TSTP Solution File: HWV023-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV023-1 : 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 02:10:41 EDT 2022
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HWV023-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 22:03:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(gt_type, type, (
% 0.20/0.46 gt: ( $i * $i ) > $o)).
% 0.20/0.46 tff(n0_type, type, (
% 0.20/0.46 n0: $i)).
% 0.20/0.46 tff(int_level_type, type, (
% 0.20/0.46 int_level: $i > $i)).
% 0.20/0.46 tff(plus_type, type, (
% 0.20/0.46 plus: ( $i * $i ) > $i)).
% 0.20/0.46 tff(level_type, type, (
% 0.20/0.46 level: $i > $i)).
% 0.20/0.46 tff(t_139_type, type, (
% 0.20/0.46 t_139: $i)).
% 0.20/0.46 tff(minus_type, type, (
% 0.20/0.46 minus: ( $i * $i ) > $i)).
% 0.20/0.46 tff(n1_type, type, (
% 0.20/0.46 n1: $i)).
% 0.20/0.46 tff(p_Reset_type, type, (
% 0.20/0.46 p_Reset: $i > $o)).
% 0.20/0.46 tff(p_Rd_type, type, (
% 0.20/0.46 p_Rd: $i > $o)).
% 0.20/0.46 tff(p_Wr_type, type, (
% 0.20/0.46 p_Wr: $i > $o)).
% 0.20/0.46 tff(p_Empty_type, type, (
% 0.20/0.46 p_Empty: $i > $o)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (^[X_t_32: $i] : refl((level(X_t_32) = int_level(X_t_32)) <=> (level(X_t_32) = int_level(X_t_32)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32)) <=> ![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32)) <=> ![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(4,axiom,(![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_21')).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.46 tff(6,plain,(
% 0.20/0.46 ![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.46 inference(skolemize,[status(sab)],[5])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 ((~![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))) | (level(t_139) = int_level(t_139))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (level(t_139) = int_level(t_139)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 ((n1 = plus(n0, n1)) <=> (level(t_139) = plus(n0, level(t_139)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 ((n1 = plus(n0, n1)) <=> (n1 = plus(n0, n1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(12,axiom,(n1 = plus(n0, n1)), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_20')).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (n1 = plus(n0, n1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (level(t_139) = plus(n0, level(t_139))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (plus(n0, level(t_139)) = level(t_139)),
% 0.20/0.46 inference(symmetry,[status(thm)],[14])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (plus(n0, level(t_139)) = int_level(t_139)),
% 0.20/0.46 inference(transitivity,[status(thm)],[15, 9])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (minus(plus(n0, level(t_139)), level(t_139)) = minus(int_level(t_139), level(t_139))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (minus(int_level(t_139), level(t_139)) = minus(plus(n0, level(t_139)), level(t_139))),
% 0.20/0.46 inference(symmetry,[status(thm)],[17])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (int_level(t_139) = level(t_139)),
% 0.20/0.46 inference(symmetry,[status(thm)],[9])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 (int_level(t_139) = plus(n0, level(t_139))),
% 0.20/0.46 inference(transitivity,[status(thm)],[19, 14])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (gt(int_level(t_139), n0) <=> gt(plus(n0, level(t_139)), n0)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[20])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 (gt(plus(n0, level(t_139)), n0) <=> gt(int_level(t_139), n0)),
% 0.20/0.46 inference(symmetry,[status(thm)],[21])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 (^[X_1: $i] : refl(gt(plus(X_1, level(t_139)), n0) <=> gt(plus(X_1, level(t_139)), n0))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (![X_1: $i] : gt(plus(X_1, level(t_139)), n0) <=> ![X_1: $i] : gt(plus(X_1, level(t_139)), n0)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 (^[X_1: $i] : rewrite(gt(plus(X_1, n1), n0) <=> gt(plus(X_1, level(t_139)), n0))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 (![X_1: $i] : gt(plus(X_1, n1), n0) <=> ![X_1: $i] : gt(plus(X_1, level(t_139)), n0)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (![X_1: $i] : gt(plus(X_1, n1), n0) <=> ![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(28,axiom,(![X_1: $i] : gt(plus(X_1, n1), n0)), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_2')).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (![X_1: $i] : gt(plus(X_1, level(t_139)), n0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.20/0.47 tff(31,plain,(
% 0.20/0.47 ![X_1: $i] : gt(plus(X_1, level(t_139)), n0)),
% 0.20/0.47 inference(skolemize,[status(sab)],[30])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (![X_1: $i] : gt(plus(X_1, level(t_139)), n0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 ((~![X_1: $i] : gt(plus(X_1, level(t_139)), n0)) | gt(plus(n0, level(t_139)), n0)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (gt(plus(n0, level(t_139)), n0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (gt(int_level(t_139), n0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[34, 22])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 ((~p_Reset(t_139)) <=> (~p_Reset(t_139))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(37,axiom,(~p_Reset(t_139)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_4')).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (~p_Reset(t_139)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (p_Rd(t_139) <=> p_Rd(t_139)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(40,axiom,(p_Rd(t_139)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_3')).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (p_Rd(t_139)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 ((~p_Wr(t_139)) <=> (~p_Wr(t_139))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(43,axiom,(~p_Wr(t_139)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_2')).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 (~p_Wr(t_139)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (^[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, level(t_139))) = minus(int_level(X_t_42), level(t_139)))) <=> (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, level(t_139))) = minus(int_level(X_t_42), level(t_139)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (![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, level(t_139))) = minus(int_level(X_t_42), level(t_139)))) <=> ![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (^[X_t_42: $i] : trans(monotonicity(rewrite((int_level(plus(X_t_42, n1)) = minus(int_level(X_t_42), n1)) <=> (int_level(plus(X_t_42, level(t_139))) = minus(int_level(X_t_42), level(t_139)))), ((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, level(t_139))) = minus(int_level(X_t_42), level(t_139)))))), 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, level(t_139))) = minus(int_level(X_t_42), level(t_139)))) <=> (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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))), ((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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.47 tff(52,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/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_71')).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[54, 48])).
% 0.20/0.47 tff(56,plain,(
% 0.20/0.47 ![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[55])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (((~![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))) | (p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139))))) <=> ((~![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))) | p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 ((p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139)))) <=> (p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (((~![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))) | (p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139))))) <=> ((~![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))) | (p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (((~![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))) | (p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139))))) <=> ((~![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))) | p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[60, 58])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 ((~![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))) | (p_Reset(t_139) | (~p_Rd(t_139)) | p_Wr(t_139) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 ((~![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, level(t_139))) = minus(int_level(X_t_42), level(t_139))))) | p_Reset(t_139) | p_Wr(t_139) | (~p_Rd(t_139)) | (~gt(int_level(t_139), n0)) | (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 ((~gt(int_level(t_139), n0)) | (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[63, 57, 44, 41, 38])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 (int_level(plus(t_139, level(t_139))) = minus(int_level(t_139), level(t_139))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[64, 35])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (int_level(plus(t_139, level(t_139))) = minus(plus(n0, level(t_139)), level(t_139))),
% 0.20/0.47 inference(transitivity,[status(thm)],[65, 18])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (gt(plus(n0, level(t_139)), int_level(plus(t_139, level(t_139)))) <=> gt(plus(n0, level(t_139)), minus(plus(n0, level(t_139)), level(t_139)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 (gt(plus(n0, level(t_139)), minus(plus(n0, level(t_139)), level(t_139))) <=> gt(plus(n0, level(t_139)), int_level(plus(t_139, level(t_139))))),
% 0.20/0.48 inference(symmetry,[status(thm)],[67])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 (^[X_2: $i] : refl(((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139)))) <=> ((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139)))) <=> ![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (^[X_2: $i] : rewrite(((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1))) <=> ((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 (![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, level(t_139))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1))) <=> ![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(74,axiom,(![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_3')).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, n1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[75, 72])).
% 0.20/0.48 tff(77,plain,(
% 0.20/0.48 ![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[76])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.20/0.48 tff(79,plain,
% 0.20/0.48 (((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139))))) | ((~gt(plus(n0, level(t_139)), n0)) | gt(plus(n0, level(t_139)), minus(plus(n0, level(t_139)), level(t_139))))) <=> ((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139))))) | (~gt(plus(n0, level(t_139)), n0)) | gt(plus(n0, level(t_139)), minus(plus(n0, level(t_139)), level(t_139))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(80,plain,
% 0.20/0.48 ((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139))))) | ((~gt(plus(n0, level(t_139)), n0)) | gt(plus(n0, level(t_139)), minus(plus(n0, level(t_139)), level(t_139))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 ((~![X_2: $i] : ((~gt(X_2, n0)) | gt(X_2, minus(X_2, level(t_139))))) | (~gt(plus(n0, level(t_139)), n0)) | gt(plus(n0, level(t_139)), minus(plus(n0, level(t_139)), level(t_139)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.48 tff(82,plain,
% 0.20/0.48 (gt(plus(n0, level(t_139)), minus(plus(n0, level(t_139)), level(t_139)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[81, 78, 34])).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 (gt(plus(n0, level(t_139)), int_level(plus(t_139, level(t_139))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[82, 68])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 ((n0 = int_level(plus(t_139, level(t_139)))) <=> (int_level(plus(t_139, level(t_139))) = n0)),
% 0.20/0.48 inference(commutativity,[status(thm)],[])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 ((int_level(plus(t_139, level(t_139))) = n0) <=> (n0 = int_level(plus(t_139, level(t_139))))),
% 0.20/0.48 inference(symmetry,[status(thm)],[84])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 ((~(int_level(plus(t_139, level(t_139))) = n0)) <=> (~(n0 = int_level(plus(t_139, level(t_139)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[85])).
% 0.20/0.48 tff(87,plain,
% 0.20/0.48 ((~p_Empty(plus(t_139, n1))) <=> (~p_Empty(plus(t_139, level(t_139))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 ((~p_Empty(plus(t_139, n1))) <=> (~p_Empty(plus(t_139, n1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(89,axiom,(~p_Empty(plus(t_139, n1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_5')).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 (~p_Empty(plus(t_139, n1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (~p_Empty(plus(t_139, level(t_139)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[90, 87])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 (^[X_t_35: $i] : refl((p_Empty(X_t_35) | (~(int_level(X_t_35) = n0))) <=> (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0))) <=> ![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0))) <=> ![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 (^[X_t_35: $i] : rewrite(((~(int_level(X_t_35) = n0)) | p_Empty(X_t_35)) <=> (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 (![X_t_35: $i] : ((~(int_level(X_t_35) = n0)) | p_Empty(X_t_35)) <=> ![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.48 tff(97,axiom,(![X_t_35: $i] : ((~(int_level(X_t_35) = n0)) | p_Empty(X_t_35))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_24')).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.48 tff(99,plain,
% 0.20/0.48 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.20/0.48 tff(100,plain,(
% 0.20/0.48 ![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[99])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 (((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | (p_Empty(plus(t_139, level(t_139))) | (~(int_level(plus(t_139, level(t_139))) = n0)))) <=> ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | p_Empty(plus(t_139, level(t_139))) | (~(int_level(plus(t_139, level(t_139))) = n0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | (p_Empty(plus(t_139, level(t_139))) | (~(int_level(plus(t_139, level(t_139))) = n0)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | p_Empty(plus(t_139, level(t_139))) | (~(int_level(plus(t_139, level(t_139))) = n0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 (~(int_level(plus(t_139, level(t_139))) = n0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[104, 101, 91])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 (~(n0 = int_level(plus(t_139, level(t_139))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[105, 86])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 (^[Y_16: $i, X_15: $i] : refl((gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16))) <=> (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16))) <=> ![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.48 tff(109,plain,
% 0.20/0.48 (^[Y_16: $i, X_15: $i] : trans(monotonicity(rewrite((~gt(plus(X_15, n1), Y_16)) <=> (~gt(plus(X_15, level(t_139)), Y_16))), ((gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16))) <=> (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16))))), rewrite((gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16))) <=> (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16)))), ((gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16))) <=> (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(110,plain,
% 0.20/0.48 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16))) <=> ![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16))) <=> ![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(112,plain,
% 0.20/0.48 (^[Y_16: $i, X_15: $i] : rewrite((((~gt(plus(X_15, n1), Y_16)) | gt(X_15, Y_16)) | (X_15 = Y_16)) <=> (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (![Y_16: $i, X_15: $i] : (((~gt(plus(X_15, n1), Y_16)) | gt(X_15, Y_16)) | (X_15 = Y_16)) <=> ![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.48 tff(114,axiom,(![Y_16: $i, X_15: $i] : (((~gt(plus(X_15, n1), Y_16)) | gt(X_15, Y_16)) | (X_15 = Y_16))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_11')).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[116, 110])).
% 0.20/0.48 tff(118,plain,(
% 0.20/0.48 ![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[117])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[118, 108])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 (((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16)))) | (gt(n0, int_level(plus(t_139, level(t_139)))) | (n0 = int_level(plus(t_139, level(t_139)))) | (~gt(plus(n0, level(t_139)), int_level(plus(t_139, level(t_139))))))) <=> ((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16)))) | gt(n0, int_level(plus(t_139, level(t_139)))) | (n0 = int_level(plus(t_139, level(t_139)))) | (~gt(plus(n0, level(t_139)), int_level(plus(t_139, level(t_139))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 ((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16)))) | (gt(n0, int_level(plus(t_139, level(t_139)))) | (n0 = int_level(plus(t_139, level(t_139)))) | (~gt(plus(n0, level(t_139)), int_level(plus(t_139, level(t_139))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 ((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, level(t_139)), Y_16)))) | gt(n0, int_level(plus(t_139, level(t_139)))) | (n0 = int_level(plus(t_139, level(t_139)))) | (~gt(plus(n0, level(t_139)), int_level(plus(t_139, level(t_139)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 (gt(n0, int_level(plus(t_139, level(t_139)))) | (n0 = int_level(plus(t_139, level(t_139)))) | (~gt(plus(n0, level(t_139)), int_level(plus(t_139, level(t_139)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[122, 119])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (gt(n0, int_level(plus(t_139, level(t_139))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[123, 106, 83])).
% 0.20/0.48 tff(125,assumption,(~gt(int_level(plus(t_139, level(t_139))), n0)), introduced(assumption)).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 (^[X_25: $i] : refl(((X_25 = n0) | gt(X_25, n0)) <=> ((X_25 = n0) | gt(X_25, n0)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (![X_25: $i] : ((X_25 = n0) | gt(X_25, n0)) <=> ![X_25: $i] : ((X_25 = n0) | gt(X_25, n0))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.49 (![X_25: $i] : ((X_25 = n0) | gt(X_25, n0)) <=> ![X_25: $i] : ((X_25 = n0) | gt(X_25, n0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(129,axiom,(![X_25: $i] : ((X_25 = n0) | gt(X_25, n0))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_15')).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 (![X_25: $i] : ((X_25 = n0) | gt(X_25, n0))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.49 tff(131,plain,(
% 0.20/0.49 ![X_25: $i] : ((X_25 = n0) | gt(X_25, n0))),
% 0.20/0.49 inference(skolemize,[status(sab)],[130])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (![X_25: $i] : ((X_25 = n0) | gt(X_25, n0))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (((~![X_25: $i] : ((X_25 = n0) | gt(X_25, n0))) | ((int_level(plus(t_139, level(t_139))) = n0) | gt(int_level(plus(t_139, level(t_139))), n0))) <=> ((~![X_25: $i] : ((X_25 = n0) | gt(X_25, n0))) | (int_level(plus(t_139, level(t_139))) = n0) | gt(int_level(plus(t_139, level(t_139))), n0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 ((~![X_25: $i] : ((X_25 = n0) | gt(X_25, n0))) | ((int_level(plus(t_139, level(t_139))) = n0) | gt(int_level(plus(t_139, level(t_139))), n0))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 ((~![X_25: $i] : ((X_25 = n0) | gt(X_25, n0))) | (int_level(plus(t_139, level(t_139))) = n0) | gt(int_level(plus(t_139, level(t_139))), n0)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[135, 132, 105, 125])).
% 0.20/0.49 tff(137,plain,(gt(int_level(plus(t_139, level(t_139))), n0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20))) <=> ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20))) <=> ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 (^[Z_21: $i, Y_20: $i, X_19: $i] : rewrite((((~gt(Z_21, Y_20)) | gt(Z_21, X_19)) | (~gt(Y_20, X_19))) <=> ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 (![Z_21: $i, Y_20: $i, X_19: $i] : (((~gt(Z_21, Y_20)) | gt(Z_21, X_19)) | (~gt(Y_20, X_19))) <=> ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.49 tff(142,axiom,(![Z_21: $i, Y_20: $i, X_19: $i] : (((~gt(Z_21, Y_20)) | gt(Z_21, X_19)) | (~gt(Y_20, X_19)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_13')).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.20/0.49 tff(145,plain,(
% 0.20/0.49 ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[144])).
% 0.20/0.49 tff(146,plain,
% 0.20/0.49 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 (((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | ((~gt(int_level(plus(t_139, level(t_139))), n0)) | (~gt(n0, int_level(plus(t_139, level(t_139))))) | gt(n0, n0))) <=> ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | (~gt(int_level(plus(t_139, level(t_139))), n0)) | (~gt(n0, int_level(plus(t_139, level(t_139))))) | gt(n0, n0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 (((~gt(int_level(plus(t_139, level(t_139))), n0)) | gt(n0, n0) | (~gt(n0, int_level(plus(t_139, level(t_139)))))) <=> ((~gt(int_level(plus(t_139, level(t_139))), n0)) | (~gt(n0, int_level(plus(t_139, level(t_139))))) | gt(n0, n0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(149,plain,
% 0.20/0.49 (((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | ((~gt(int_level(plus(t_139, level(t_139))), n0)) | gt(n0, n0) | (~gt(n0, int_level(plus(t_139, level(t_139))))))) <=> ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | ((~gt(int_level(plus(t_139, level(t_139))), n0)) | (~gt(n0, int_level(plus(t_139, level(t_139))))) | gt(n0, n0)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[148])).
% 0.20/0.49 tff(150,plain,
% 0.20/0.49 (((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | ((~gt(int_level(plus(t_139, level(t_139))), n0)) | gt(n0, n0) | (~gt(n0, int_level(plus(t_139, level(t_139))))))) <=> ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | (~gt(int_level(plus(t_139, level(t_139))), n0)) | (~gt(n0, int_level(plus(t_139, level(t_139))))) | gt(n0, n0))),
% 0.20/0.49 inference(transitivity,[status(thm)],[149, 147])).
% 0.20/0.49 tff(151,plain,
% 0.20/0.49 ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | ((~gt(int_level(plus(t_139, level(t_139))), n0)) | gt(n0, n0) | (~gt(n0, int_level(plus(t_139, level(t_139))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(152,plain,
% 0.20/0.49 ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | (~gt(int_level(plus(t_139, level(t_139))), n0)) | (~gt(n0, int_level(plus(t_139, level(t_139))))) | gt(n0, n0)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.49 tff(153,plain,
% 0.20/0.49 (gt(n0, n0)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[152, 146, 137, 124])).
% 0.20/0.49 tff(154,plain,
% 0.20/0.49 (^[X_28: $i] : refl((~gt(X_28, X_28)) <=> (~gt(X_28, X_28)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(155,plain,
% 0.20/0.49 (![X_28: $i] : (~gt(X_28, X_28)) <=> ![X_28: $i] : (~gt(X_28, X_28))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[154])).
% 0.20/0.49 tff(156,plain,
% 0.20/0.49 (![X_28: $i] : (~gt(X_28, X_28)) <=> ![X_28: $i] : (~gt(X_28, X_28))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(157,axiom,(![X_28: $i] : (~gt(X_28, X_28))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_17')).
% 0.20/0.49 tff(158,plain,
% 0.20/0.49 (![X_28: $i] : (~gt(X_28, X_28))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.49 tff(159,plain,(
% 0.20/0.49 ![X_28: $i] : (~gt(X_28, X_28))),
% 0.20/0.49 inference(skolemize,[status(sab)],[158])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 (![X_28: $i] : (~gt(X_28, X_28))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.20/0.49 tff(161,plain,
% 0.20/0.49 ((~![X_28: $i] : (~gt(X_28, X_28))) | (~gt(n0, n0))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(162,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[161, 160, 153])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------