TSTP Solution File: HWV022-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV022-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 02:10:40 EDT 2022
% Result : Unsatisfiable 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HWV022-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.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 : Wed Aug 31 22:13:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.51 % SZS status Unsatisfiable
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 tff(gt_type, type, (
% 0.20/0.51 gt: ( $i * $i ) > $o)).
% 0.20/0.51 tff(plus_type, type, (
% 0.20/0.51 plus: ( $i * $i ) > $i)).
% 0.20/0.51 tff(n1_type, type, (
% 0.20/0.51 n1: $i)).
% 0.20/0.51 tff(n0_type, type, (
% 0.20/0.51 n0: $i)).
% 0.20/0.51 tff(level_type, type, (
% 0.20/0.51 level: $i > $i)).
% 0.20/0.51 tff(t_139_type, type, (
% 0.20/0.51 t_139: $i)).
% 0.20/0.51 tff(def_10_type, type, (
% 0.20/0.51 def_10: ( $i * $i ) > $o)).
% 0.20/0.51 tff(minus_type, type, (
% 0.20/0.51 minus: ( $i * $i ) > $i)).
% 0.20/0.51 tff(int_level_type, type, (
% 0.20/0.51 int_level: $i > $i)).
% 0.20/0.51 tff(fifo_length_type, type, (
% 0.20/0.51 fifo_length: $i)).
% 0.20/0.51 tff(p_Reset_type, type, (
% 0.20/0.51 p_Reset: $i > $o)).
% 0.20/0.51 tff(p_Wr_type, type, (
% 0.20/0.51 p_Wr: $i > $o)).
% 0.20/0.51 tff(p_Rd_type, type, (
% 0.20/0.51 p_Rd: $i > $o)).
% 0.20/0.51 tff(1,assumption,(gt(plus(level(t_139), n1), plus(n0, n1))), introduced(assumption)).
% 0.20/0.51 tff(2,plain,
% 0.20/0.51 ((minus(plus(level(t_139), n1), n1) = level(t_139)) <=> (level(t_139) = minus(plus(level(t_139), n1), n1))),
% 0.20/0.51 inference(commutativity,[status(thm)],[])).
% 0.20/0.51 tff(3,plain,
% 0.20/0.51 ((n1 = plus(n0, n1)) <=> (n1 = plus(n0, n1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(4,axiom,(n1 = plus(n0, n1)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_20')).
% 0.20/0.51 tff(5,plain,
% 0.20/0.51 (n1 = plus(n0, n1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.51 tff(6,plain,
% 0.20/0.51 (plus(n0, n1) = n1),
% 0.20/0.51 inference(symmetry,[status(thm)],[5])).
% 0.20/0.51 tff(7,plain,
% 0.20/0.51 (minus(plus(level(t_139), n1), plus(n0, n1)) = minus(plus(level(t_139), n1), n1)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[6])).
% 0.20/0.51 tff(8,plain,
% 0.20/0.51 ((minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139)) <=> (minus(plus(level(t_139), n1), n1) = level(t_139))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[7])).
% 0.20/0.51 tff(9,plain,
% 0.20/0.51 ((minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139)) <=> (level(t_139) = minus(plus(level(t_139), n1), n1))),
% 0.20/0.51 inference(transitivity,[status(thm)],[8, 2])).
% 0.20/0.51 tff(10,plain,
% 0.20/0.51 ((~(minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139))) <=> (~(level(t_139) = minus(plus(level(t_139), n1), n1)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.51 tff(11,plain,
% 0.20/0.51 (^[X_t_32: $i] : refl((level(X_t_32) = int_level(X_t_32)) <=> (level(X_t_32) = int_level(X_t_32)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(12,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.51 tff(13,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(14,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')).
% 0.20/0.51 tff(15,plain,
% 0.20/0.51 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.51 tff(16,plain,(
% 0.20/0.51 ![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.51 inference(skolemize,[status(sab)],[15])).
% 0.20/0.51 tff(17,plain,
% 0.20/0.51 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.51 tff(18,plain,
% 0.20/0.51 ((~![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))) | (level(t_139) = int_level(t_139))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(19,plain,
% 0.20/0.51 (level(t_139) = int_level(t_139)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.51 tff(20,assumption,(minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139)), introduced(assumption)).
% 0.20/0.51 tff(21,plain,
% 0.20/0.51 (minus(plus(level(t_139), n1), n1) = minus(plus(level(t_139), n1), plus(n0, n1))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[5])).
% 0.20/0.51 tff(22,plain,
% 0.20/0.51 (minus(plus(level(t_139), n1), n1) = int_level(t_139)),
% 0.20/0.51 inference(transitivity,[status(thm)],[21, 20, 19])).
% 0.20/0.51 tff(23,plain,
% 0.20/0.51 (gt(plus(level(t_139), n1), minus(plus(level(t_139), n1), n1)) <=> gt(plus(level(t_139), n1), int_level(t_139))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.51 tff(24,plain,
% 0.20/0.51 (gt(plus(level(t_139), n1), int_level(t_139)) <=> gt(plus(level(t_139), n1), minus(plus(level(t_139), n1), n1))),
% 0.20/0.51 inference(symmetry,[status(thm)],[23])).
% 0.20/0.51 tff(25,plain,
% 0.20/0.51 ((~gt(plus(level(t_139), n1), int_level(t_139))) <=> (~gt(plus(level(t_139), n1), minus(plus(level(t_139), n1), n1)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[24])).
% 0.20/0.51 tff(26,plain,
% 0.20/0.51 (int_level(t_139) = level(t_139)),
% 0.20/0.51 inference(symmetry,[status(thm)],[19])).
% 0.20/0.51 tff(27,plain,
% 0.20/0.51 (plus(int_level(t_139), n1) = plus(level(t_139), n1)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.51 tff(28,plain,
% 0.20/0.51 ((~![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))) | (level(plus(t_139, n1)) = int_level(plus(t_139, n1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(29,plain,
% 0.20/0.51 (level(plus(t_139, n1)) = int_level(plus(t_139, n1))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[28, 17])).
% 0.20/0.51 tff(30,plain,
% 0.20/0.51 (int_level(plus(t_139, n1)) = level(plus(t_139, n1))),
% 0.20/0.51 inference(symmetry,[status(thm)],[29])).
% 0.20/0.51 tff(31,plain,
% 0.20/0.51 ((int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)) <=> (level(plus(t_139, n1)) = plus(level(t_139), n1))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[30, 27])).
% 0.20/0.51 tff(32,plain,
% 0.20/0.51 ((level(plus(t_139, n1)) = plus(level(t_139), n1)) <=> (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))),
% 0.20/0.51 inference(symmetry,[status(thm)],[31])).
% 0.20/0.51 tff(33,plain,
% 0.20/0.51 ((~(level(plus(t_139, n1)) = plus(level(t_139), n1))) <=> (~(int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.51 tff(34,plain,
% 0.20/0.51 ((~(level(plus(t_139, n1)) = fifo_length)) <=> (~(level(plus(t_139, n1)) = plus(level(t_139), n1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(35,plain,
% 0.20/0.51 ((~(level(plus(t_139, n1)) = fifo_length)) <=> (~(level(plus(t_139, n1)) = fifo_length))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(36,axiom,(~(level(plus(t_139, n1)) = fifo_length)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_5')).
% 0.20/0.51 tff(37,plain,
% 0.20/0.51 (~(level(plus(t_139, n1)) = fifo_length)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.51 tff(38,plain,
% 0.20/0.51 (~(level(plus(t_139, n1)) = plus(level(t_139), n1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.20/0.51 tff(39,plain,
% 0.20/0.51 (~(int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.20/0.51 tff(40,plain,
% 0.20/0.51 ((~p_Reset(t_139)) <=> (~p_Reset(t_139))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(41,axiom,(~p_Reset(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_4')).
% 0.20/0.51 tff(42,plain,
% 0.20/0.51 (~p_Reset(t_139)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.51 tff(43,plain,
% 0.20/0.51 (p_Wr(t_139) <=> p_Wr(t_139)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(44,axiom,(p_Wr(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_3')).
% 0.20/0.51 tff(45,plain,
% 0.20/0.51 (p_Wr(t_139)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.51 tff(46,plain,
% 0.20/0.51 ((~p_Rd(t_139)) <=> (~p_Rd(t_139))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(47,axiom,(~p_Rd(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_2')).
% 0.20/0.51 tff(48,plain,
% 0.20/0.51 (~p_Rd(t_139)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.51 tff(49,plain,
% 0.20/0.51 (^[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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), 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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(50,plain,
% 0.20/0.51 (![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), 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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.51 tff(51,plain,
% 0.20/0.51 (^[X_t_42: $i] : trans(monotonicity(rewrite((~gt(fifo_length, int_level(X_t_42))) <=> (~gt(plus(level(t_139), n1), int_level(X_t_42)))), ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1))))), rewrite((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))), ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(52,plain,
% 0.20/0.51 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1))) <=> ![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.51 tff(53,plain,
% 0.20/0.51 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(54,plain,
% 0.20/0.51 (^[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(fifo_length, int_level(X_t_42)))) <=> ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42))) | (~gt(fifo_length, int_level(X_t_42)))))), rewrite(((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42))) | (~gt(fifo_length, int_level(X_t_42)))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1))) <=> ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1))))), rewrite(((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(55,plain,
% 0.20/0.51 (![X_t_42: $i] : ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.51 tff(56,axiom,(![X_t_42: $i] : ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_35')).
% 0.20/0.51 tff(57,plain,
% 0.20/0.51 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.51 tff(58,plain,
% 0.20/0.51 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 (![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[58, 52])).
% 0.20/0.51 tff(60,plain,(
% 0.20/0.51 ![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[59])).
% 0.20/0.51 tff(61,plain,
% 0.20/0.51 (![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 (((~![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))) | (p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (~gt(plus(level(t_139), n1), int_level(t_139))) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)))) <=> ((~![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))) | p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (~gt(plus(level(t_139), n1), int_level(t_139))) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(63,plain,
% 0.20/0.51 ((p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)) | (~gt(plus(level(t_139), n1), int_level(t_139)))) <=> (p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (~gt(plus(level(t_139), n1), int_level(t_139))) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 (((~![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)) | (~gt(plus(level(t_139), n1), int_level(t_139))))) <=> ((~![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))) | (p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (~gt(plus(level(t_139), n1), int_level(t_139))) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[63])).
% 0.20/0.51 tff(65,plain,
% 0.20/0.51 (((~![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)) | (~gt(plus(level(t_139), n1), int_level(t_139))))) <=> ((~![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))) | p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (~gt(plus(level(t_139), n1), int_level(t_139))) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[64, 62])).
% 0.20/0.51 tff(66,plain,
% 0.20/0.51 ((~![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)) | (~gt(plus(level(t_139), n1), int_level(t_139))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(67,plain,
% 0.20/0.51 ((~![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)) = plus(int_level(X_t_42), n1)) | (~gt(plus(level(t_139), n1), int_level(X_t_42))))) | p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (~gt(plus(level(t_139), n1), int_level(t_139))) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.51 tff(68,plain,
% 0.20/0.51 ((~gt(plus(level(t_139), n1), int_level(t_139))) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[67, 61, 48, 45, 42])).
% 0.20/0.51 tff(69,plain,
% 0.20/0.51 (~gt(plus(level(t_139), n1), int_level(t_139))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[68, 39])).
% 0.20/0.51 tff(70,plain,
% 0.20/0.51 (~gt(plus(level(t_139), n1), minus(plus(level(t_139), n1), n1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[69, 25])).
% 0.20/0.51 tff(71,plain,
% 0.20/0.51 (^[X_1: $i] : refl(gt(plus(X_1, n1), n0) <=> gt(plus(X_1, n1), n0))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(72,plain,
% 0.20/0.51 (![X_1: $i] : gt(plus(X_1, n1), n0) <=> ![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.51 tff(73,plain,
% 0.20/0.51 (![X_1: $i] : gt(plus(X_1, n1), n0) <=> ![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(74,axiom,(![X_1: $i] : gt(plus(X_1, n1), n0)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_2')).
% 0.20/0.51 tff(75,plain,
% 0.20/0.51 (![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.51 tff(76,plain,(
% 0.20/0.51 ![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.20/0.51 inference(skolemize,[status(sab)],[75])).
% 0.20/0.51 tff(77,plain,
% 0.20/0.51 (![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.20/0.51 tff(78,plain,
% 0.20/0.51 ((~![X_1: $i] : gt(plus(X_1, n1), n0)) | gt(plus(level(t_139), n1), n0)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 (gt(plus(level(t_139), n1), n0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.51 tff(80,plain,
% 0.20/0.51 (^[X_2: $i] : refl(((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1))) <=> ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(81,plain,
% 0.20/0.51 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1))) <=> ![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.51 tff(82,plain,
% 0.20/0.51 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1))) <=> ![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(83,axiom,(![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_3')).
% 0.20/0.51 tff(84,plain,
% 0.20/0.51 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.51 tff(85,plain,(
% 0.20/0.51 ![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[84])).
% 0.20/0.51 tff(86,plain,
% 0.20/0.51 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.20/0.51 tff(87,plain,
% 0.20/0.51 (((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))) | ((~gt(plus(level(t_139), n1), n0)) | gt(plus(level(t_139), n1), minus(plus(level(t_139), n1), n1)))) <=> ((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))) | (~gt(plus(level(t_139), n1), n0)) | gt(plus(level(t_139), n1), minus(plus(level(t_139), n1), n1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(88,plain,
% 0.20/0.51 ((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))) | ((~gt(plus(level(t_139), n1), n0)) | gt(plus(level(t_139), n1), minus(plus(level(t_139), n1), n1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(89,plain,
% 0.20/0.51 ((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))) | (~gt(plus(level(t_139), n1), n0)) | gt(plus(level(t_139), n1), minus(plus(level(t_139), n1), n1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.52 tff(90,plain,
% 0.20/0.52 (gt(plus(level(t_139), n1), minus(plus(level(t_139), n1), n1))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[89, 86, 79])).
% 0.20/0.52 tff(91,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[90, 70])).
% 0.20/0.52 tff(92,plain,(~(minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(93,plain,
% 0.20/0.52 (~(level(t_139) = minus(plus(level(t_139), n1), n1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[92, 10])).
% 0.20/0.52 tff(94,plain,
% 0.20/0.52 (plus(level(t_139), plus(n0, n1)) = plus(level(t_139), n1)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[6])).
% 0.20/0.52 tff(95,assumption,(~def_10(plus(n0, n1), plus(level(t_139), n1))), introduced(assumption)).
% 0.20/0.52 tff(96,plain,
% 0.20/0.52 ((level(t_139) = minus(plus(level(t_139), n1), n1)) <=> (minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139))),
% 0.20/0.52 inference(symmetry,[status(thm)],[9])).
% 0.20/0.52 tff(97,plain,
% 0.20/0.52 ((~(level(t_139) = minus(plus(level(t_139), n1), n1))) <=> (~(minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.52 tff(98,assumption,(~(level(t_139) = minus(plus(level(t_139), n1), n1))), introduced(assumption)).
% 0.20/0.52 tff(99,plain,
% 0.20/0.52 (~(minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.52 tff(100,plain,
% 0.20/0.52 (^[Y_4: $i, Z_5: $i, X_3: $i] : refl((def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) <=> (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(101,plain,
% 0.20/0.52 (![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) <=> ![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.52 tff(102,plain,
% 0.20/0.52 (![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) <=> ![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(103,plain,
% 0.20/0.52 (^[Y_4: $i, Z_5: $i, X_3: $i] : trans(monotonicity(rewrite(((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) <=> ((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))), ((((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3)) <=> (((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3)))), rewrite((((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3)) <=> (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))), ((((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3)) <=> (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(104,plain,
% 0.20/0.52 (![Y_4: $i, Z_5: $i, X_3: $i] : (((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3)) <=> ![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.52 tff(105,axiom,(![Y_4: $i, Z_5: $i, X_3: $i] : (((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_5')).
% 0.20/0.52 tff(106,plain,
% 0.20/0.52 (![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.52 tff(107,plain,
% 0.20/0.52 (![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.52 tff(108,plain,(
% 0.20/0.52 ![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[107])).
% 0.20/0.52 tff(109,plain,
% 0.20/0.52 (![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.52 tff(110,plain,
% 0.20/0.52 (((~![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))) | (def_10(plus(n0, n1), plus(level(t_139), n1)) | (minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139)) | (~(plus(level(t_139), plus(n0, n1)) = plus(level(t_139), n1))))) <=> ((~![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))) | def_10(plus(n0, n1), plus(level(t_139), n1)) | (minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139)) | (~(plus(level(t_139), plus(n0, n1)) = plus(level(t_139), n1))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(111,plain,
% 0.20/0.52 ((~![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))) | (def_10(plus(n0, n1), plus(level(t_139), n1)) | (minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139)) | (~(plus(level(t_139), plus(n0, n1)) = plus(level(t_139), n1))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(112,plain,
% 0.20/0.52 ((~![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))) | def_10(plus(n0, n1), plus(level(t_139), n1)) | (minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139)) | (~(plus(level(t_139), plus(n0, n1)) = plus(level(t_139), n1)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.52 tff(113,plain,
% 0.20/0.52 (def_10(plus(n0, n1), plus(level(t_139), n1)) | (minus(plus(level(t_139), n1), plus(n0, n1)) = level(t_139)) | (~(plus(level(t_139), plus(n0, n1)) = plus(level(t_139), n1)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[112, 109])).
% 0.20/0.52 tff(114,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[113, 99, 95, 94])).
% 0.20/0.52 tff(115,plain,(def_10(plus(n0, n1), plus(level(t_139), n1)) | (level(t_139) = minus(plus(level(t_139), n1), n1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(116,plain,
% 0.20/0.52 (def_10(plus(n0, n1), plus(level(t_139), n1))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[115, 93])).
% 0.20/0.52 tff(117,plain,
% 0.20/0.52 (^[Y_4: $i, X_3: $i] : refl(((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4))) <=> ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(118,plain,
% 0.20/0.52 (![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4))) <=> ![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.52 tff(119,plain,
% 0.20/0.52 (![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4))) <=> ![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(120,axiom,(![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_6')).
% 0.20/0.52 tff(121,plain,
% 0.20/0.52 (![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.52 tff(122,plain,(
% 0.20/0.52 ![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[121])).
% 0.20/0.52 tff(123,plain,
% 0.20/0.52 (![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.20/0.52 tff(124,plain,
% 0.20/0.52 (((~![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))) | ((~def_10(plus(n0, n1), plus(level(t_139), n1))) | (~gt(plus(level(t_139), n1), plus(n0, n1))))) <=> ((~![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))) | (~def_10(plus(n0, n1), plus(level(t_139), n1))) | (~gt(plus(level(t_139), n1), plus(n0, n1))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(125,plain,
% 0.20/0.52 ((~![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))) | ((~def_10(plus(n0, n1), plus(level(t_139), n1))) | (~gt(plus(level(t_139), n1), plus(n0, n1))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(126,plain,
% 0.20/0.52 ((~![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))) | (~def_10(plus(n0, n1), plus(level(t_139), n1))) | (~gt(plus(level(t_139), n1), plus(n0, n1)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.52 tff(127,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[126, 123, 116, 1])).
% 0.20/0.52 tff(128,plain,(~gt(plus(level(t_139), n1), plus(n0, n1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(129,plain,
% 0.20/0.52 (gt(plus(level(t_139), n1), level(t_139)) <=> gt(plus(level(t_139), n1), int_level(t_139))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.52 tff(130,plain,
% 0.20/0.52 (gt(plus(level(t_139), n1), int_level(t_139)) <=> gt(plus(level(t_139), n1), level(t_139))),
% 0.20/0.52 inference(symmetry,[status(thm)],[129])).
% 0.20/0.52 tff(131,plain,
% 0.20/0.52 ((~gt(plus(level(t_139), n1), int_level(t_139))) <=> (~gt(plus(level(t_139), n1), level(t_139)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.52 tff(132,plain,
% 0.20/0.52 (~gt(plus(level(t_139), n1), level(t_139))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[69, 131])).
% 0.20/0.52 tff(133,plain,
% 0.20/0.52 ((level(t_139) = plus(level(t_139), n1)) <=> (int_level(t_139) = plus(level(t_139), n1))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.52 tff(134,plain,
% 0.20/0.52 ((int_level(t_139) = plus(level(t_139), n1)) <=> (level(t_139) = plus(level(t_139), n1))),
% 0.20/0.52 inference(symmetry,[status(thm)],[133])).
% 0.20/0.52 tff(135,plain,
% 0.20/0.52 ((~(int_level(t_139) = plus(level(t_139), n1))) <=> (~(level(t_139) = plus(level(t_139), n1)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.52 tff(136,plain,
% 0.20/0.52 (^[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(plus(level(t_139), 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(plus(level(t_139), n1), int_level(X_t_42))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(137,plain,
% 0.20/0.52 (![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(plus(level(t_139), 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(plus(level(t_139), n1), int_level(X_t_42)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.52 tff(138,plain,
% 0.20/0.52 (^[X_t_42: $i] : trans(monotonicity(rewrite(gt(fifo_length, int_level(X_t_42)) <=> gt(plus(level(t_139), n1), int_level(X_t_42))), ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (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(plus(level(t_139), n1), int_level(X_t_42)) | (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(plus(level(t_139), n1), int_level(X_t_42)) | (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(plus(level(t_139), n1), int_level(X_t_42)))), ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (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(plus(level(t_139), n1), int_level(X_t_42)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(139,plain,
% 0.20/0.52 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (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(plus(level(t_139), n1), int_level(X_t_42)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.52 tff(140,plain,
% 0.20/0.52 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (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)) | gt(fifo_length, int_level(X_t_42)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(141,plain,
% 0.20/0.52 (^[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(fifo_length, int_level(X_t_42))) <=> ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42))) | gt(fifo_length, int_level(X_t_42))))), rewrite(((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42))) | gt(fifo_length, int_level(X_t_42))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | gt(fifo_length, int_level(X_t_42))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42))))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | gt(fifo_length, int_level(X_t_42))) | (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(fifo_length, int_level(X_t_42))) | (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(fifo_length, int_level(X_t_42))) | (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(fifo_length, int_level(X_t_42)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | gt(fifo_length, int_level(X_t_42))) | (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(fifo_length, int_level(X_t_42)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(142,plain,
% 0.20/0.52 (![X_t_42: $i] : ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | gt(fifo_length, int_level(X_t_42))) | (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)) | gt(fifo_length, int_level(X_t_42)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.52 tff(143,axiom,(![X_t_42: $i] : ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_44')).
% 0.20/0.52 tff(144,plain,
% 0.20/0.52 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.20/0.52 tff(146,plain,
% 0.20/0.52 (![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(plus(level(t_139), n1), int_level(X_t_42)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[145, 139])).
% 0.20/0.52 tff(147,plain,(
% 0.20/0.52 ![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(plus(level(t_139), n1), int_level(X_t_42)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[146])).
% 0.20/0.52 tff(148,plain,
% 0.20/0.52 (![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(plus(level(t_139), n1), int_level(X_t_42)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[147, 137])).
% 0.20/0.52 tff(149,plain,
% 0.20/0.52 (((~![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(plus(level(t_139), n1), int_level(X_t_42)))) | (p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(plus(level(t_139), n1), int_level(t_139)))) <=> ((~![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(plus(level(t_139), n1), int_level(X_t_42)))) | p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(plus(level(t_139), n1), int_level(t_139)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(150,plain,
% 0.20/0.52 ((p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(plus(level(t_139), n1), int_level(t_139))) <=> (p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(plus(level(t_139), n1), int_level(t_139)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(151,plain,
% 0.20/0.52 (((~![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(plus(level(t_139), n1), int_level(X_t_42)))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(plus(level(t_139), n1), int_level(t_139)))) <=> ((~![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(plus(level(t_139), n1), int_level(X_t_42)))) | (p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(plus(level(t_139), n1), int_level(t_139))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.52 tff(152,plain,
% 0.20/0.52 (((~![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(plus(level(t_139), n1), int_level(X_t_42)))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(plus(level(t_139), n1), int_level(t_139)))) <=> ((~![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(plus(level(t_139), n1), int_level(X_t_42)))) | p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(plus(level(t_139), n1), int_level(t_139)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[151, 149])).
% 0.20/0.52 tff(153,plain,
% 0.20/0.52 ((~![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(plus(level(t_139), n1), int_level(X_t_42)))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(plus(level(t_139), n1), int_level(t_139)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(154,plain,
% 0.20/0.52 ((~![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(plus(level(t_139), n1), int_level(X_t_42)))) | p_Rd(t_139) | p_Reset(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(plus(level(t_139), n1), int_level(t_139))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.52 tff(155,plain,
% 0.20/0.52 ((int_level(plus(t_139, n1)) = int_level(t_139)) | gt(plus(level(t_139), n1), int_level(t_139))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[154, 148, 48, 45, 42])).
% 0.20/0.52 tff(156,plain,
% 0.20/0.52 (int_level(plus(t_139, n1)) = int_level(t_139)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[155, 69])).
% 0.20/0.52 tff(157,plain,
% 0.20/0.52 (int_level(t_139) = int_level(plus(t_139, n1))),
% 0.20/0.52 inference(symmetry,[status(thm)],[156])).
% 0.20/0.52 tff(158,plain,
% 0.20/0.52 (int_level(t_139) = level(plus(t_139, n1))),
% 0.20/0.52 inference(transitivity,[status(thm)],[157, 30])).
% 0.20/0.52 tff(159,plain,
% 0.20/0.52 ((int_level(t_139) = plus(level(t_139), n1)) <=> (level(plus(t_139, n1)) = plus(level(t_139), n1))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[158])).
% 0.20/0.52 tff(160,plain,
% 0.20/0.52 ((level(plus(t_139, n1)) = plus(level(t_139), n1)) <=> (int_level(t_139) = plus(level(t_139), n1))),
% 0.20/0.52 inference(symmetry,[status(thm)],[159])).
% 0.20/0.52 tff(161,plain,
% 0.20/0.52 ((~(level(plus(t_139, n1)) = plus(level(t_139), n1))) <=> (~(int_level(t_139) = plus(level(t_139), n1)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.52 tff(162,plain,
% 0.20/0.52 (~(int_level(t_139) = plus(level(t_139), n1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[38, 161])).
% 0.20/0.52 tff(163,plain,
% 0.20/0.52 (~(level(t_139) = plus(level(t_139), n1))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[162, 135])).
% 0.20/0.52 tff(164,plain,
% 0.20/0.52 (^[Y_18: $i, X_17: $i] : refl((gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17)) <=> (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(165,plain,
% 0.20/0.52 (![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17)) <=> ![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.52 tff(166,plain,
% 0.20/0.52 (![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17)) <=> ![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(167,plain,
% 0.20/0.52 (^[Y_18: $i, X_17: $i] : trans(monotonicity(rewrite((gt(Y_18, X_17) | (X_17 = Y_18)) <=> ((X_17 = Y_18) | gt(Y_18, X_17))), (((gt(Y_18, X_17) | (X_17 = Y_18)) | gt(X_17, Y_18)) <=> (((X_17 = Y_18) | gt(Y_18, X_17)) | gt(X_17, Y_18)))), rewrite((((X_17 = Y_18) | gt(Y_18, X_17)) | gt(X_17, Y_18)) <=> (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))), (((gt(Y_18, X_17) | (X_17 = Y_18)) | gt(X_17, Y_18)) <=> (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(168,plain,
% 0.20/0.52 (![Y_18: $i, X_17: $i] : ((gt(Y_18, X_17) | (X_17 = Y_18)) | gt(X_17, Y_18)) <=> ![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.52 tff(169,axiom,(![Y_18: $i, X_17: $i] : ((gt(Y_18, X_17) | (X_17 = Y_18)) | gt(X_17, Y_18))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_12')).
% 0.20/0.52 tff(170,plain,
% 0.20/0.52 (![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.52 tff(171,plain,
% 0.20/0.52 (![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.20/0.52 tff(172,plain,(
% 0.20/0.52 ![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))),
% 0.20/0.52 inference(skolemize,[status(sab)],[171])).
% 0.20/0.52 tff(173,plain,
% 0.20/0.52 (![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.20/0.52 tff(174,plain,
% 0.20/0.52 (((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | (gt(level(t_139), plus(level(t_139), n1)) | (level(t_139) = plus(level(t_139), n1)) | gt(plus(level(t_139), n1), level(t_139)))) <=> ((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | gt(level(t_139), plus(level(t_139), n1)) | (level(t_139) = plus(level(t_139), n1)) | gt(plus(level(t_139), n1), level(t_139)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(175,plain,
% 0.20/0.52 ((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | (gt(level(t_139), plus(level(t_139), n1)) | (level(t_139) = plus(level(t_139), n1)) | gt(plus(level(t_139), n1), level(t_139)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(176,plain,
% 0.20/0.52 ((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | gt(level(t_139), plus(level(t_139), n1)) | (level(t_139) = plus(level(t_139), n1)) | gt(plus(level(t_139), n1), level(t_139))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.52 tff(177,plain,
% 0.20/0.52 (gt(level(t_139), plus(level(t_139), n1)) | (level(t_139) = plus(level(t_139), n1)) | gt(plus(level(t_139), n1), level(t_139))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[176, 173])).
% 0.20/0.52 tff(178,plain,
% 0.20/0.52 (gt(level(t_139), plus(level(t_139), n1))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[177, 163, 132])).
% 0.20/0.52 tff(179,plain,
% 0.20/0.52 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20))) <=> ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(180,plain,
% 0.20/0.52 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20))) <=> ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(181,plain,
% 0.20/0.52 (^[Z_21: $i, Y_20: $i, X_19: $i] : rewrite((((~gt(Z_21, Y_20)) | gt(Z_21, X_19)) | (~gt(Y_20, X_19))) <=> ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(182,plain,
% 0.20/0.52 (![Z_21: $i, Y_20: $i, X_19: $i] : (((~gt(Z_21, Y_20)) | gt(Z_21, X_19)) | (~gt(Y_20, X_19))) <=> ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[181])).
% 0.20/0.53 tff(183,axiom,(![Z_21: $i, Y_20: $i, X_19: $i] : (((~gt(Z_21, Y_20)) | gt(Z_21, X_19)) | (~gt(Y_20, X_19)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_13')).
% 0.20/0.53 tff(184,plain,
% 0.20/0.53 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.53 tff(185,plain,
% 0.20/0.53 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.20/0.53 tff(186,plain,(
% 0.20/0.53 ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[185])).
% 0.20/0.53 tff(187,plain,
% 0.20/0.53 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.20/0.53 tff(188,plain,
% 0.20/0.53 (((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | (gt(level(t_139), n0) | (~gt(plus(level(t_139), n1), n0)) | (~gt(level(t_139), plus(level(t_139), n1))))) <=> ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | gt(level(t_139), n0) | (~gt(plus(level(t_139), n1), n0)) | (~gt(level(t_139), plus(level(t_139), n1))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(189,plain,
% 0.20/0.53 (((~gt(plus(level(t_139), n1), n0)) | gt(level(t_139), n0) | (~gt(level(t_139), plus(level(t_139), n1)))) <=> (gt(level(t_139), n0) | (~gt(plus(level(t_139), n1), n0)) | (~gt(level(t_139), plus(level(t_139), n1))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(190,plain,
% 0.20/0.53 (((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | ((~gt(plus(level(t_139), n1), n0)) | gt(level(t_139), n0) | (~gt(level(t_139), plus(level(t_139), n1))))) <=> ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | (gt(level(t_139), n0) | (~gt(plus(level(t_139), n1), n0)) | (~gt(level(t_139), plus(level(t_139), n1)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[189])).
% 0.20/0.53 tff(191,plain,
% 0.20/0.53 (((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | ((~gt(plus(level(t_139), n1), n0)) | gt(level(t_139), n0) | (~gt(level(t_139), plus(level(t_139), n1))))) <=> ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | gt(level(t_139), n0) | (~gt(plus(level(t_139), n1), n0)) | (~gt(level(t_139), plus(level(t_139), n1))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[190, 188])).
% 0.20/0.53 tff(192,plain,
% 0.20/0.53 ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | ((~gt(plus(level(t_139), n1), n0)) | gt(level(t_139), n0) | (~gt(level(t_139), plus(level(t_139), n1))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(193,plain,
% 0.20/0.53 ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | gt(level(t_139), n0) | (~gt(plus(level(t_139), n1), n0)) | (~gt(level(t_139), plus(level(t_139), n1)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.53 tff(194,plain,
% 0.20/0.53 (gt(level(t_139), n0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[193, 187, 79, 178])).
% 0.20/0.53 tff(195,plain,
% 0.20/0.53 (^[X_11: $i, Y_12: $i] : refl(((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1))) <=> ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(196,plain,
% 0.20/0.53 (![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1))) <=> ![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[195])).
% 0.20/0.53 tff(197,plain,
% 0.20/0.53 (![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1))) <=> ![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(198,axiom,(![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_8')).
% 0.20/0.53 tff(199,plain,
% 0.20/0.53 (![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.53 tff(200,plain,(
% 0.20/0.53 ![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[199])).
% 0.20/0.53 tff(201,plain,
% 0.20/0.53 (![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.20/0.53 tff(202,plain,
% 0.20/0.53 (((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | ((~gt(level(t_139), n0)) | gt(plus(level(t_139), n1), plus(n0, n1)))) <=> ((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | (~gt(level(t_139), n0)) | gt(plus(level(t_139), n1), plus(n0, n1)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(203,plain,
% 0.20/0.53 ((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | ((~gt(level(t_139), n0)) | gt(plus(level(t_139), n1), plus(n0, n1)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(204,plain,
% 0.20/0.53 ((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | (~gt(level(t_139), n0)) | gt(plus(level(t_139), n1), plus(n0, n1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.53 tff(205,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[204, 201, 194, 128])).
% 0.20/0.53 % SZS output end Proof
%------------------------------------------------------------------------------