%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV020-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:08:57 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HWV020-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 17:20:17 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(n0_type, type, (
% 0.20/0.40 n0: $i)).
% 0.20/0.40 tff(int_level_type, type, (
% 0.20/0.40 int_level: $i > $i)).
% 0.20/0.40 tff(plus_type, type, (
% 0.20/0.40 plus: ( $i * $i ) > $i)).
% 0.20/0.40 tff(n1_type, type, (
% 0.20/0.40 n1: $i)).
% 0.20/0.40 tff(t_139_type, type, (
% 0.20/0.40 t_139: $i)).
% 0.20/0.40 tff(p_Empty_type, type, (
% 0.20/0.40 p_Empty: $i > $o)).
% 0.20/0.40 tff(gt_type, type, (
% 0.20/0.40 gt: ( $i * $i ) > $o)).
% 0.20/0.40 tff(p_Reset_type, type, (
% 0.20/0.40 p_Reset: $i > $o)).
% 0.20/0.40 tff(p_Wr_type, type, (
% 0.20/0.40 p_Wr: $i > $o)).
% 0.20/0.40 tff(p_Rd_type, type, (
% 0.20/0.40 p_Rd: $i > $o)).
% 0.20/0.40 tff(p_Rd_error_type, type, (
% 0.20/0.40 p_Rd_error: $i > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (p_Empty(t_139) <=> p_Empty(t_139)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(2,axiom,(p_Empty(t_139)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_2')).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (p_Empty(t_139)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (^[X_t_36: $i] : refl(((int_level(X_t_36) = n0) | (~p_Empty(X_t_36))) <=> ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36))) <=> ![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36))) <=> ![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(7,axiom,(![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_25')).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.40 tff(9,plain,(
% 0.20/0.40 ![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[8])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | ((int_level(t_139) = n0) | (~p_Empty(t_139)))) <=> ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | (int_level(t_139) = n0) | (~p_Empty(t_139)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | ((int_level(t_139) = n0) | (~p_Empty(t_139)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | (int_level(t_139) = n0) | (~p_Empty(t_139))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (int_level(t_139) = n0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (gt(int_level(t_139), n0) <=> gt(n0, n0)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[14])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (gt(n0, n0) <=> gt(int_level(t_139), n0)),
% 0.20/0.40 inference(symmetry,[status(thm)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 ((~gt(n0, n0)) <=> (~gt(int_level(t_139), n0))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.40 tff(18,assumption,(gt(n0, n0)), introduced(assumption)).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (^[X_28: $i] : refl((~gt(X_28, X_28)) <=> (~gt(X_28, X_28)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![X_28: $i] : (~gt(X_28, X_28)) <=> ![X_28: $i] : (~gt(X_28, X_28))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![X_28: $i] : (~gt(X_28, X_28)) <=> ![X_28: $i] : (~gt(X_28, X_28))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(22,axiom,(![X_28: $i] : (~gt(X_28, X_28))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_17')).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (![X_28: $i] : (~gt(X_28, X_28))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.40 tff(24,plain,(
% 0.20/0.40 ![X_28: $i] : (~gt(X_28, X_28))),
% 0.20/0.40 inference(skolemize,[status(sab)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![X_28: $i] : (~gt(X_28, X_28))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~![X_28: $i] : (~gt(X_28, X_28))) | (~gt(n0, n0))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[26, 25, 18])).
% 0.20/0.41 tff(28,plain,(~gt(n0, n0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (~gt(int_level(t_139), n0)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 17])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ((~p_Reset(t_139)) <=> (~p_Reset(t_139))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(31,axiom,(~p_Reset(t_139)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_4')).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (~p_Reset(t_139)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 ((~p_Wr(t_139)) <=> (~p_Wr(t_139))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(34,axiom,(~p_Wr(t_139)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_3')).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (~p_Wr(t_139)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (p_Rd(t_139) <=> p_Rd(t_139)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(37,axiom,(p_Rd(t_139)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_1')).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (p_Rd(t_139)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (^[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)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.41 tff(44,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/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_78')).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.41 tff(47,plain,(
% 0.20/0.41 ![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))),
% 0.20/0.41 inference(skolemize,[status(sab)],[46])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (((~![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_Wr(t_139) | p_Reset(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_Wr(t_139) | p_Reset(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((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_Wr(t_139) | p_Reset(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (((~![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_Wr(t_139) | p_Reset(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (((~![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_Wr(t_139) | p_Reset(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0))),
% 0.20/0.41 inference(transitivity,[status(thm)],[51, 49])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((~![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))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 ((~![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_Wr(t_139) | p_Reset(t_139) | (~p_Rd(t_139)) | (int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 ((int_level(plus(t_139, n1)) = int_level(t_139)) | gt(int_level(t_139), n0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[54, 48, 38, 35, 32])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (int_level(plus(t_139, n1)) = int_level(t_139)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[55, 29])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (int_level(plus(t_139, n1)) = n0),
% 0.20/0.41 inference(transitivity,[status(thm)],[56, 14])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (^[X_t_42: $i] : refl((p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)) <=> (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0)) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (^[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)) | p_Rd_error(plus(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)) | p_Rd_error(plus(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)) | p_Rd_error(plus(X_t_42, n1))) <=> (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~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_Rd_error(plus(X_t_42, n1))) <=> (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (![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)) | p_Rd_error(plus(X_t_42, n1))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.41 tff(63,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)) | p_Rd_error(plus(X_t_42, n1)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_76')).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.41 tff(66,plain,(
% 0.20/0.41 ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.20/0.41 inference(skolemize,[status(sab)],[65])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | (p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | p_Wr(t_139) | gt(int_level(t_139), n0)) <=> (p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | (p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | p_Wr(t_139) | gt(int_level(t_139), n0))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | (p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | (p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | p_Wr(t_139) | gt(int_level(t_139), n0))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0))),
% 0.20/0.41 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | (p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | p_Wr(t_139) | gt(int_level(t_139), n0))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd_error(plus(X_t_42, n1)) | (~p_Rd(X_t_42)) | p_Wr(X_t_42) | gt(int_level(X_t_42), n0))) | p_Wr(t_139) | p_Reset(t_139) | p_Rd_error(plus(t_139, n1)) | (~p_Rd(t_139)) | gt(int_level(t_139), n0)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (p_Rd_error(plus(t_139, n1)) | gt(int_level(t_139), n0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[73, 67, 38, 35, 32])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (p_Rd_error(plus(t_139, n1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[74, 29])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (((~p_Empty(plus(t_139, n1))) | (~p_Rd_error(plus(t_139, n1)))) <=> ((~p_Empty(plus(t_139, n1))) | (~p_Rd_error(plus(t_139, n1))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(77,axiom,((~p_Empty(plus(t_139, n1))) | (~p_Rd_error(plus(t_139, n1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_5')).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 ((~p_Empty(plus(t_139, n1))) | (~p_Rd_error(plus(t_139, n1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (~p_Empty(plus(t_139, n1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.42 tff(85,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')).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.42 tff(88,plain,(
% 0.20/0.42 ![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[87])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | (p_Empty(plus(t_139, n1)) | (~(int_level(plus(t_139, n1)) = n0)))) <=> ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | p_Empty(plus(t_139, n1)) | (~(int_level(plus(t_139, n1)) = n0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | (p_Empty(plus(t_139, n1)) | (~(int_level(plus(t_139, n1)) = n0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | p_Empty(plus(t_139, n1)) | (~(int_level(plus(t_139, n1)) = n0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[92, 89, 79, 57])).
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------