TSTP Solution File: HWV017-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV017-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 02:10:37 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : HWV017-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n006.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 22:00:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(gt_type, type, (
% 0.19/0.42 gt: ( $i * $i ) > $o)).
% 0.19/0.42 tff(n0_type, type, (
% 0.19/0.42 n0: $i)).
% 0.19/0.42 tff(int_level_type, type, (
% 0.19/0.42 int_level: $i > $i)).
% 0.19/0.42 tff(t_139_type, type, (
% 0.19/0.42 t_139: $i)).
% 0.19/0.42 tff(fifo_length_type, type, (
% 0.19/0.42 fifo_length: $i)).
% 0.19/0.42 tff(plus_type, type, (
% 0.19/0.42 plus: ( $i * $i ) > $i)).
% 0.19/0.42 tff(n1_type, type, (
% 0.19/0.42 n1: $i)).
% 0.19/0.42 tff(p_Full_type, type, (
% 0.19/0.42 p_Full: $i > $o)).
% 0.19/0.42 tff(minus_type, type, (
% 0.19/0.42 minus: ( $i * $i ) > $i)).
% 0.19/0.42 tff(level_type, type, (
% 0.19/0.42 level: $i > $i)).
% 0.19/0.42 tff(p_Reset_type, type, (
% 0.19/0.42 p_Reset: $i > $o)).
% 0.19/0.42 tff(p_Wr_type, type, (
% 0.19/0.42 p_Wr: $i > $o)).
% 0.19/0.42 tff(p_Rd_type, type, (
% 0.19/0.42 p_Rd: $i > $o)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 (p_Full(plus(t_139, n1)) <=> p_Full(plus(t_139, n1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(2,axiom,(p_Full(plus(t_139, n1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_5')).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (p_Full(plus(t_139, n1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (^[X_t_34: $i] : refl(((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34))) <=> ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34))) <=> ![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34))) <=> ![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(7,axiom,(![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_23')).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.42 tff(9,plain,(
% 0.19/0.42 ![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[8])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (((~![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))) | ((int_level(plus(t_139, n1)) = fifo_length) | (~p_Full(plus(t_139, n1))))) <=> ((~![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))) | (int_level(plus(t_139, n1)) = fifo_length) | (~p_Full(plus(t_139, n1))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 ((~![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))) | ((int_level(plus(t_139, n1)) = fifo_length) | (~p_Full(plus(t_139, n1))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 ((~![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))) | (int_level(plus(t_139, n1)) = fifo_length) | (~p_Full(plus(t_139, n1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (int_level(plus(t_139, n1)) = fifo_length),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.19/0.42 tff(15,assumption,(gt(int_level(t_139), n0)), introduced(assumption)).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 ((~p_Reset(t_139)) <=> (~p_Reset(t_139))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(17,axiom,(~p_Reset(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_4')).
% 0.19/0.42 tff(18,plain,
% 0.19/0.42 (~p_Reset(t_139)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 ((~p_Wr(t_139)) <=> (~p_Wr(t_139))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(20,axiom,(~p_Wr(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_3')).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 (~p_Wr(t_139)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (p_Rd(t_139) <=> p_Rd(t_139)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(23,axiom,(p_Rd(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_2')).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 (p_Rd(t_139)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (^[X_t_42: $i] : refl((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (~gt(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = minus(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)) = minus(int_level(X_t_42), n1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (![X_t_42: $i] : (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)) = minus(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(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = minus(int_level(X_t_42), n1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (![X_t_42: $i] : (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)) = minus(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(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = minus(int_level(X_t_42), n1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (^[X_t_42: $i] : trans(monotonicity(trans(monotonicity(rewrite(((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42))), ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | (~gt(int_level(X_t_42), n0))) <=> ((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42)) | (~gt(int_level(X_t_42), n0))))), rewrite(((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42)) | (~gt(int_level(X_t_42), n0))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (~gt(int_level(X_t_42), n0)))), ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | (~gt(int_level(X_t_42), n0))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (~gt(int_level(X_t_42), n0))))), (((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | (~gt(int_level(X_t_42), n0))) | (int_level(plus(X_t_42, n1)) = minus(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)) = minus(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)) = minus(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)) = minus(int_level(X_t_42), n1)))), (((((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)) = minus(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)) = minus(int_level(X_t_42), n1)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (![X_t_42: $i] : ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | (~gt(int_level(X_t_42), n0))) | (int_level(plus(X_t_42, n1)) = minus(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(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = minus(int_level(X_t_42), n1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.42 tff(30,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)) = minus(int_level(X_t_42), n1)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_71')).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (![X_t_42: $i] : (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)) = minus(int_level(X_t_42), n1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (![X_t_42: $i] : (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)) = minus(int_level(X_t_42), n1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.42 tff(33,plain,(
% 0.19/0.42 ![X_t_42: $i] : (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)) = minus(int_level(X_t_42), n1)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[32])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (![X_t_42: $i] : (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)) = minus(int_level(X_t_42), n1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (((~![X_t_42: $i] : (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)) = minus(int_level(X_t_42), n1)))) | (p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(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(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = minus(int_level(X_t_42), n1)))) | p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(int_level(t_139), n1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 ((p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(int_level(t_139), n1))) <=> (p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(int_level(t_139), n1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (((~![X_t_42: $i] : (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)) = minus(int_level(X_t_42), n1)))) | (p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(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(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = minus(int_level(X_t_42), n1)))) | (p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(int_level(t_139), n1))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 (((~![X_t_42: $i] : (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)) = minus(int_level(X_t_42), n1)))) | (p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(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(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = minus(int_level(X_t_42), n1)))) | p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(int_level(t_139), n1)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[37, 35])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 ((~![X_t_42: $i] : (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)) = minus(int_level(X_t_42), n1)))) | (p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(int_level(t_139), n1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 ((~![X_t_42: $i] : (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)) = minus(int_level(X_t_42), n1)))) | p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(int_level(t_139), n1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 ((~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(int_level(t_139), n1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[40, 34, 24, 21, 18])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (int_level(plus(t_139, n1)) = minus(int_level(t_139), n1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[41, 15])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (minus(int_level(t_139), n1) = int_level(plus(t_139, n1))),
% 0.19/0.43 inference(symmetry,[status(thm)],[42])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (minus(int_level(t_139), n1) = fifo_length),
% 0.19/0.43 inference(transitivity,[status(thm)],[43, 14])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (^[X_t_32: $i] : refl((level(X_t_32) = int_level(X_t_32)) <=> (level(X_t_32) = int_level(X_t_32)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(48,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')).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.43 tff(50,plain,(
% 0.19/0.43 ![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.19/0.43 inference(skolemize,[status(sab)],[49])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 ((~![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))) | (level(t_139) = int_level(t_139))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (level(t_139) = int_level(t_139)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (int_level(t_139) = level(t_139)),
% 0.19/0.43 inference(symmetry,[status(thm)],[53])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (gt(int_level(t_139), minus(int_level(t_139), n1)) <=> gt(level(t_139), fifo_length)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[54, 44])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (gt(level(t_139), fifo_length) <=> gt(int_level(t_139), minus(int_level(t_139), n1))),
% 0.19/0.43 inference(symmetry,[status(thm)],[55])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 ((~gt(level(t_139), fifo_length)) <=> (~gt(int_level(t_139), minus(int_level(t_139), n1)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[56])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 ((~gt(level(t_139), fifo_length)) <=> (~gt(level(t_139), fifo_length))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(59,axiom,(~gt(level(t_139), fifo_length)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_1')).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (~gt(level(t_139), fifo_length)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (~gt(int_level(t_139), minus(int_level(t_139), n1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[60, 57])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(65,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')).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.43 tff(67,plain,(
% 0.19/0.43 ![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[66])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))) | ((~gt(int_level(t_139), n0)) | gt(int_level(t_139), minus(int_level(t_139), n1)))) <=> ((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))) | (~gt(int_level(t_139), n0)) | gt(int_level(t_139), minus(int_level(t_139), n1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 ((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))) | ((~gt(int_level(t_139), n0)) | gt(int_level(t_139), minus(int_level(t_139), n1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 ((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))) | (~gt(int_level(t_139), n0)) | gt(int_level(t_139), minus(int_level(t_139), n1))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 (gt(int_level(t_139), minus(int_level(t_139), n1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[71, 68, 15])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[72, 61])).
% 0.19/0.43 tff(74,plain,(~gt(int_level(t_139), n0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (^[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)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.43 tff(80,axiom,(![X_t_42: $i] : ((((p_Reset(X_t_42) | p_Wr(X_t_42)) | (~p_Rd(X_t_42))) | gt(int_level(X_t_42), n0)) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_78')).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.43 tff(83,plain,(
% 0.19/0.43 ![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))),
% 0.19/0.43 inference(skolemize,[status(sab)],[82])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 (((~![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_Wr(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))) | p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 ((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_Wr(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (((~![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_Wr(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 (((~![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_Wr(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))),
% 0.19/0.43 inference(transitivity,[status(thm)],[87, 85])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 ((~![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))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))) | p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 ((int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[90, 84, 24, 21, 18])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 (int_level(plus(t_139, n1)) = int_level(t_139)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[91, 74])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 (int_level(t_139) = int_level(plus(t_139, n1))),
% 0.19/0.43 inference(symmetry,[status(thm)],[92])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 (int_level(t_139) = fifo_length),
% 0.19/0.43 inference(transitivity,[status(thm)],[93, 14])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (gt(int_level(t_139), n0) <=> gt(fifo_length, n0)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 (gt(fifo_length, n0) <=> gt(int_level(t_139), n0)),
% 0.19/0.43 inference(symmetry,[status(thm)],[95])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 (gt(fifo_length, n0) <=> gt(fifo_length, n0)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(98,axiom,(gt(fifo_length, n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_6')).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 (gt(fifo_length, n0)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 (gt(int_level(t_139), n0)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[74, 100])).
% 0.19/0.44 % SZS output end Proof
%------------------------------------------------------------------------------