%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV010-1 : 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 05:08:54 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
% 0.11/0.12 % Problem : HWV010-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 17:19:32 EDT 2025
% 0.20/0.34 % 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(t_139_type, type, (
% 0.20/0.40 t_139: $i)).
% 0.20/0.40 tff(level_type, type, (
% 0.20/0.40 level: $i > $i)).
% 0.20/0.40 tff(p_Empty_type, type, (
% 0.20/0.40 p_Empty: $i > $o)).
% 0.20/0.40 tff(1,assumption,(~(level(t_139) = n0)), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 ((p_Empty(t_139) | (level(t_139) = n0)) <=> (p_Empty(t_139) | (level(t_139) = n0))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(3,axiom,(p_Empty(t_139) | (level(t_139) = n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_2')).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (p_Empty(t_139) | (level(t_139) = n0)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (p_Empty(t_139)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.20/0.40 tff(6,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(7,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)],[6])).
% 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))) <=> ![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(9,axiom,(![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_25')).
% 0.20/0.40 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, 8])).
% 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)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[10])).
% 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)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 7])).
% 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)))) | ((~p_Empty(t_139)) | (int_level(t_139) = n0))) <=> ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | (~p_Empty(t_139)) | (int_level(t_139) = n0))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (((int_level(t_139) = n0) | (~p_Empty(t_139))) <=> ((~p_Empty(t_139)) | (int_level(t_139) = n0))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(15,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)))) | ((~p_Empty(t_139)) | (int_level(t_139) = n0)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[14])).
% 0.20/0.40 tff(16,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)))) | (~p_Empty(t_139)) | (int_level(t_139) = n0))),
% 0.20/0.40 inference(transitivity,[status(thm)],[15, 13])).
% 0.20/0.40 tff(17,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(18,plain,
% 0.20/0.40 ((~![X_t_36: $i] : ((int_level(X_t_36) = n0) | (~p_Empty(X_t_36)))) | (~p_Empty(t_139)) | (int_level(t_139) = n0)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (int_level(t_139) = n0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[18, 12, 5])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (^[X_t_32: $i] : refl((level(X_t_32) = int_level(X_t_32)) <=> (level(X_t_32) = int_level(X_t_32)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![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))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![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))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(23,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')).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.41 tff(25,plain,(
% 0.20/0.41 ![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.41 inference(skolemize,[status(sab)],[24])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~![X_t_32: $i] : (level(X_t_32) = int_level(X_t_32))) | (level(t_139) = int_level(t_139))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (level(t_139) = int_level(t_139)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (level(t_139) = n0),
% 0.20/0.41 inference(transitivity,[status(thm)],[28, 19])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[1, 29])).
% 0.20/0.41 tff(31,plain,(level(t_139) = n0), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (int_level(t_139) = level(t_139)),
% 0.20/0.41 inference(symmetry,[status(thm)],[28])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (int_level(t_139) = n0),
% 0.20/0.41 inference(transitivity,[status(thm)],[32, 31])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (((~p_Empty(t_139)) | (~(level(t_139) = n0))) <=> ((~p_Empty(t_139)) | (~(level(t_139) = n0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(35,axiom,((~p_Empty(t_139)) | (~(level(t_139) = n0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_1')).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 ((~p_Empty(t_139)) | (~(level(t_139) = n0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (~p_Empty(t_139)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[36, 31])).
% 0.20/0.41 tff(38,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(39,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)],[38])).
% 0.20/0.41 tff(40,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(41,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(42,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.41 tff(43,axiom,(![X_t_35: $i] : ((~(int_level(X_t_35) = n0)) | p_Empty(X_t_35))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax','axiom_24')).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.41 tff(46,plain,(
% 0.20/0.41 ![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[45])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | (p_Empty(t_139) | (~(int_level(t_139) = n0)))) <=> ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | p_Empty(t_139) | (~(int_level(t_139) = n0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | (p_Empty(t_139) | (~(int_level(t_139) = n0)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((~![X_t_35: $i] : (p_Empty(X_t_35) | (~(int_level(X_t_35) = n0)))) | p_Empty(t_139) | (~(int_level(t_139) = n0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (~(int_level(t_139) = n0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[50, 47, 37])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[51, 33])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------