TSTP Solution File: HWV020-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV020-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Sat Sep 17 02:10:39 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HWV020-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n026.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 22:17:22 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.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(n0_type, type, (
% 0.19/0.42 n0: $i)).
% 0.19/0.42 tff(int_level_type, type, (
% 0.19/0.42 int_level: $i > $i)).
% 0.19/0.42 tff(plus_type, type, (
% 0.19/0.42 plus: ( $i * $i ) > $i)).
% 0.19/0.42 tff(n1_type, type, (
% 0.19/0.42 n1: $i)).
% 0.19/0.42 tff(t_139_type, type, (
% 0.19/0.42 t_139: $i)).
% 0.19/0.42 tff(p_Empty_type, type, (
% 0.19/0.42 p_Empty: $i > $o)).
% 0.19/0.42 tff(gt_type, type, (
% 0.19/0.42 gt: ( $i * $i ) > $o)).
% 0.19/0.42 tff(p_Reset_type, type, (
% 0.19/0.42 p_Reset: $i > $o)).
% 0.19/0.42 tff(p_Wr_type, type, (
% 0.19/0.42 p_Wr: $i > $o)).
% 0.19/0.42 tff(p_Rd_type, type, (
% 0.19/0.42 p_Rd: $i > $o)).
% 0.19/0.42 tff(p_Rd_error_type, type, (
% 0.19/0.42 p_Rd_error: $i > $o)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 (p_Empty(t_139) <=> p_Empty(t_139)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(2,axiom,(p_Empty(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_2')).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (p_Empty(t_139)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(7,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')).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.42 tff(9,plain,(
% 0.19/0.42 ![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[8])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (((~![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)))) | (int_level(t_139) = n0) | (~p_Empty(t_139)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | ((int_level(t_139) = n0) | (~p_Empty(t_139)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | (int_level(t_139) = n0) | (~p_Empty(t_139))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (int_level(t_139) = n0),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (n0 = int_level(t_139)),
% 0.19/0.42 inference(symmetry,[status(thm)],[14])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (gt(n0, n0) <=> gt(int_level(t_139), n0)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 (gt(int_level(t_139), n0) <=> gt(n0, n0)),
% 0.19/0.42 inference(symmetry,[status(thm)],[16])).
% 0.19/0.42 tff(18,assumption,(gt(int_level(t_139), n0)), introduced(assumption)).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 (gt(n0, n0)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 (^[X_28: $i] : refl((~gt(X_28, X_28)) <=> (~gt(X_28, X_28)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 (![X_28: $i] : (~gt(X_28, X_28)) <=> ![X_28: $i] : (~gt(X_28, X_28))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (![X_28: $i] : (~gt(X_28, X_28)) <=> ![X_28: $i] : (~gt(X_28, X_28))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(23,axiom,(![X_28: $i] : (~gt(X_28, X_28))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_17')).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 (![X_28: $i] : (~gt(X_28, X_28))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.42 tff(25,plain,(
% 0.19/0.42 ![X_28: $i] : (~gt(X_28, X_28))),
% 0.19/0.42 inference(skolemize,[status(sab)],[24])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (![X_28: $i] : (~gt(X_28, X_28))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 ((~![X_28: $i] : (~gt(X_28, X_28))) | (~gt(n0, n0))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (~gt(n0, n0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[28, 19])).
% 0.19/0.42 tff(30,plain,(~gt(int_level(t_139), n0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 ((~p_Reset(t_139)) <=> (~p_Reset(t_139))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(32,axiom,(~p_Reset(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_4')).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (~p_Reset(t_139)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 ((~p_Wr(t_139)) <=> (~p_Wr(t_139))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(35,axiom,(~p_Wr(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_3')).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (~p_Wr(t_139)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (p_Rd(t_139) <=> p_Rd(t_139)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(38,axiom,(p_Rd(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_1')).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (p_Rd(t_139)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (^[X_t_42: $i] : refl((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0)) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0)) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0)) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (^[X_t_42: $i] : trans(monotonicity(trans(monotonicity(rewrite(((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42))), ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) <=> ((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42)) | gt(int_level(X_t_42), n0)))), rewrite(((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42)) | gt(int_level(X_t_42), n0)) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))), ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)))), (((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42))) <=> ((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42))))), rewrite(((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))), (((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (![X_t_42: $i] : ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.42 tff(45,axiom,(![X_t_42: $i] : ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_78')).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.42 tff(48,plain,(
% 0.19/0.42 ![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(skolemize,[status(sab)],[47])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))) | (p_Wr(t_139) | p_Reset(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))) | p_Wr(t_139) | p_Reset(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 ((p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)) <=> (p_Wr(t_139) | p_Reset(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))) | (p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))) | (p_Wr(t_139) | p_Reset(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))) | (p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))) | p_Wr(t_139) | p_Reset(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))),
% 0.19/0.42 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))) | (p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))) | p_Wr(t_139) | p_Reset(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 ((int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[55, 49, 39, 36, 33])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (int_level(plus(t_139, n1)) = int_level(t_139)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[56, 30])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (int_level(plus(t_139, n1)) = n0),
% 0.19/0.42 inference(transitivity,[status(thm)],[57, 14])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (^[X_t_42: $i] : refl((p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)) <=> (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (^[X_t_42: $i] : trans(monotonicity(trans(monotonicity(rewrite(((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42))), ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) <=> ((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42)) | gt(int_level(X_t_42), n0)))), rewrite(((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42)) | gt(int_level(X_t_42), n0)) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))), ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)))), (((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) | p_Rd_error(plus(X_t_42, n1))) <=> ((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)) | p_Rd_error(plus(X_t_42, n1))))), rewrite(((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)) | p_Rd_error(plus(X_t_42, n1))) <=> (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))), (((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) | p_Rd_error(plus(X_t_42, n1))) <=> (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (![X_t_42: $i] : ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) | p_Rd_error(plus(X_t_42, n1))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.42 tff(64,axiom,(![X_t_42: $i] : ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) | p_Rd_error(plus(X_t_42, n1)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_76')).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.19/0.42 tff(67,plain,(
% 0.19/0.42 ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(skolemize,[status(sab)],[66])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | (p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 ((p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | p_Wr(t_139) | gt(int_level(t_139), n0)) <=> (p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | (p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | p_Wr(t_139) | gt(int_level(t_139), n0))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | (p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[70])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | (p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | p_Wr(t_139) | gt(int_level(t_139), n0))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0))),
% 0.19/0.43 inference(transitivity,[status(thm)],[71, 69])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | (p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | p_Wr(t_139) | gt(int_level(t_139), n0))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (p_Rd_error(plus(t_139, n1)) | gt(int_level(t_139), n0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[74, 68, 39, 36, 33])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (p_Rd_error(plus(t_139, n1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[75, 30])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (((~p_Empty(plus(t_139, n1))) | (~p_Rd_error(plus(t_139, n1)))) <=> ((~p_Empty(plus(t_139, n1))) | (~p_Rd_error(plus(t_139, n1))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(78,axiom,((~p_Empty(plus(t_139, n1))) | (~p_Rd_error(plus(t_139, n1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_5')).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 ((~p_Empty(plus(t_139, n1))) | (~p_Rd_error(plus(t_139, n1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 (~p_Empty(plus(t_139, n1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[79, 76])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.43 tff(86,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')).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.43 tff(89,plain,(
% 0.19/0.43 ![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[88])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | (p_Empty(plus(t_139, n1)) | (~(int_level(plus(t_139, n1)) = n0)))) <=> ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | p_Empty(plus(t_139, n1)) | (~(int_level(plus(t_139, n1)) = n0)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | (p_Empty(plus(t_139, n1)) | (~(int_level(plus(t_139, n1)) = n0)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | p_Empty(plus(t_139, n1)) | (~(int_level(plus(t_139, n1)) = n0))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[93, 90, 80, 58])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------