%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV017-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 Jun 21 05:08:56 AM UTC 2025
% Result : Unsatisfiable 0.24s 0.44s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : HWV017-1 : TPTP v9.0.0. Released v2.5.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 17:19:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.24/0.44 % SZS status Unsatisfiable
% 0.24/0.44 % SZS output start Proof
% 0.24/0.44 tff(gt_type, type, (
% 0.24/0.44 gt: ( $i * $i ) > $o)).
% 0.24/0.44 tff(n0_type, type, (
% 0.24/0.44 n0: $i)).
% 0.24/0.44 tff(int_level_type, type, (
% 0.24/0.44 int_level: $i > $i)).
% 0.24/0.44 tff(t_139_type, type, (
% 0.24/0.44 t_139: $i)).
% 0.24/0.44 tff(fifo_length_type, type, (
% 0.24/0.44 fifo_length: $i)).
% 0.24/0.44 tff(plus_type, type, (
% 0.24/0.44 plus: ( $i * $i ) > $i)).
% 0.24/0.44 tff(n1_type, type, (
% 0.24/0.44 n1: $i)).
% 0.24/0.44 tff(p_Full_type, type, (
% 0.24/0.44 p_Full: $i > $o)).
% 0.24/0.44 tff(minus_type, type, (
% 0.24/0.44 minus: ( $i * $i ) > $i)).
% 0.24/0.44 tff(level_type, type, (
% 0.24/0.44 level: $i > $i)).
% 0.24/0.44 tff(p_Reset_type, type, (
% 0.24/0.44 p_Reset: $i > $o)).
% 0.24/0.44 tff(p_Wr_type, type, (
% 0.24/0.44 p_Wr: $i > $o)).
% 0.24/0.44 tff(p_Rd_type, type, (
% 0.24/0.44 p_Rd: $i > $o)).
% 0.24/0.44 tff(1,plain,
% 0.24/0.44 (p_Full(plus(t_139, n1)) <=> p_Full(plus(t_139, n1))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(2,axiom,(p_Full(plus(t_139, n1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_5')).
% 0.24/0.44 tff(3,plain,
% 0.24/0.44 (p_Full(plus(t_139, n1))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.24/0.44 tff(4,plain,
% 0.24/0.44 (^[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))))),
% 0.24/0.44 inference(bind,[status(th)],[])).
% 0.24/0.44 tff(5,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(quant_intro,[status(thm)],[4])).
% 0.24/0.44 tff(6,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 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')).
% 0.24/0.44 tff(8,plain,
% 0.24/0.44 (![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.24/0.44 tff(9,plain,(
% 0.24/0.44 ![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))),
% 0.24/0.44 inference(skolemize,[status(sab)],[8])).
% 0.24/0.44 tff(10,plain,
% 0.24/0.44 (![X_t_34: $i] : ((int_level(X_t_34) = fifo_length) | (~p_Full(X_t_34)))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.24/0.44 tff(11,plain,
% 0.24/0.44 (((~![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))))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(12,plain,
% 0.24/0.44 ((~![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))))),
% 0.24/0.44 inference(quant_inst,[status(thm)],[])).
% 0.24/0.44 tff(13,plain,
% 0.24/0.44 ((~![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)))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.24/0.44 tff(14,plain,
% 0.24/0.44 (int_level(plus(t_139, n1)) = fifo_length),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.24/0.44 tff(15,assumption,(gt(int_level(t_139), n0)), introduced(assumption)).
% 0.24/0.44 tff(16,plain,
% 0.24/0.44 ((~p_Reset(t_139)) <=> (~p_Reset(t_139))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(17,axiom,(~p_Reset(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_4')).
% 0.24/0.44 tff(18,plain,
% 0.24/0.44 (~p_Reset(t_139)),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.24/0.44 tff(19,plain,
% 0.24/0.44 ((~p_Wr(t_139)) <=> (~p_Wr(t_139))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(20,axiom,(~p_Wr(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_3')).
% 0.24/0.44 tff(21,plain,
% 0.24/0.44 (~p_Wr(t_139)),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.24/0.44 tff(22,plain,
% 0.24/0.44 (p_Rd(t_139) <=> p_Rd(t_139)),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(23,axiom,(p_Rd(t_139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_2')).
% 0.24/0.44 tff(24,plain,
% 0.24/0.44 (p_Rd(t_139)),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.24/0.44 tff(25,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(26,plain,
% 0.24/0.44 (^[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))))),
% 0.24/0.44 inference(bind,[status(th)],[])).
% 0.24/0.44 tff(27,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(quant_intro,[status(thm)],[26])).
% 0.24/0.44 tff(28,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(29,plain,
% 0.24/0.44 (^[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)) = 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)))))),
% 0.24/0.44 inference(bind,[status(th)],[])).
% 0.24/0.44 tff(30,plain,
% 0.24/0.44 (![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)) = 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)))),
% 0.24/0.44 inference(quant_intro,[status(thm)],[29])).
% 0.24/0.44 tff(31,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')).
% 0.24/0.44 tff(32,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.24/0.44 tff(33,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.24/0.44 tff(34,plain,(
% 0.24/0.44 ![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)))),
% 0.24/0.44 inference(skolemize,[status(sab)],[33])).
% 0.24/0.44 tff(35,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.24/0.44 tff(36,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.24/0.44 tff(37,plain,
% 0.24/0.44 (((~![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)))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(38,plain,
% 0.24/0.44 ((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)))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(39,plain,
% 0.24/0.44 (((~![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))))),
% 0.24/0.44 inference(monotonicity,[status(thm)],[38])).
% 0.24/0.44 tff(40,plain,
% 0.24/0.44 (((~![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)))),
% 0.24/0.44 inference(transitivity,[status(thm)],[39, 37])).
% 0.24/0.44 tff(41,plain,
% 0.24/0.44 ((~![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)))),
% 0.24/0.44 inference(quant_inst,[status(thm)],[])).
% 0.24/0.44 tff(42,plain,
% 0.24/0.44 ((~![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))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.24/0.44 tff(43,plain,
% 0.24/0.44 ((~gt(int_level(t_139), n0)) | (int_level(plus(t_139, n1)) = minus(int_level(t_139), n1))),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[42, 36, 24, 21, 18])).
% 0.24/0.45 tff(44,plain,
% 0.24/0.45 (int_level(plus(t_139, n1)) = minus(int_level(t_139), n1)),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[43, 15])).
% 0.24/0.45 tff(45,plain,
% 0.24/0.45 (minus(int_level(t_139), n1) = int_level(plus(t_139, n1))),
% 0.24/0.45 inference(symmetry,[status(thm)],[44])).
% 0.24/0.45 tff(46,plain,
% 0.24/0.45 (minus(int_level(t_139), n1) = fifo_length),
% 0.24/0.45 inference(transitivity,[status(thm)],[45, 14])).
% 0.24/0.45 tff(47,plain,
% 0.24/0.45 (^[X_t_32: $i] : refl((level(X_t_32) = int_level(X_t_32)) <=> (level(X_t_32) = int_level(X_t_32)))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(48,plain,
% 0.24/0.45 (![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))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[47])).
% 0.24/0.45 tff(49,plain,
% 0.24/0.45 (![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))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(50,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')).
% 0.24/0.45 tff(51,plain,
% 0.24/0.45 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.24/0.45 tff(52,plain,(
% 0.24/0.45 ![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.24/0.45 inference(skolemize,[status(sab)],[51])).
% 0.24/0.45 tff(53,plain,
% 0.24/0.45 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.24/0.45 tff(54,plain,
% 0.24/0.45 ((~![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))) | (level(t_139) = int_level(t_139))),
% 0.24/0.45 inference(quant_inst,[status(thm)],[])).
% 0.24/0.45 tff(55,plain,
% 0.24/0.45 (level(t_139) = int_level(t_139)),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.24/0.45 tff(56,plain,
% 0.24/0.45 (int_level(t_139) = level(t_139)),
% 0.24/0.45 inference(symmetry,[status(thm)],[55])).
% 0.24/0.45 tff(57,plain,
% 0.24/0.45 (gt(int_level(t_139), minus(int_level(t_139), n1)) <=> gt(level(t_139), fifo_length)),
% 0.24/0.45 inference(monotonicity,[status(thm)],[56, 46])).
% 0.24/0.45 tff(58,plain,
% 0.24/0.45 (gt(level(t_139), fifo_length) <=> gt(int_level(t_139), minus(int_level(t_139), n1))),
% 0.24/0.45 inference(symmetry,[status(thm)],[57])).
% 0.24/0.45 tff(59,plain,
% 0.24/0.45 ((~gt(level(t_139), fifo_length)) <=> (~gt(int_level(t_139), minus(int_level(t_139), n1)))),
% 0.24/0.45 inference(monotonicity,[status(thm)],[58])).
% 0.24/0.45 tff(60,plain,
% 0.24/0.45 ((~gt(level(t_139), fifo_length)) <=> (~gt(level(t_139), fifo_length))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(61,axiom,(~gt(level(t_139), fifo_length)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_1')).
% 0.24/0.45 tff(62,plain,
% 0.24/0.45 (~gt(level(t_139), fifo_length)),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.24/0.45 tff(63,plain,
% 0.24/0.45 (~gt(int_level(t_139), minus(int_level(t_139), n1))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.24/0.45 tff(64,plain,
% 0.24/0.45 (^[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))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(65,plain,
% 0.24/0.45 (![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)))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[64])).
% 0.24/0.45 tff(66,plain,
% 0.24/0.45 (![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)))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(67,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')).
% 0.24/0.45 tff(68,plain,
% 0.24/0.45 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.24/0.45 tff(69,plain,(
% 0.24/0.45 ![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.24/0.45 inference(skolemize,[status(sab)],[68])).
% 0.24/0.45 tff(70,plain,
% 0.24/0.45 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.24/0.45 tff(71,plain,
% 0.24/0.45 (((~![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)))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(72,plain,
% 0.24/0.45 ((~![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)))),
% 0.24/0.45 inference(quant_inst,[status(thm)],[])).
% 0.24/0.45 tff(73,plain,
% 0.24/0.45 ((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))) | (~gt(int_level(t_139), n0)) | gt(int_level(t_139), minus(int_level(t_139), n1))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.24/0.45 tff(74,plain,
% 0.24/0.45 (gt(int_level(t_139), minus(int_level(t_139), n1))),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[73, 70, 15])).
% 0.24/0.45 tff(75,plain,
% 0.24/0.45 ($false),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[74, 63])).
% 0.24/0.45 tff(76,plain,(~gt(int_level(t_139), n0)), inference(lemma,lemma(discharge,[]))).
% 0.24/0.45 tff(77,plain,
% 0.24/0.45 (^[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)))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(78,plain,
% 0.24/0.45 (![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)) = 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))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.24/0.45 tff(79,plain,
% 0.24/0.45 (![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)) = 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))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(80,plain,
% 0.24/0.45 (^[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))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(81,plain,
% 0.24/0.45 (![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))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.24/0.45 tff(82,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')).
% 0.24/0.45 tff(83,plain,
% 0.24/0.45 (![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)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.24/0.45 tff(84,plain,
% 0.24/0.45 (![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)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.24/0.45 tff(85,plain,(
% 0.24/0.45 ![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)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))),
% 0.24/0.45 inference(skolemize,[status(sab)],[84])).
% 0.24/0.45 tff(86,plain,
% 0.24/0.45 (![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)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.24/0.45 tff(87,plain,
% 0.24/0.45 (((~![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)) = 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))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(88,plain,
% 0.24/0.45 ((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))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(89,plain,
% 0.24/0.45 (((~![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)) = 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)))),
% 0.24/0.45 inference(monotonicity,[status(thm)],[88])).
% 0.24/0.45 tff(90,plain,
% 0.24/0.45 (((~![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)) = 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))),
% 0.24/0.45 inference(transitivity,[status(thm)],[89, 87])).
% 0.24/0.45 tff(91,plain,
% 0.24/0.45 ((~![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)) = 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))),
% 0.24/0.45 inference(quant_inst,[status(thm)],[])).
% 0.24/0.45 tff(92,plain,
% 0.24/0.45 ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | (int_level(plus(X_t_42, n1)) = int_level(X_t_42)) | gt(int_level(X_t_42), n0))) | p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.24/0.45 tff(93,plain,
% 0.24/0.45 ((int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[92, 86, 24, 21, 18])).
% 0.24/0.45 tff(94,plain,
% 0.24/0.45 (int_level(plus(t_139, n1)) = int_level(t_139)),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[93, 76])).
% 0.24/0.46 tff(95,plain,
% 0.24/0.46 (int_level(t_139) = int_level(plus(t_139, n1))),
% 0.24/0.46 inference(symmetry,[status(thm)],[94])).
% 0.24/0.46 tff(96,plain,
% 0.24/0.46 (int_level(t_139) = fifo_length),
% 0.24/0.46 inference(transitivity,[status(thm)],[95, 14])).
% 0.24/0.46 tff(97,plain,
% 0.24/0.46 (gt(int_level(t_139), n0) <=> gt(fifo_length, n0)),
% 0.24/0.46 inference(monotonicity,[status(thm)],[96])).
% 0.24/0.46 tff(98,plain,
% 0.24/0.46 (gt(fifo_length, n0) <=> gt(int_level(t_139), n0)),
% 0.24/0.46 inference(symmetry,[status(thm)],[97])).
% 0.24/0.46 tff(99,plain,
% 0.24/0.46 (gt(fifo_length, n0) <=> gt(fifo_length, n0)),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(100,axiom,(gt(fifo_length, n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_6')).
% 0.24/0.46 tff(101,plain,
% 0.24/0.46 (gt(fifo_length, n0)),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.24/0.46 tff(102,plain,
% 0.24/0.46 (gt(int_level(t_139), n0)),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[101, 98])).
% 0.24/0.46 tff(103,plain,
% 0.24/0.46 ($false),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[76, 102])).
% 0.24/0.46 % SZS output end Proof
% 0.24/0.46 % E exiting
%------------------------------------------------------------------------------