TSTP Solution File: HWV016-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV016-1 : 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 02:10:36 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : HWV016-1 : 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 22:16:37 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.
% 0.18/0.42 % SZS status Unsatisfiable
% 0.18/0.42 % SZS output start Proof
% 0.18/0.42 tff(plus_type, type, (
% 0.18/0.42 plus: ( $i * $i ) > $i)).
% 0.18/0.42 tff(n1_type, type, (
% 0.18/0.42 n1: $i)).
% 0.18/0.42 tff(int_level_type, type, (
% 0.18/0.42 int_level: $i > $i)).
% 0.18/0.42 tff(t_139_type, type, (
% 0.18/0.42 t_139: $i)).
% 0.18/0.42 tff(n0_type, type, (
% 0.18/0.42 n0: $i)).
% 0.18/0.42 tff(p_Empty_type, type, (
% 0.18/0.42 p_Empty: $i > $o)).
% 0.18/0.42 tff(gt_type, type, (
% 0.18/0.42 gt: ( $i * $i ) > $o)).
% 0.18/0.42 tff(level_type, type, (
% 0.18/0.42 level: $i > $i)).
% 0.18/0.42 tff(p_Rd_type, type, (
% 0.18/0.42 p_Rd: $i > $o)).
% 0.18/0.42 tff(p_Reset_type, type, (
% 0.18/0.42 p_Reset: $i > $o)).
% 0.18/0.42 tff(p_Wr_type, type, (
% 0.18/0.42 p_Wr: $i > $o)).
% 0.18/0.42 tff(fifo_length_type, type, (
% 0.18/0.42 fifo_length: $i)).
% 0.18/0.42 tff(1,plain,
% 0.18/0.42 ((plus(int_level(t_139), n1) = int_level(plus(t_139, n1))) <=> (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))),
% 0.18/0.42 inference(commutativity,[status(thm)],[])).
% 0.18/0.42 tff(2,plain,
% 0.18/0.42 (p_Empty(plus(t_139, n1)) <=> p_Empty(plus(t_139, n1))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(3,axiom,(p_Empty(plus(t_139, n1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_4')).
% 0.18/0.42 tff(4,plain,
% 0.18/0.42 (p_Empty(plus(t_139, n1))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.42 tff(5,plain,
% 0.18/0.42 (^[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))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(6,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.18/0.42 tff(7,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(8,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')).
% 0.18/0.42 tff(9,plain,
% 0.18/0.42 (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.18/0.42 tff(10,plain,(
% 0.18/0.42 ![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[9])).
% 0.18/0.42 tff(11,plain,
% 0.18/0.42 (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.18/0.42 tff(12,plain,
% 0.18/0.42 (((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | ((int_level(plus(t_139, n1)) = n0) | (~p_Empty(plus(t_139, n1))))) <=> ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | (int_level(plus(t_139, n1)) = n0) | (~p_Empty(plus(t_139, n1))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(13,plain,
% 0.18/0.42 ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | ((int_level(plus(t_139, n1)) = n0) | (~p_Empty(plus(t_139, n1))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(14,plain,
% 0.18/0.42 ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | (int_level(plus(t_139, n1)) = n0) | (~p_Empty(plus(t_139, n1)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.42 tff(15,plain,
% 0.18/0.42 (int_level(plus(t_139, n1)) = n0),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[14, 11, 4])).
% 0.18/0.42 tff(16,plain,
% 0.18/0.42 (n0 = int_level(plus(t_139, n1))),
% 0.18/0.42 inference(symmetry,[status(thm)],[15])).
% 0.18/0.42 tff(17,plain,
% 0.18/0.42 ((plus(int_level(t_139), n1) = n0) <=> (plus(int_level(t_139), n1) = int_level(plus(t_139, n1)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[16])).
% 0.18/0.42 tff(18,plain,
% 0.18/0.42 ((plus(int_level(t_139), n1) = n0) <=> (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))),
% 0.18/0.42 inference(transitivity,[status(thm)],[17, 1])).
% 0.18/0.42 tff(19,plain,
% 0.18/0.42 ((~(plus(int_level(t_139), n1) = n0)) <=> (~(int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[18])).
% 0.18/0.42 tff(20,assumption,(plus(int_level(t_139), n1) = n0), introduced(assumption)).
% 0.18/0.42 tff(21,plain,
% 0.18/0.42 (^[X_0: $i] : refl((~(plus(X_0, n1) = n0)) <=> (~(plus(X_0, n1) = n0)))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(22,plain,
% 0.18/0.42 (![X_0: $i] : (~(plus(X_0, n1) = n0)) <=> ![X_0: $i] : (~(plus(X_0, n1) = n0))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.18/0.42 tff(23,plain,
% 0.18/0.42 (![X_0: $i] : (~(plus(X_0, n1) = n0)) <=> ![X_0: $i] : (~(plus(X_0, n1) = n0))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(24,axiom,(![X_0: $i] : (~(plus(X_0, n1) = n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_1')).
% 0.18/0.42 tff(25,plain,
% 0.18/0.42 (![X_0: $i] : (~(plus(X_0, n1) = n0))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.42 tff(26,plain,(
% 0.18/0.42 ![X_0: $i] : (~(plus(X_0, n1) = n0))),
% 0.18/0.42 inference(skolemize,[status(sab)],[25])).
% 0.18/0.42 tff(27,plain,
% 0.18/0.42 (![X_0: $i] : (~(plus(X_0, n1) = n0))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.18/0.42 tff(28,plain,
% 0.18/0.42 ((~![X_0: $i] : (~(plus(X_0, n1) = n0))) | (~(plus(int_level(t_139), n1) = n0))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(29,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[28, 27, 20])).
% 0.18/0.42 tff(30,plain,(~(plus(int_level(t_139), n1) = n0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(31,plain,
% 0.18/0.42 (~(int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[30, 19])).
% 0.18/0.42 tff(32,assumption,(~(int_level(plus(t_139, n1)) = int_level(t_139))), introduced(assumption)).
% 0.18/0.42 tff(33,plain,
% 0.18/0.42 (^[X_t_32: $i] : refl((level(X_t_32) = int_level(X_t_32)) <=> (level(X_t_32) = int_level(X_t_32)))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(34,plain,
% 0.18/0.42 (![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))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.42 tff(35,plain,
% 0.18/0.42 (![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))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(36,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')).
% 0.18/0.42 tff(37,plain,
% 0.18/0.42 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.18/0.42 tff(38,plain,(
% 0.18/0.42 ![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.18/0.42 inference(skolemize,[status(sab)],[37])).
% 0.18/0.42 tff(39,plain,
% 0.18/0.42 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.18/0.43 tff(40,plain,
% 0.18/0.43 ((~![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))) | (level(t_139) = int_level(t_139))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(41,plain,
% 0.18/0.43 (level(t_139) = int_level(t_139)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.18/0.43 tff(42,plain,
% 0.18/0.43 (gt(level(t_139), n0) <=> gt(int_level(t_139), n0)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[41])).
% 0.18/0.43 tff(43,plain,
% 0.18/0.43 ((n0 = level(t_139)) <=> (level(t_139) = n0)),
% 0.18/0.43 inference(commutativity,[status(thm)],[])).
% 0.18/0.43 tff(44,plain,
% 0.18/0.43 ((level(t_139) = n0) <=> (n0 = level(t_139))),
% 0.18/0.43 inference(symmetry,[status(thm)],[43])).
% 0.18/0.43 tff(45,plain,
% 0.18/0.43 (int_level(t_139) = level(t_139)),
% 0.18/0.43 inference(symmetry,[status(thm)],[41])).
% 0.18/0.43 tff(46,plain,
% 0.18/0.43 ((int_level(plus(t_139, n1)) = int_level(t_139)) <=> (n0 = level(t_139))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[15, 45])).
% 0.18/0.43 tff(47,plain,
% 0.18/0.43 ((int_level(plus(t_139, n1)) = int_level(t_139)) <=> (level(t_139) = n0)),
% 0.18/0.43 inference(transitivity,[status(thm)],[46, 43])).
% 0.18/0.43 tff(48,plain,
% 0.18/0.43 ((int_level(plus(t_139, n1)) = int_level(t_139)) <=> (n0 = level(t_139))),
% 0.18/0.43 inference(transitivity,[status(thm)],[47, 44])).
% 0.18/0.43 tff(49,plain,
% 0.18/0.43 ((~(int_level(plus(t_139, n1)) = int_level(t_139))) <=> (~(n0 = level(t_139)))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[48])).
% 0.18/0.43 tff(50,plain,
% 0.18/0.43 (~(n0 = level(t_139))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[32, 49])).
% 0.18/0.43 tff(51,assumption,(n0 = level(t_139)), introduced(assumption)).
% 0.18/0.43 tff(52,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.18/0.43 tff(53,plain,((~(n0 = level(t_139))) | (int_level(plus(t_139, n1)) = int_level(t_139))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(54,plain,
% 0.18/0.43 (~(n0 = level(t_139))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[53, 32])).
% 0.18/0.43 tff(55,plain,
% 0.18/0.43 ((~gt(n0, level(t_139))) <=> (~gt(n0, level(t_139)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(56,axiom,(~gt(n0, level(t_139))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_1')).
% 0.18/0.43 tff(57,plain,
% 0.18/0.43 (~gt(n0, level(t_139))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.43 tff(58,plain,
% 0.18/0.43 (^[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)))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(59,plain,
% 0.18/0.43 (![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))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.18/0.43 tff(60,plain,
% 0.18/0.43 (![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))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(61,plain,
% 0.18/0.43 (^[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))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(62,plain,
% 0.18/0.43 (![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))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.43 tff(63,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')).
% 0.18/0.43 tff(64,plain,
% 0.18/0.43 (![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.43 tff(65,plain,
% 0.18/0.43 (![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.18/0.43 tff(66,plain,(
% 0.18/0.43 ![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))),
% 0.18/0.43 inference(skolemize,[status(sab)],[65])).
% 0.18/0.43 tff(67,plain,
% 0.18/0.43 (![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.18/0.43 tff(68,plain,
% 0.18/0.43 (((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | (gt(n0, level(t_139)) | gt(level(t_139), n0) | (n0 = level(t_139)))) <=> ((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | gt(n0, level(t_139)) | gt(level(t_139), n0) | (n0 = level(t_139)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(69,plain,
% 0.18/0.43 ((gt(n0, level(t_139)) | (n0 = level(t_139)) | gt(level(t_139), n0)) <=> (gt(n0, level(t_139)) | gt(level(t_139), n0) | (n0 = level(t_139)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(70,plain,
% 0.18/0.43 (((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | (gt(n0, level(t_139)) | (n0 = level(t_139)) | gt(level(t_139), n0))) <=> ((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | (gt(n0, level(t_139)) | gt(level(t_139), n0) | (n0 = level(t_139))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[69])).
% 0.18/0.43 tff(71,plain,
% 0.18/0.43 (((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | (gt(n0, level(t_139)) | (n0 = level(t_139)) | gt(level(t_139), n0))) <=> ((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | gt(n0, level(t_139)) | gt(level(t_139), n0) | (n0 = level(t_139)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[70, 68])).
% 0.18/0.43 tff(72,plain,
% 0.18/0.43 ((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | (gt(n0, level(t_139)) | (n0 = level(t_139)) | gt(level(t_139), n0))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(73,plain,
% 0.18/0.43 ((~![Y_18: $i, X_17: $i] : (gt(X_17, Y_18) | (X_17 = Y_18) | gt(Y_18, X_17))) | gt(n0, level(t_139)) | gt(level(t_139), n0) | (n0 = level(t_139))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.18/0.43 tff(74,plain,
% 0.18/0.43 (gt(level(t_139), n0) | (n0 = level(t_139))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[73, 67, 57])).
% 0.18/0.43 tff(75,plain,
% 0.18/0.43 (gt(level(t_139), n0)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[74, 54])).
% 0.18/0.43 tff(76,plain,
% 0.18/0.43 (gt(int_level(t_139), n0)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[75, 42])).
% 0.18/0.43 tff(77,plain,
% 0.18/0.43 ((~p_Reset(t_139)) <=> (~p_Reset(t_139))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(78,axiom,(~p_Reset(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_3')).
% 0.18/0.43 tff(79,plain,
% 0.18/0.43 (~p_Reset(t_139)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.43 tff(80,plain,
% 0.18/0.43 (p_Wr(t_139) <=> p_Wr(t_139)),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(81,axiom,(p_Wr(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_2')).
% 0.18/0.43 tff(82,plain,
% 0.18/0.43 (p_Wr(t_139)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.43 tff(83,plain,
% 0.18/0.43 (^[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))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(84,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.43 tff(85,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(86,plain,
% 0.18/0.43 (^[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)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(87,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.43 tff(88,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_53')).
% 0.18/0.43 tff(89,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.43 tff(90,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.18/0.43 tff(91,plain,(
% 0.18/0.43 ![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)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[90])).
% 0.18/0.43 tff(92,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.18/0.43 tff(93,plain,
% 0.18/0.43 (((~![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)) | (~gt(int_level(t_139), n0)) | (int_level(plus(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(int_level(X_t_42), n0)))) | p_Reset(t_139) | (~p_Rd(t_139)) | (~p_Wr(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = int_level(t_139)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(94,plain,
% 0.18/0.43 ((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_Reset(t_139) | (~p_Rd(t_139)) | (~p_Wr(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = int_level(t_139)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(95,plain,
% 0.18/0.43 (((~![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_Reset(t_139) | (~p_Rd(t_139)) | (~p_Wr(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = int_level(t_139))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[94])).
% 0.18/0.43 tff(96,plain,
% 0.18/0.43 (((~![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_Reset(t_139) | (~p_Rd(t_139)) | (~p_Wr(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = int_level(t_139)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[95, 93])).
% 0.18/0.43 tff(97,plain,
% 0.18/0.43 ((~![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)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(98,plain,
% 0.18/0.43 ((~![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)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = int_level(t_139))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.18/0.43 tff(99,plain,
% 0.18/0.43 ((~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = int_level(t_139))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[98, 92, 82, 79])).
% 0.18/0.43 tff(100,plain,
% 0.18/0.43 (~p_Rd(t_139)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[99, 76, 32])).
% 0.18/0.43 tff(101,plain,
% 0.18/0.43 (^[X_t_42: $i] : refl((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))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(102,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[101])).
% 0.18/0.43 tff(103,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(104,plain,
% 0.18/0.43 (^[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)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(105,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[104])).
% 0.18/0.43 tff(106,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')).
% 0.18/0.43 tff(107,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.18/0.43 tff(108,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.18/0.44 tff(109,plain,(
% 0.18/0.44 ![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)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[108])).
% 0.18/0.44 tff(110,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.18/0.44 tff(111,plain,
% 0.18/0.44 (((~![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)))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(fifo_length, int_level(t_139)))) <=> ((~![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)))) | p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(fifo_length, int_level(t_139)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(112,plain,
% 0.18/0.44 ((p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | gt(fifo_length, int_level(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139))) <=> (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(fifo_length, int_level(t_139)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(113,plain,
% 0.18/0.44 (((~![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)))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | gt(fifo_length, int_level(t_139)) | (int_level(plus(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)) | gt(fifo_length, int_level(X_t_42)) | (int_level(plus(X_t_42, 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(fifo_length, int_level(t_139))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[112])).
% 0.18/0.44 tff(114,plain,
% 0.18/0.44 (((~![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)))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | gt(fifo_length, int_level(t_139)) | (int_level(plus(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)) | gt(fifo_length, int_level(X_t_42)) | (int_level(plus(X_t_42, 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(fifo_length, int_level(t_139)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[113, 111])).
% 0.18/0.44 tff(115,plain,
% 0.18/0.44 ((~![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)))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | gt(fifo_length, int_level(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(116,plain,
% 0.18/0.44 ((~![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)))) | p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(fifo_length, int_level(t_139))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.18/0.44 tff(117,plain,
% 0.18/0.44 (p_Rd(t_139) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(fifo_length, int_level(t_139))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[116, 110, 82, 79])).
% 0.18/0.44 tff(118,plain,
% 0.18/0.44 (gt(fifo_length, int_level(t_139))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[117, 100, 32])).
% 0.18/0.44 tff(119,plain,
% 0.18/0.44 (^[X_t_42: $i] : refl((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))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(120,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[119])).
% 0.18/0.44 tff(121,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(122,plain,
% 0.18/0.44 (^[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)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(123,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[122])).
% 0.18/0.44 tff(124,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')).
% 0.18/0.44 tff(125,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.44 tff(126,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.18/0.44 tff(127,plain,(
% 0.18/0.44 ![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)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[126])).
% 0.18/0.44 tff(128,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.18/0.44 tff(129,plain,
% 0.18/0.44 (((~![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)))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (~gt(fifo_length, 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)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)))) | p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (~gt(fifo_length, int_level(t_139))) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(130,plain,
% 0.18/0.44 ((~![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)))) | (p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (~gt(fifo_length, int_level(t_139))) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(131,plain,
% 0.18/0.44 ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)))) | p_Reset(t_139) | p_Rd(t_139) | (~p_Wr(t_139)) | (~gt(fifo_length, int_level(t_139))) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.18/0.44 tff(132,plain,
% 0.18/0.44 (p_Rd(t_139) | (~gt(fifo_length, int_level(t_139))) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[131, 128, 82, 79])).
% 0.18/0.44 tff(133,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[132, 118, 100, 31])).
% 0.18/0.44 tff(134,plain,(int_level(plus(t_139, n1)) = int_level(t_139)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(135,plain,
% 0.18/0.44 (gt(int_level(plus(t_139, n1)), n0) <=> gt(int_level(t_139), n0)),
% 0.18/0.44 inference(monotonicity,[status(thm)],[134])).
% 0.18/0.44 tff(136,plain,
% 0.18/0.44 (int_level(t_139) = int_level(plus(t_139, n1))),
% 0.18/0.44 inference(symmetry,[status(thm)],[134])).
% 0.18/0.44 tff(137,plain,
% 0.18/0.44 (level(t_139) = n0),
% 0.18/0.44 inference(transitivity,[status(thm)],[41, 136, 15])).
% 0.18/0.44 tff(138,plain,
% 0.18/0.44 (gt(n0, level(t_139)) <=> gt(int_level(plus(t_139, n1)), n0)),
% 0.18/0.44 inference(monotonicity,[status(thm)],[16, 137])).
% 0.18/0.44 tff(139,plain,
% 0.18/0.44 (gt(n0, level(t_139)) <=> gt(int_level(t_139), n0)),
% 0.18/0.44 inference(transitivity,[status(thm)],[138, 135])).
% 0.18/0.44 tff(140,plain,
% 0.18/0.44 ((~gt(n0, level(t_139))) <=> (~gt(int_level(t_139), n0))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[139])).
% 0.18/0.44 tff(141,plain,
% 0.18/0.44 (~gt(int_level(t_139), n0)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[57, 140])).
% 0.18/0.44 tff(142,plain,
% 0.18/0.44 (int_level(t_139) = n0),
% 0.18/0.44 inference(transitivity,[status(thm)],[136, 15])).
% 0.18/0.44 tff(143,plain,
% 0.18/0.44 (gt(fifo_length, int_level(t_139)) <=> gt(fifo_length, n0)),
% 0.18/0.44 inference(monotonicity,[status(thm)],[142])).
% 0.18/0.44 tff(144,plain,
% 0.18/0.44 (gt(fifo_length, n0) <=> gt(fifo_length, int_level(t_139))),
% 0.18/0.44 inference(symmetry,[status(thm)],[143])).
% 0.18/0.44 tff(145,plain,
% 0.18/0.44 (gt(fifo_length, n0) <=> gt(fifo_length, n0)),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(146,axiom,(gt(fifo_length, n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_5')).
% 0.18/0.44 tff(147,plain,
% 0.18/0.44 (gt(fifo_length, n0)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.18/0.44 tff(148,plain,
% 0.18/0.44 (gt(fifo_length, int_level(t_139))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[147, 144])).
% 0.18/0.44 tff(149,plain,
% 0.18/0.44 (p_Rd(t_139)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[132, 148, 31])).
% 0.18/0.44 tff(150,plain,
% 0.18/0.44 (^[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(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)) = plus(int_level(X_t_42), n1)) | gt(int_level(X_t_42), n0)))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(151,plain,
% 0.18/0.44 (![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(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)) = plus(int_level(X_t_42), n1)) | gt(int_level(X_t_42), n0))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[150])).
% 0.18/0.44 tff(152,plain,
% 0.18/0.44 (![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(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)) = plus(int_level(X_t_42), n1)) | gt(int_level(X_t_42), n0))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(153,plain,
% 0.18/0.44 (^[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)) = plus(int_level(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)) | (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(int_level(X_t_42), n0)) | (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(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)) = 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(int_level(X_t_42), n0))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(154,plain,
% 0.18/0.44 (![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)) = 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(int_level(X_t_42), n0))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[153])).
% 0.18/0.44 tff(155,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)) = plus(int_level(X_t_42), n1)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_59')).
% 0.18/0.44 tff(156,plain,
% 0.18/0.44 (![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(int_level(X_t_42), n0))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.18/0.44 tff(157,plain,
% 0.18/0.44 (![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(int_level(X_t_42), n0))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.18/0.44 tff(158,plain,(
% 0.18/0.44 ![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(int_level(X_t_42), n0))),
% 0.18/0.44 inference(skolemize,[status(sab)],[157])).
% 0.18/0.44 tff(159,plain,
% 0.18/0.44 (![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(int_level(X_t_42), n0))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.18/0.45 tff(160,plain,
% 0.18/0.45 (((~![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(int_level(X_t_42), n0))) | (p_Reset(t_139) | (~p_Rd(t_139)) | (~p_Wr(t_139)) | gt(int_level(t_139), n0) | (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(int_level(X_t_42), n0))) | p_Reset(t_139) | (~p_Rd(t_139)) | (~p_Wr(t_139)) | gt(int_level(t_139), n0) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(161,plain,
% 0.18/0.45 ((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(int_level(t_139), n0)) <=> (p_Reset(t_139) | (~p_Rd(t_139)) | (~p_Wr(t_139)) | gt(int_level(t_139), n0) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(162,plain,
% 0.18/0.45 (((~![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(int_level(X_t_42), n0))) | (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(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)) = plus(int_level(X_t_42), n1)) | gt(int_level(X_t_42), n0))) | (p_Reset(t_139) | (~p_Rd(t_139)) | (~p_Wr(t_139)) | gt(int_level(t_139), n0) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[161])).
% 0.18/0.45 tff(163,plain,
% 0.18/0.45 (((~![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(int_level(X_t_42), n0))) | (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(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)) = plus(int_level(X_t_42), n1)) | gt(int_level(X_t_42), n0))) | p_Reset(t_139) | (~p_Rd(t_139)) | (~p_Wr(t_139)) | gt(int_level(t_139), n0) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[162, 160])).
% 0.18/0.45 tff(164,plain,
% 0.18/0.45 ((~![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(int_level(X_t_42), n0))) | (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(int_level(t_139), n0))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(165,plain,
% 0.18/0.45 ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (int_level(plus(X_t_42, n1)) = plus(int_level(X_t_42), n1)) | gt(int_level(X_t_42), n0))) | p_Reset(t_139) | (~p_Rd(t_139)) | (~p_Wr(t_139)) | gt(int_level(t_139), n0) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.18/0.45 tff(166,plain,
% 0.18/0.45 ((~p_Rd(t_139)) | gt(int_level(t_139), n0) | (int_level(plus(t_139, n1)) = plus(int_level(t_139), n1))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[165, 159, 82, 79])).
% 0.18/0.45 tff(167,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[166, 149, 141, 31])).
% 0.18/0.45 % SZS output end Proof
%------------------------------------------------------------------------------