32, 31])).
% 0.20/0.42  tff(34,plain,
% 0.20/0.42      (((~p_Empty(t_139)) | (~(level(t_139) = n0))) <=> ((~p_Empty(t_139)) | (~(level(t_139) = n0)))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(35,axiom,((~p_Empty(t_139)) | (~(level(t_139) = n0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_1')).
% 0.20/0.42  tff(36,plain,
% 0.20/0.42      ((~p_Empty(t_139)) | (~(level(t_139) = n0))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.42  tff(37,plain,
% 0.20/0.42      (~p_Empty(t_139)),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[36, 31])).
% 0.20/0.42  tff(38,plain,
% 0.20/0.42      (^[X_t_35: $i] : refl((p_Empty(X_t_35) | (~(int_level(X_t_35) = n0))) <=> (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(39,plain,
% 0.20/0.42      (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0))) <=> ![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[38])).
% 0.20/0.42  tff(40,plain,
% 0.20/0.42      (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0))) <=> ![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(41,plain,
% 0.20/0.42      (^[X_t_35: $i] : rewrite(((~(int_level(X_t_35) = n0)) | p_Empty(X_t_35)) <=> (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0))))),
% 0.20/0.42      inference(bind,[status(th)],[])).
% 0.20/0.42  tff(42,plain,
% 0.20/0.42      (![X_t_35: $i] : ((~(int_level(X_t_35) = n0)) | p_Empty(X_t_35)) <=> ![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.42      inference(quant_intro,[status(thm)],[41])).
% 0.20/0.42  tff(43,axiom,(![X_t_35: $i] : ((~(int_level(X_t_35) = n0)) | p_Empty(X_t_35))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_24')).
% 0.20/0.42  tff(44,plain,
% 0.20/0.42      (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.42  tff(45,plain,
% 0.20/0.42      (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.42  tff(46,plain,(
% 0.20/0.42      ![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.42      inference(skolemize,[status(sab)],[45])).
% 0.20/0.42  tff(47,plain,
% 0.20/0.42      (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[46, 39])).
% 0.20/0.42  tff(48,plain,
% 0.20/0.42      (((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | (p_Empty(t_139) | (~(int_level(t_139) = n0)))) <=> ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | p_Empty(t_139) | (~(int_level(t_139) = n0)))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(49,plain,
% 0.20/0.42      ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | (p_Empty(t_139) | (~(int_level(t_139) = n0)))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(50,plain,
% 0.20/0.42      ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | p_Empty(t_139) | (~(int_level(t_139) = n0))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.42  tff(51,plain,
% 0.20/0.42      (~(int_level(t_139) = n0)),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[50, 47, 37])).
% 0.20/0.42  tff(52,plain,
% 0.20/0.42      ($false),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[51, 33])).
% 0.20/0.42  % SZS output end Proof
%------------------------------------------------------------------------------