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
%------------------------------------------------------------------------------