%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV052-1.001.001 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:10:35 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HWV052-1.001.001 : TPTP v9.0.0. Released v4.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.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 17:28:53 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 tff(pack1_type, type, (
% 0.19/0.50 pack1: $i > $i)).
% 0.19/0.50 tff(elem_0_type, type, (
% 0.19/0.50 elem_0: $i)).
% 0.19/0.50 tff(inv_type, type, (
% 0.19/0.50 inv: $i > $i)).
% 0.19/0.50 tff(unpack1_type, type, (
% 0.19/0.50 unpack1: ( $i * $i ) > $i)).
% 0.19/0.50 tff(o_type, type, (
% 0.19/0.50 o: $i)).
% 0.19/0.50 tff(i_type, type, (
% 0.19/0.50 i: $i)).
% 0.19/0.50 tff(1,plain,
% 0.19/0.50 (^[X1: $i] : refl((unpack1(inv(X1), pack1(X1)) = X1) <=> (unpack1(inv(X1), pack1(X1)) = X1))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(2,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1) <=> ![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1)),
% 0.19/0.50 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.50 tff(3,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1) <=> ![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(4,axiom,(![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unpack1_01')).
% 0.19/0.50 tff(5,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.50 tff(6,plain,(
% 0.19/0.50 ![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1)),
% 0.19/0.50 inference(skolemize,[status(sab)],[5])).
% 0.19/0.50 tff(7,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 ((~![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1)) | (unpack1(inv(pack1(elem!0)), pack1(pack1(elem!0))) = pack1(elem!0))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 (unpack1(inv(pack1(elem!0)), pack1(pack1(elem!0))) = pack1(elem!0)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 ((~![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1)) | (unpack1(inv(pack1(pack1(elem!0))), pack1(pack1(pack1(elem!0)))) = pack1(pack1(elem!0)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(11,plain,
% 0.19/0.50 (unpack1(inv(pack1(pack1(elem!0))), pack1(pack1(pack1(elem!0)))) = pack1(pack1(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.19/0.50 tff(12,assumption,(~(pack1(pack1(elem!0)) = o)), introduced(assumption)).
% 0.19/0.50 tff(13,plain,
% 0.19/0.50 (![X: $i] : ((X = i) | (X = o)) <=> ![X: $i] : ((X = i) | (X = o))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(14,plain,
% 0.19/0.50 (^[X: $i] : rewrite(((X = o) | (X = i)) <=> ((X = i) | (X = o)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(15,plain,
% 0.19/0.50 (![X: $i] : ((X = o) | (X = i)) <=> ![X: $i] : ((X = i) | (X = o))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.50 tff(16,axiom,(![X: $i] : ((X = o) | (X = i))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bit_domain')).
% 0.19/0.50 tff(17,plain,
% 0.19/0.50 (![X: $i] : ((X = i) | (X = o))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 (![X: $i] : ((X = i) | (X = o))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.50 tff(19,plain,(
% 0.19/0.50 ![X: $i] : ((X = i) | (X = o))),
% 0.19/0.50 inference(skolemize,[status(sab)],[18])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (((~![X: $i] : ((X = i) | (X = o))) | ((pack1(pack1(elem!0)) = i) | (pack1(pack1(elem!0)) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (pack1(pack1(elem!0)) = i) | (pack1(pack1(elem!0)) = o))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | ((pack1(pack1(elem!0)) = i) | (pack1(pack1(elem!0)) = o))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | (pack1(pack1(elem!0)) = i) | (pack1(pack1(elem!0)) = o)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 ((pack1(pack1(elem!0)) = i) | (pack1(pack1(elem!0)) = o)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[22, 19])).
% 0.19/0.50 tff(24,plain,
% 0.19/0.50 (pack1(pack1(elem!0)) = i),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[23, 12])).
% 0.19/0.50 tff(25,plain,
% 0.19/0.50 ((~![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1)) | (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0))))) = pack1(inv(pack1(elem!0))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0))))) = pack1(inv(pack1(elem!0)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[25, 7])).
% 0.19/0.50 tff(27,assumption,(pack1(pack1(inv(pack1(elem!0)))) = o), introduced(assumption)).
% 0.19/0.50 tff(28,plain,
% 0.19/0.50 (o = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[27])).
% 0.19/0.50 tff(29,assumption,(pack1(pack1(elem!0)) = i), introduced(assumption)).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (i = pack1(pack1(elem!0))),
% 0.19/0.50 inference(symmetry,[status(thm)],[29])).
% 0.19/0.50 tff(31,assumption,(inv(pack1(inv(pack1(elem!0)))) = i), introduced(assumption)).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(elem!0)))) = pack1(pack1(elem!0))),
% 0.19/0.50 inference(transitivity,[status(thm)],[31, 30])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 (unpack1(inv(pack1(elem!0)), inv(pack1(inv(pack1(elem!0))))) = unpack1(inv(pack1(elem!0)), pack1(pack1(elem!0)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.50 tff(34,plain,
% 0.19/0.50 (^[X1: $i] : refl((unpack1(X1, inv(pack1(X1))) = X1) <=> (unpack1(X1, inv(pack1(X1))) = X1))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(X1, inv(pack1(X1))) = X1) <=> ![X1: $i] : (unpack1(X1, inv(pack1(X1))) = X1)),
% 0.19/0.50 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(X1, inv(pack1(X1))) = X1) <=> ![X1: $i] : (unpack1(X1, inv(pack1(X1))) = X1)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(37,axiom,(![X1: $i] : (unpack1(X1, inv(pack1(X1))) = X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unpack1_02')).
% 0.19/0.50 tff(38,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(X1, inv(pack1(X1))) = X1)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.50 tff(39,plain,(
% 0.19/0.50 ![X1: $i] : (unpack1(X1, inv(pack1(X1))) = X1)),
% 0.19/0.50 inference(skolemize,[status(sab)],[38])).
% 0.19/0.50 tff(40,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(X1, inv(pack1(X1))) = X1)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.50 tff(41,plain,
% 0.19/0.50 ((~![X1: $i] : (unpack1(X1, inv(pack1(X1))) = X1)) | (unpack1(inv(pack1(elem!0)), inv(pack1(inv(pack1(elem!0))))) = inv(pack1(elem!0)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(42,plain,
% 0.19/0.50 (unpack1(inv(pack1(elem!0)), inv(pack1(inv(pack1(elem!0))))) = inv(pack1(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.50 tff(43,plain,
% 0.19/0.50 (inv(pack1(elem!0)) = unpack1(inv(pack1(elem!0)), inv(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[42])).
% 0.19/0.50 tff(44,plain,
% 0.19/0.50 (inv(pack1(elem!0)) = pack1(elem!0)),
% 0.19/0.50 inference(transitivity,[status(thm)],[43, 33, 9])).
% 0.19/0.50 tff(45,plain,
% 0.19/0.50 (^[X: $i] : refl((~(inv(X) = X)) <=> (~(inv(X) = X)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(46,plain,
% 0.19/0.50 (![X: $i] : (~(inv(X) = X)) <=> ![X: $i] : (~(inv(X) = X))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.50 tff(47,plain,
% 0.19/0.50 (![X: $i] : (~(inv(X) = X)) <=> ![X: $i] : (~(inv(X) = X))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(48,axiom,(![X: $i] : (~(inv(X) = X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bit_inverse')).
% 0.19/0.50 tff(49,plain,
% 0.19/0.50 (![X: $i] : (~(inv(X) = X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.50 tff(50,plain,(
% 0.19/0.50 ![X: $i] : (~(inv(X) = X))),
% 0.19/0.50 inference(skolemize,[status(sab)],[49])).
% 0.19/0.50 tff(51,plain,
% 0.19/0.50 (![X: $i] : (~(inv(X) = X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.50 tff(52,plain,
% 0.19/0.50 ((~![X: $i] : (~(inv(X) = X))) | (~(inv(pack1(elem!0)) = pack1(elem!0)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(53,plain,
% 0.19/0.50 (~(inv(pack1(elem!0)) = pack1(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.50 tff(54,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[53, 44])).
% 0.19/0.50 tff(55,plain,((~(inv(pack1(inv(pack1(elem!0)))) = i)) | (~(pack1(pack1(elem!0)) = i))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(56,plain,
% 0.19/0.50 (~(inv(pack1(inv(pack1(elem!0)))) = i)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[55, 29])).
% 0.19/0.50 tff(57,plain,
% 0.19/0.50 (((~![X: $i] : ((X = i) | (X = o))) | ((inv(pack1(inv(pack1(elem!0)))) = i) | (inv(pack1(inv(pack1(elem!0)))) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (inv(pack1(inv(pack1(elem!0)))) = i) | (inv(pack1(inv(pack1(elem!0)))) = o))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(58,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | ((inv(pack1(inv(pack1(elem!0)))) = i) | (inv(pack1(inv(pack1(elem!0)))) = o))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(59,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | (inv(pack1(inv(pack1(elem!0)))) = i) | (inv(pack1(inv(pack1(elem!0)))) = o)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.50 tff(60,plain,
% 0.19/0.50 ((inv(pack1(inv(pack1(elem!0)))) = i) | (inv(pack1(inv(pack1(elem!0)))) = o)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[59, 19])).
% 0.19/0.50 tff(61,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(elem!0)))) = o),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[60, 56])).
% 0.19/0.50 tff(62,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(elem!0)))) = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[61, 28])).
% 0.19/0.50 tff(63,plain,
% 0.19/0.50 (pack1(inv(pack1(inv(pack1(elem!0))))) = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.50 tff(64,plain,
% 0.19/0.50 (pack1(pack1(pack1(inv(pack1(elem!0))))) = pack1(inv(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[63])).
% 0.19/0.50 tff(65,assumption,(pack1(pack1(pack1(inv(pack1(elem!0))))) = i), introduced(assumption)).
% 0.19/0.50 tff(66,plain,
% 0.19/0.50 (pack1(inv(pack1(inv(pack1(elem!0))))) = pack1(pack1(elem!0))),
% 0.19/0.50 inference(transitivity,[status(thm)],[63, 65, 30])).
% 0.19/0.50 tff(67,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(inv(pack1(elem!0)))))) = inv(pack1(pack1(elem!0)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.50 tff(68,plain,
% 0.19/0.50 (inv(pack1(pack1(elem!0))) = inv(pack1(inv(pack1(inv(pack1(elem!0))))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[67])).
% 0.19/0.50 tff(69,plain,
% 0.19/0.50 ((inv(pack1(pack1(elem!0))) = i) <=> (inv(pack1(pack1(elem!0))) = pack1(pack1(elem!0)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.50 tff(70,plain,
% 0.19/0.50 ((inv(pack1(pack1(elem!0))) = pack1(pack1(elem!0))) <=> (inv(pack1(pack1(elem!0))) = i)),
% 0.19/0.50 inference(symmetry,[status(thm)],[69])).
% 0.19/0.50 tff(71,plain,
% 0.19/0.50 ((~(inv(pack1(pack1(elem!0))) = pack1(pack1(elem!0)))) <=> (~(inv(pack1(pack1(elem!0))) = i))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[70])).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 ((~![X: $i] : (~(inv(X) = X))) | (~(inv(pack1(pack1(elem!0))) = pack1(pack1(elem!0))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(73,plain,
% 0.19/0.50 (~(inv(pack1(pack1(elem!0))) = pack1(pack1(elem!0)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[72, 51])).
% 0.19/0.50 tff(74,plain,
% 0.19/0.50 (~(inv(pack1(pack1(elem!0))) = i)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[73, 71])).
% 0.19/0.50 tff(75,plain,
% 0.19/0.50 (((~![X: $i] : ((X = i) | (X = o))) | ((inv(pack1(pack1(elem!0))) = i) | (inv(pack1(pack1(elem!0))) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (inv(pack1(pack1(elem!0))) = i) | (inv(pack1(pack1(elem!0))) = o))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(76,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | ((inv(pack1(pack1(elem!0))) = i) | (inv(pack1(pack1(elem!0))) = o))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(77,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | (inv(pack1(pack1(elem!0))) = i) | (inv(pack1(pack1(elem!0))) = o)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.50 tff(78,plain,
% 0.19/0.50 ((inv(pack1(pack1(elem!0))) = i) | (inv(pack1(pack1(elem!0))) = o)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[77, 19])).
% 0.19/0.50 tff(79,plain,
% 0.19/0.50 (inv(pack1(pack1(elem!0))) = o),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[78, 74])).
% 0.19/0.50 tff(80,plain,
% 0.19/0.50 (o = inv(pack1(pack1(elem!0)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[79])).
% 0.19/0.50 tff(81,plain,
% 0.19/0.50 (pack1(pack1(inv(pack1(elem!0)))) = inv(pack1(inv(pack1(inv(pack1(elem!0))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[27, 80, 68])).
% 0.19/0.50 tff(82,plain,
% 0.19/0.50 (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0))))) = unpack1(inv(pack1(inv(pack1(elem!0)))), inv(pack1(inv(pack1(inv(pack1(elem!0)))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.50 tff(83,plain,
% 0.19/0.50 (unpack1(inv(pack1(inv(pack1(elem!0)))), inv(pack1(inv(pack1(inv(pack1(elem!0))))))) = unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[82])).
% 0.19/0.50 tff(84,plain,
% 0.19/0.50 ((~![X1: $i] : (unpack1(X1, inv(pack1(X1))) = X1)) | (unpack1(inv(pack1(inv(pack1(elem!0)))), inv(pack1(inv(pack1(inv(pack1(elem!0))))))) = inv(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(85,plain,
% 0.19/0.50 (unpack1(inv(pack1(inv(pack1(elem!0)))), inv(pack1(inv(pack1(inv(pack1(elem!0))))))) = inv(pack1(inv(pack1(elem!0))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[84, 40])).
% 0.19/0.50 tff(86,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(elem!0)))) = unpack1(inv(pack1(inv(pack1(elem!0)))), inv(pack1(inv(pack1(inv(pack1(elem!0)))))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[85])).
% 0.19/0.50 tff(87,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(elem!0)))) = pack1(inv(pack1(elem!0)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[86, 83, 26])).
% 0.19/0.50 tff(88,plain,
% 0.19/0.50 ((~![X: $i] : (~(inv(X) = X))) | (~(inv(pack1(inv(pack1(elem!0)))) = pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(89,plain,
% 0.19/0.50 (~(inv(pack1(inv(pack1(elem!0)))) = pack1(inv(pack1(elem!0))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[88, 51])).
% 0.19/0.50 tff(90,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[89, 87])).
% 0.19/0.50 tff(91,plain,((~(pack1(pack1(pack1(inv(pack1(elem!0))))) = i)) | (~(pack1(pack1(inv(pack1(elem!0)))) = o)) | (~(pack1(pack1(elem!0)) = i))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(92,plain,
% 0.19/0.50 (~(pack1(pack1(pack1(inv(pack1(elem!0))))) = i)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[91, 27, 29])).
% 0.19/0.50 tff(93,plain,
% 0.19/0.50 (((~![X: $i] : ((X = i) | (X = o))) | ((pack1(pack1(pack1(inv(pack1(elem!0))))) = i) | (pack1(pack1(pack1(inv(pack1(elem!0))))) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (pack1(pack1(pack1(inv(pack1(elem!0))))) = i) | (pack1(pack1(pack1(inv(pack1(elem!0))))) = o))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(94,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | ((pack1(pack1(pack1(inv(pack1(elem!0))))) = i) | (pack1(pack1(pack1(inv(pack1(elem!0))))) = o))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(95,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | (pack1(pack1(pack1(inv(pack1(elem!0))))) = i) | (pack1(pack1(pack1(inv(pack1(elem!0))))) = o)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.50 tff(96,plain,
% 0.19/0.50 ((pack1(pack1(pack1(inv(pack1(elem!0))))) = i) | (pack1(pack1(pack1(inv(pack1(elem!0))))) = o)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[95, 19])).
% 0.19/0.50 tff(97,plain,
% 0.19/0.50 (pack1(pack1(pack1(inv(pack1(elem!0))))) = o),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[96, 92])).
% 0.19/0.50 tff(98,plain,
% 0.19/0.50 (o = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[97])).
% 0.19/0.50 tff(99,plain,
% 0.19/0.50 (pack1(pack1(inv(pack1(elem!0)))) = pack1(inv(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[27, 98, 64])).
% 0.19/0.50 tff(100,plain,
% 0.19/0.50 (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0))))) = unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(inv(pack1(inv(pack1(elem!0))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.50 tff(101,plain,
% 0.19/0.50 (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(inv(pack1(inv(pack1(elem!0)))))) = unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[100])).
% 0.19/0.50 tff(102,plain,
% 0.19/0.50 (^[X1: $i] : refl((unpack1(X1, pack1(X1)) = X1) <=> (unpack1(X1, pack1(X1)) = X1))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(103,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(X1, pack1(X1)) = X1) <=> ![X1: $i] : (unpack1(X1, pack1(X1)) = X1)),
% 0.19/0.50 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.50 tff(104,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(X1, pack1(X1)) = X1) <=> ![X1: $i] : (unpack1(X1, pack1(X1)) = X1)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(105,axiom,(![X1: $i] : (unpack1(X1, pack1(X1)) = X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unpack1')).
% 0.19/0.50 tff(106,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(X1, pack1(X1)) = X1)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.50 tff(107,plain,(
% 0.19/0.50 ![X1: $i] : (unpack1(X1, pack1(X1)) = X1)),
% 0.19/0.50 inference(skolemize,[status(sab)],[106])).
% 0.19/0.50 tff(108,plain,
% 0.19/0.50 (![X1: $i] : (unpack1(X1, pack1(X1)) = X1)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.19/0.50 tff(109,plain,
% 0.19/0.50 ((~![X1: $i] : (unpack1(X1, pack1(X1)) = X1)) | (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(inv(pack1(inv(pack1(elem!0)))))) = inv(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(110,plain,
% 0.19/0.50 (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(inv(pack1(inv(pack1(elem!0)))))) = inv(pack1(inv(pack1(elem!0))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.50 tff(111,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(elem!0)))) = unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(inv(pack1(inv(pack1(elem!0))))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[110])).
% 0.19/0.50 tff(112,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(elem!0)))) = pack1(inv(pack1(elem!0)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[111, 101, 26])).
% 0.19/0.50 tff(113,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[89, 112])).
% 0.19/0.50 tff(114,plain,((~(pack1(pack1(inv(pack1(elem!0)))) = o)) | (~(pack1(pack1(elem!0)) = i))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(115,plain,
% 0.19/0.50 (~(pack1(pack1(inv(pack1(elem!0)))) = o)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[114, 24])).
% 0.19/0.50 tff(116,plain,
% 0.19/0.50 (((~![X: $i] : ((X = i) | (X = o))) | ((pack1(pack1(inv(pack1(elem!0)))) = i) | (pack1(pack1(inv(pack1(elem!0)))) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (pack1(pack1(inv(pack1(elem!0)))) = i) | (pack1(pack1(inv(pack1(elem!0)))) = o))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(117,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | ((pack1(pack1(inv(pack1(elem!0)))) = i) | (pack1(pack1(inv(pack1(elem!0)))) = o))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(118,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | (pack1(pack1(inv(pack1(elem!0)))) = i) | (pack1(pack1(inv(pack1(elem!0)))) = o)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.50 tff(119,plain,
% 0.19/0.50 ((pack1(pack1(inv(pack1(elem!0)))) = i) | (pack1(pack1(inv(pack1(elem!0)))) = o)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[118, 19])).
% 0.19/0.50 tff(120,plain,
% 0.19/0.50 (pack1(pack1(inv(pack1(elem!0)))) = i),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[119, 115])).
% 0.19/0.50 tff(121,plain,
% 0.19/0.50 (i = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[120])).
% 0.19/0.50 tff(122,plain,
% 0.19/0.50 (pack1(pack1(elem!0)) = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[24, 121])).
% 0.19/0.50 tff(123,plain,
% 0.19/0.50 (pack1(pack1(pack1(elem!0))) = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.50 tff(124,plain,
% 0.19/0.50 (pack1(pack1(pack1(inv(pack1(elem!0))))) = pack1(pack1(pack1(elem!0)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[123])).
% 0.19/0.50 tff(125,plain,
% 0.19/0.50 (i = pack1(pack1(elem!0))),
% 0.19/0.50 inference(symmetry,[status(thm)],[24])).
% 0.19/0.50 tff(126,plain,
% 0.19/0.50 (pack1(pack1(inv(pack1(elem!0)))) = pack1(pack1(elem!0))),
% 0.19/0.50 inference(transitivity,[status(thm)],[120, 125])).
% 0.19/0.50 tff(127,plain,
% 0.19/0.50 (pack1(pack1(pack1(inv(pack1(elem!0))))) = pack1(pack1(pack1(elem!0)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[126])).
% 0.19/0.50 tff(128,plain,
% 0.19/0.50 (pack1(pack1(pack1(elem!0))) = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[127])).
% 0.19/0.50 tff(129,plain,
% 0.19/0.50 (pack1(pack1(pack1(pack1(elem!0)))) = pack1(pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.50 tff(130,plain,
% 0.19/0.50 (pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = pack1(pack1(pack1(pack1(elem!0))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[129])).
% 0.19/0.50 tff(131,assumption,(pack1(pack1(pack1(inv(pack1(elem!0))))) = o), introduced(assumption)).
% 0.19/0.50 tff(132,plain,
% 0.19/0.50 ((~![X1: $i] : (unpack1(X1, pack1(X1)) = X1)) | (unpack1(pack1(pack1(pack1(inv(pack1(elem!0))))), pack1(pack1(pack1(pack1(inv(pack1(elem!0))))))) = pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(133,plain,
% 0.19/0.50 (unpack1(pack1(pack1(pack1(inv(pack1(elem!0))))), pack1(pack1(pack1(pack1(inv(pack1(elem!0))))))) = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[132, 108])).
% 0.19/0.50 tff(134,assumption,(pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = o), introduced(assumption)).
% 0.19/0.50 tff(135,plain,
% 0.19/0.50 (o = pack1(pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[134])).
% 0.19/0.50 tff(136,plain,
% 0.19/0.50 (pack1(pack1(pack1(inv(pack1(elem!0))))) = pack1(pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[131, 135])).
% 0.19/0.50 tff(137,plain,
% 0.19/0.50 (o = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[131])).
% 0.19/0.50 tff(138,plain,
% 0.19/0.50 ((inv(pack1(pack1(elem!0))) = i) <=> (inv(pack1(pack1(elem!0))) = pack1(pack1(elem!0)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.50 tff(139,plain,
% 0.19/0.50 ((inv(pack1(pack1(elem!0))) = pack1(pack1(elem!0))) <=> (inv(pack1(pack1(elem!0))) = i)),
% 0.19/0.50 inference(symmetry,[status(thm)],[138])).
% 0.19/0.50 tff(140,plain,
% 0.19/0.50 ((~(inv(pack1(pack1(elem!0))) = pack1(pack1(elem!0)))) <=> (~(inv(pack1(pack1(elem!0))) = i))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[139])).
% 0.19/0.50 tff(141,plain,
% 0.19/0.50 (~(inv(pack1(pack1(elem!0))) = i)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[73, 140])).
% 0.19/0.50 tff(142,plain,
% 0.19/0.50 (inv(pack1(pack1(elem!0))) = o),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[78, 141])).
% 0.19/0.50 tff(143,assumption,(pack1(pack1(inv(pack1(elem!0)))) = i), introduced(assumption)).
% 0.19/0.50 tff(144,plain,
% 0.19/0.50 (pack1(pack1(inv(pack1(elem!0)))) = pack1(pack1(elem!0))),
% 0.19/0.50 inference(transitivity,[status(thm)],[143, 125])).
% 0.19/0.50 tff(145,plain,
% 0.19/0.50 (inv(pack1(pack1(inv(pack1(elem!0))))) = inv(pack1(pack1(elem!0)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.50 tff(146,plain,
% 0.19/0.50 (inv(pack1(pack1(inv(pack1(elem!0))))) = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[145, 142, 137])).
% 0.19/0.50 tff(147,plain,
% 0.19/0.50 (unpack1(inv(pack1(pack1(inv(pack1(elem!0))))), pack1(pack1(pack1(inv(pack1(elem!0)))))) = unpack1(pack1(pack1(pack1(inv(pack1(elem!0))))), pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[146, 136])).
% 0.19/0.50 tff(148,plain,
% 0.19/0.50 ((~![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1)) | (unpack1(inv(pack1(pack1(inv(pack1(elem!0))))), pack1(pack1(pack1(inv(pack1(elem!0)))))) = pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(149,plain,
% 0.19/0.50 (unpack1(inv(pack1(pack1(inv(pack1(elem!0))))), pack1(pack1(pack1(inv(pack1(elem!0)))))) = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[148, 7])).
% 0.19/0.50 tff(150,plain,
% 0.19/0.50 (pack1(pack1(inv(pack1(elem!0)))) = unpack1(inv(pack1(pack1(inv(pack1(elem!0))))), pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[149])).
% 0.19/0.50 tff(151,plain,
% 0.19/0.50 (i = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[143])).
% 0.19/0.50 tff(152,plain,
% 0.19/0.50 (pack1(pack1(elem!0)) = o),
% 0.19/0.50 inference(transitivity,[status(thm)],[24, 151, 150, 147, 133, 131])).
% 0.19/0.50 tff(153,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[12, 152])).
% 0.19/0.50 tff(154,plain,((~(pack1(pack1(inv(pack1(elem!0)))) = i)) | (pack1(pack1(elem!0)) = o) | (~(pack1(pack1(pack1(inv(pack1(elem!0))))) = o)) | (~(pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = o))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(155,plain,
% 0.19/0.50 (~(pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = o)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[154, 131, 12, 120])).
% 0.19/0.50 tff(156,plain,
% 0.19/0.50 (((~![X: $i] : ((X = i) | (X = o))) | ((pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = i) | (pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = i) | (pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = o))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(157,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | ((pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = i) | (pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = o))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(158,plain,
% 0.19/0.50 ((~![X: $i] : ((X = i) | (X = o))) | (pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = i) | (pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = o)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.19/0.50 tff(159,plain,
% 0.19/0.50 ((pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = i) | (pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = o)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[158, 19])).
% 0.19/0.50 tff(160,plain,
% 0.19/0.50 (pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = i),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[159, 155])).
% 0.19/0.50 tff(161,plain,
% 0.19/0.50 (i = pack1(pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[160])).
% 0.19/0.50 tff(162,plain,
% 0.19/0.50 (pack1(pack1(inv(pack1(elem!0)))) = pack1(pack1(pack1(pack1(elem!0))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[120, 161, 130])).
% 0.19/0.50 tff(163,plain,
% 0.19/0.50 (~(inv(pack1(inv(pack1(elem!0)))) = i)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[55, 24])).
% 0.19/0.50 tff(164,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(elem!0)))) = o),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[60, 163])).
% 0.19/0.50 tff(165,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(elem!0)))) = pack1(pack1(pack1(elem!0)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[164, 137, 127])).
% 0.19/0.50 tff(166,plain,
% 0.19/0.50 (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0))))) = unpack1(pack1(pack1(pack1(elem!0))), pack1(pack1(pack1(pack1(elem!0)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[165, 162])).
% 0.19/0.50 tff(167,plain,
% 0.19/0.50 (unpack1(pack1(pack1(pack1(elem!0))), pack1(pack1(pack1(pack1(elem!0))))) = unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[166])).
% 0.19/0.50 tff(168,plain,
% 0.19/0.50 ((~![X1: $i] : (unpack1(X1, pack1(X1)) = X1)) | (unpack1(pack1(pack1(pack1(elem!0))), pack1(pack1(pack1(pack1(elem!0))))) = pack1(pack1(pack1(elem!0))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(169,plain,
% 0.19/0.50 (unpack1(pack1(pack1(pack1(elem!0))), pack1(pack1(pack1(pack1(elem!0))))) = pack1(pack1(pack1(elem!0)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[168, 108])).
% 0.19/0.50 tff(170,plain,
% 0.19/0.50 (pack1(pack1(pack1(elem!0))) = unpack1(pack1(pack1(pack1(elem!0))), pack1(pack1(pack1(pack1(elem!0)))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[169])).
% 0.19/0.50 tff(171,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(elem!0)))) = pack1(inv(pack1(elem!0)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[164, 137, 127, 170, 167, 26])).
% 0.19/0.50 tff(172,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[89, 171])).
% 0.19/0.50 tff(173,plain,((~(pack1(pack1(pack1(inv(pack1(elem!0))))) = o)) | (pack1(pack1(elem!0)) = o)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(174,plain,
% 0.19/0.50 (~(pack1(pack1(pack1(inv(pack1(elem!0))))) = o)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[173, 12])).
% 0.19/0.50 tff(175,plain,
% 0.19/0.50 (pack1(pack1(pack1(inv(pack1(elem!0))))) = i),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[96, 174])).
% 0.19/0.50 tff(176,plain,
% 0.19/0.50 (i = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[175])).
% 0.19/0.50 tff(177,plain,
% 0.19/0.50 (pack1(pack1(inv(pack1(elem!0)))) = pack1(pack1(pack1(elem!0)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[120, 176, 124])).
% 0.19/0.50 tff(178,plain,
% 0.19/0.50 (o = inv(pack1(pack1(elem!0)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[142])).
% 0.19/0.50 tff(179,plain,
% 0.19/0.50 (inv(pack1(inv(pack1(elem!0)))) = inv(pack1(pack1(elem!0)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[164, 178])).
% 0.19/0.50 tff(180,plain,
% 0.19/0.50 (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0))))) = unpack1(inv(pack1(pack1(elem!0))), pack1(pack1(pack1(elem!0))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[179, 177])).
% 0.19/0.50 tff(181,plain,
% 0.19/0.50 (pack1(inv(pack1(elem!0))) = unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[26])).
% 0.19/0.50 tff(182,plain,
% 0.19/0.50 (pack1(inv(pack1(elem!0))) = pack1(pack1(elem!0))),
% 0.19/0.50 inference(transitivity,[status(thm)],[181, 180, 11])).
% 0.19/0.50 tff(183,plain,
% 0.19/0.50 (unpack1(inv(pack1(elem!0)), pack1(inv(pack1(elem!0)))) = unpack1(inv(pack1(elem!0)), pack1(pack1(elem!0)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[182])).
% 0.19/0.50 tff(184,plain,
% 0.19/0.50 ((~![X1: $i] : (unpack1(X1, pack1(X1)) = X1)) | (unpack1(inv(pack1(elem!0)), pack1(inv(pack1(elem!0)))) = inv(pack1(elem!0)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(185,plain,
% 0.19/0.50 (unpack1(inv(pack1(elem!0)), pack1(inv(pack1(elem!0)))) = inv(pack1(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[184, 108])).
% 0.19/0.50 tff(186,plain,
% 0.19/0.50 (inv(pack1(elem!0)) = unpack1(inv(pack1(elem!0)), pack1(inv(pack1(elem!0))))),
% 0.19/0.50 inference(symmetry,[status(thm)],[185])).
% 0.19/0.50 tff(187,plain,
% 0.19/0.50 (inv(pack1(elem!0)) = pack1(elem!0)),
% 0.19/0.50 inference(transitivity,[status(thm)],[186, 183, 9])).
% 0.19/0.50 tff(188,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[53, 187])).
% 0.19/0.51 tff(189,plain,(pack1(pack1(elem!0)) = o), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(190,plain,
% 0.19/0.51 (o = pack1(pack1(elem!0))),
% 0.19/0.51 inference(symmetry,[status(thm)],[189])).
% 0.19/0.51 tff(191,assumption,(~(inv(pack1(inv(pack1(elem!0)))) = o)), introduced(assumption)).
% 0.19/0.51 tff(192,plain,
% 0.19/0.51 (inv(pack1(inv(pack1(elem!0)))) = i),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[60, 191])).
% 0.19/0.51 tff(193,plain,
% 0.19/0.51 (i = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[65])).
% 0.19/0.51 tff(194,plain,
% 0.19/0.51 (pack1(pack1(inv(pack1(elem!0)))) = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[143, 193])).
% 0.19/0.51 tff(195,plain,
% 0.19/0.51 (inv(pack1(inv(pack1(elem!0)))) = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[31, 151])).
% 0.19/0.51 tff(196,plain,
% 0.19/0.51 (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0))))) = unpack1(pack1(pack1(inv(pack1(elem!0)))), pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[195, 194])).
% 0.19/0.51 tff(197,plain,
% 0.19/0.51 (unpack1(pack1(pack1(inv(pack1(elem!0)))), pack1(pack1(pack1(inv(pack1(elem!0)))))) = unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[196])).
% 0.19/0.51 tff(198,plain,
% 0.19/0.51 ((~![X1: $i] : (unpack1(X1, pack1(X1)) = X1)) | (unpack1(pack1(pack1(inv(pack1(elem!0)))), pack1(pack1(pack1(inv(pack1(elem!0)))))) = pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(199,plain,
% 0.19/0.51 (unpack1(pack1(pack1(inv(pack1(elem!0)))), pack1(pack1(pack1(inv(pack1(elem!0)))))) = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[198, 108])).
% 0.19/0.51 tff(200,plain,
% 0.19/0.51 (pack1(pack1(inv(pack1(elem!0)))) = unpack1(pack1(pack1(inv(pack1(elem!0)))), pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[199])).
% 0.19/0.51 tff(201,plain,
% 0.19/0.51 (inv(pack1(inv(pack1(elem!0)))) = pack1(inv(pack1(elem!0)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[31, 151, 200, 197, 26])).
% 0.19/0.51 tff(202,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[89, 201])).
% 0.19/0.51 tff(203,plain,((~(pack1(pack1(inv(pack1(elem!0)))) = i)) | (~(inv(pack1(inv(pack1(elem!0)))) = i)) | (~(pack1(pack1(pack1(inv(pack1(elem!0))))) = i))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(204,plain,
% 0.19/0.51 (~(pack1(pack1(inv(pack1(elem!0)))) = i)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[203, 65, 192])).
% 0.19/0.51 tff(205,plain,
% 0.19/0.51 (pack1(pack1(inv(pack1(elem!0)))) = o),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[119, 204])).
% 0.19/0.51 tff(206,plain,
% 0.19/0.51 ((~![X1: $i] : (unpack1(X1, inv(pack1(X1))) = X1)) | (unpack1(pack1(pack1(inv(pack1(elem!0)))), inv(pack1(pack1(pack1(inv(pack1(elem!0))))))) = pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(207,plain,
% 0.19/0.51 (unpack1(pack1(pack1(inv(pack1(elem!0)))), inv(pack1(pack1(pack1(inv(pack1(elem!0))))))) = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[206, 40])).
% 0.19/0.51 tff(208,plain,
% 0.19/0.51 (i = inv(pack1(inv(pack1(elem!0))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[192])).
% 0.19/0.51 tff(209,plain,
% 0.19/0.51 (pack1(pack1(pack1(inv(pack1(elem!0))))) = inv(pack1(inv(pack1(elem!0))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[65, 208])).
% 0.19/0.51 tff(210,plain,
% 0.19/0.51 (inv(pack1(pack1(pack1(inv(pack1(elem!0)))))) = inv(inv(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[209])).
% 0.19/0.51 tff(211,plain,
% 0.19/0.51 (inv(inv(pack1(inv(pack1(elem!0))))) = inv(pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[210])).
% 0.19/0.51 tff(212,plain,
% 0.19/0.51 (o = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[205])).
% 0.19/0.51 tff(213,plain,
% 0.19/0.51 (pack1(pack1(elem!0)) = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[189, 212])).
% 0.19/0.51 tff(214,plain,
% 0.19/0.51 (pack1(pack1(pack1(elem!0))) = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[213])).
% 0.19/0.51 tff(215,plain,
% 0.19/0.51 (pack1(pack1(pack1(inv(pack1(elem!0))))) = pack1(pack1(pack1(elem!0)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[214])).
% 0.19/0.51 tff(216,plain,
% 0.19/0.51 (inv(pack1(inv(pack1(elem!0)))) = pack1(pack1(pack1(elem!0)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[192, 193, 215])).
% 0.19/0.51 tff(217,plain,
% 0.19/0.51 (inv(inv(pack1(inv(pack1(elem!0))))) = inv(pack1(pack1(pack1(elem!0))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[216])).
% 0.19/0.51 tff(218,plain,
% 0.19/0.51 (inv(pack1(pack1(pack1(elem!0)))) = inv(inv(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[217])).
% 0.19/0.51 tff(219,plain,
% 0.19/0.51 (pack1(pack1(pack1(elem!0))) = i),
% 0.19/0.51 inference(transitivity,[status(thm)],[214, 65])).
% 0.19/0.51 tff(220,plain,
% 0.19/0.51 ((inv(pack1(pack1(pack1(elem!0)))) = pack1(pack1(pack1(elem!0)))) <=> (inv(pack1(pack1(pack1(elem!0)))) = i)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[219])).
% 0.19/0.51 tff(221,plain,
% 0.19/0.51 ((~(inv(pack1(pack1(pack1(elem!0)))) = pack1(pack1(pack1(elem!0))))) <=> (~(inv(pack1(pack1(pack1(elem!0)))) = i))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[220])).
% 0.19/0.51 tff(222,plain,
% 0.19/0.51 ((~![X: $i] : (~(inv(X) = X))) | (~(inv(pack1(pack1(pack1(elem!0)))) = pack1(pack1(pack1(elem!0)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(223,plain,
% 0.19/0.51 (~(inv(pack1(pack1(pack1(elem!0)))) = pack1(pack1(pack1(elem!0))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[222, 51])).
% 0.19/0.51 tff(224,plain,
% 0.19/0.51 (~(inv(pack1(pack1(pack1(elem!0)))) = i)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[223, 221])).
% 0.19/0.51 tff(225,plain,
% 0.19/0.51 (((~![X: $i] : ((X = i) | (X = o))) | ((inv(pack1(pack1(pack1(elem!0)))) = i) | (inv(pack1(pack1(pack1(elem!0)))) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (inv(pack1(pack1(pack1(elem!0)))) = i) | (inv(pack1(pack1(pack1(elem!0)))) = o))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(226,plain,
% 0.19/0.51 ((~![X: $i] : ((X = i) | (X = o))) | ((inv(pack1(pack1(pack1(elem!0)))) = i) | (inv(pack1(pack1(pack1(elem!0)))) = o))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(227,plain,
% 0.19/0.51 ((~![X: $i] : ((X = i) | (X = o))) | (inv(pack1(pack1(pack1(elem!0)))) = i) | (inv(pack1(pack1(pack1(elem!0)))) = o)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.19/0.51 tff(228,plain,
% 0.19/0.51 ((inv(pack1(pack1(pack1(elem!0)))) = i) | (inv(pack1(pack1(pack1(elem!0)))) = o)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[227, 19])).
% 0.19/0.51 tff(229,plain,
% 0.19/0.51 (inv(pack1(pack1(pack1(elem!0)))) = o),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[228, 224])).
% 0.19/0.51 tff(230,plain,
% 0.19/0.51 (o = inv(pack1(pack1(pack1(elem!0))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[229])).
% 0.19/0.51 tff(231,plain,
% 0.19/0.51 (inv(pack1(inv(pack1(elem!0)))) = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[192, 193])).
% 0.19/0.51 tff(232,plain,
% 0.19/0.51 (pack1(inv(pack1(inv(pack1(elem!0))))) = pack1(pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[231])).
% 0.19/0.51 tff(233,plain,
% 0.19/0.51 (pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = pack1(inv(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[232])).
% 0.19/0.51 tff(234,assumption,(pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = i), introduced(assumption)).
% 0.19/0.51 tff(235,plain,
% 0.19/0.51 (i = pack1(pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[234])).
% 0.19/0.51 tff(236,plain,
% 0.19/0.51 (pack1(pack1(pack1(inv(pack1(elem!0))))) = pack1(inv(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[65, 235, 233])).
% 0.19/0.51 tff(237,plain,
% 0.19/0.51 (pack1(pack1(inv(pack1(elem!0)))) = inv(inv(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[205, 230, 218])).
% 0.19/0.51 tff(238,plain,
% 0.19/0.51 (unpack1(pack1(pack1(inv(pack1(elem!0)))), pack1(pack1(pack1(inv(pack1(elem!0)))))) = unpack1(inv(inv(pack1(inv(pack1(elem!0))))), pack1(inv(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[237, 236])).
% 0.19/0.51 tff(239,plain,
% 0.19/0.51 (unpack1(inv(inv(pack1(inv(pack1(elem!0))))), pack1(inv(pack1(inv(pack1(elem!0)))))) = unpack1(pack1(pack1(inv(pack1(elem!0)))), pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[238])).
% 0.19/0.51 tff(240,plain,
% 0.19/0.51 ((~![X1: $i] : (unpack1(inv(X1), pack1(X1)) = X1)) | (unpack1(inv(inv(pack1(inv(pack1(elem!0))))), pack1(inv(pack1(inv(pack1(elem!0)))))) = inv(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(241,plain,
% 0.19/0.51 (unpack1(inv(inv(pack1(inv(pack1(elem!0))))), pack1(inv(pack1(inv(pack1(elem!0)))))) = inv(pack1(inv(pack1(elem!0))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[240, 7])).
% 0.19/0.51 tff(242,plain,
% 0.19/0.51 (inv(pack1(inv(pack1(elem!0)))) = unpack1(inv(inv(pack1(inv(pack1(elem!0))))), pack1(inv(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[241])).
% 0.19/0.51 tff(243,plain,
% 0.19/0.51 (inv(pack1(inv(pack1(elem!0)))) = o),
% 0.19/0.51 inference(transitivity,[status(thm)],[242, 239, 199, 205])).
% 0.19/0.51 tff(244,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[191, 243])).
% 0.19/0.51 tff(245,plain,((~(pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = i)) | (inv(pack1(inv(pack1(elem!0)))) = o) | (~(pack1(pack1(pack1(inv(pack1(elem!0))))) = i))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(246,plain,
% 0.19/0.51 (~(pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = i)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[245, 65, 191])).
% 0.19/0.51 tff(247,plain,
% 0.19/0.51 (pack1(pack1(pack1(pack1(inv(pack1(elem!0)))))) = o),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[159, 246])).
% 0.19/0.51 tff(248,plain,
% 0.19/0.51 (pack1(inv(pack1(inv(pack1(elem!0))))) = inv(pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[232, 247, 230, 218, 211])).
% 0.19/0.51 tff(249,plain,
% 0.19/0.51 (inv(inv(pack1(inv(pack1(elem!0))))) = pack1(pack1(inv(pack1(elem!0))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[217, 229, 212])).
% 0.19/0.51 tff(250,plain,
% 0.19/0.51 (unpack1(inv(inv(pack1(inv(pack1(elem!0))))), pack1(inv(pack1(inv(pack1(elem!0)))))) = unpack1(pack1(pack1(inv(pack1(elem!0)))), inv(pack1(pack1(pack1(inv(pack1(elem!0)))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[249, 248])).
% 0.19/0.51 tff(251,plain,
% 0.19/0.51 (inv(pack1(inv(pack1(elem!0)))) = o),
% 0.19/0.51 inference(transitivity,[status(thm)],[242, 250, 207, 205])).
% 0.19/0.51 tff(252,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[191, 251])).
% 0.19/0.51 tff(253,plain,((~(pack1(pack1(pack1(inv(pack1(elem!0))))) = i)) | (inv(pack1(inv(pack1(elem!0)))) = o)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(254,plain,
% 0.19/0.51 (~(pack1(pack1(pack1(inv(pack1(elem!0))))) = i)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[253, 191])).
% 0.19/0.51 tff(255,plain,
% 0.19/0.51 (pack1(pack1(pack1(inv(pack1(elem!0))))) = o),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[96, 254])).
% 0.19/0.51 tff(256,plain,
% 0.19/0.51 (pack1(pack1(pack1(inv(pack1(elem!0))))) = pack1(pack1(elem!0))),
% 0.19/0.51 inference(transitivity,[status(thm)],[131, 190])).
% 0.19/0.51 tff(257,plain,
% 0.19/0.51 (inv(pack1(pack1(pack1(inv(pack1(elem!0)))))) = inv(pack1(pack1(elem!0)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[256])).
% 0.19/0.51 tff(258,plain,
% 0.19/0.51 (inv(pack1(pack1(elem!0))) = inv(pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[257])).
% 0.19/0.51 tff(259,plain,
% 0.19/0.51 ((inv(pack1(pack1(elem!0))) = o) <=> (inv(pack1(pack1(elem!0))) = pack1(pack1(elem!0)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[190])).
% 0.19/0.51 tff(260,plain,
% 0.19/0.51 ((inv(pack1(pack1(elem!0))) = pack1(pack1(elem!0))) <=> (inv(pack1(pack1(elem!0))) = o)),
% 0.19/0.51 inference(symmetry,[status(thm)],[259])).
% 0.19/0.51 tff(261,plain,
% 0.19/0.51 ((~(inv(pack1(pack1(elem!0))) = pack1(pack1(elem!0)))) <=> (~(inv(pack1(pack1(elem!0))) = o))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[260])).
% 0.19/0.51 tff(262,plain,
% 0.19/0.51 (~(inv(pack1(pack1(elem!0))) = o)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[73, 261])).
% 0.19/0.51 tff(263,plain,
% 0.19/0.51 (inv(pack1(pack1(elem!0))) = i),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[78, 262])).
% 0.19/0.51 tff(264,plain,
% 0.19/0.51 (i = inv(pack1(pack1(elem!0)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[263])).
% 0.19/0.51 tff(265,plain,
% 0.19/0.51 (pack1(pack1(inv(pack1(elem!0)))) = inv(pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[143, 264, 258])).
% 0.19/0.51 tff(266,plain,
% 0.19/0.51 (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0))))) = unpack1(pack1(pack1(inv(pack1(elem!0)))), inv(pack1(pack1(pack1(inv(pack1(elem!0)))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[195, 265])).
% 0.19/0.51 tff(267,plain,
% 0.19/0.51 (unpack1(pack1(pack1(inv(pack1(elem!0)))), inv(pack1(pack1(pack1(inv(pack1(elem!0))))))) = unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[266])).
% 0.19/0.51 tff(268,plain,
% 0.19/0.51 (pack1(pack1(inv(pack1(elem!0)))) = unpack1(pack1(pack1(inv(pack1(elem!0)))), inv(pack1(pack1(pack1(inv(pack1(elem!0)))))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[207])).
% 0.19/0.51 tff(269,plain,
% 0.19/0.51 (inv(pack1(inv(pack1(elem!0)))) = pack1(inv(pack1(elem!0)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[31, 151, 268, 267, 26])).
% 0.19/0.51 tff(270,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[89, 269])).
% 0.19/0.51 tff(271,plain,((~(pack1(pack1(inv(pack1(elem!0)))) = i)) | (~(inv(pack1(inv(pack1(elem!0)))) = i)) | (~(pack1(pack1(pack1(inv(pack1(elem!0))))) = o))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(272,plain,
% 0.19/0.51 (~(pack1(pack1(inv(pack1(elem!0)))) = i)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[271, 192, 255])).
% 0.19/0.51 tff(273,plain,
% 0.19/0.51 (pack1(pack1(inv(pack1(elem!0)))) = o),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[119, 272])).
% 0.19/0.51 tff(274,plain,
% 0.19/0.51 (o = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[255])).
% 0.19/0.51 tff(275,plain,
% 0.19/0.51 (pack1(pack1(inv(pack1(elem!0)))) = pack1(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[273, 274])).
% 0.19/0.51 tff(276,plain,
% 0.19/0.51 (pack1(pack1(inv(pack1(elem!0)))) = pack1(pack1(elem!0))),
% 0.19/0.51 inference(transitivity,[status(thm)],[273, 190])).
% 0.19/0.51 tff(277,plain,
% 0.19/0.51 (inv(pack1(pack1(inv(pack1(elem!0))))) = inv(pack1(pack1(elem!0)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[276])).
% 0.19/0.51 tff(278,plain,
% 0.19/0.51 (inv(pack1(pack1(elem!0))) = inv(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[277])).
% 0.19/0.51 tff(279,plain,
% 0.19/0.51 (inv(pack1(inv(pack1(elem!0)))) = inv(pack1(pack1(inv(pack1(elem!0)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[192, 264, 278])).
% 0.19/0.51 tff(280,plain,
% 0.19/0.51 (unpack1(inv(pack1(inv(pack1(elem!0)))), pack1(pack1(inv(pack1(elem!0))))) = unpack1(inv(pack1(pack1(inv(pack1(elem!0))))), pack1(pack1(pack1(inv(pack1(elem!0))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[279, 275])).
% 0.19/0.51 tff(281,plain,
% 0.19/0.51 (pack1(inv(pack1(elem!0))) = pack1(pack1(elem!0))),
% 0.19/0.51 inference(transitivity,[status(thm)],[181, 280, 149, 273, 190])).
% 0.19/0.51 tff(282,plain,
% 0.19/0.51 (unpack1(inv(pack1(elem!0)), pack1(inv(pack1(elem!0)))) = unpack1(inv(pack1(elem!0)), pack1(pack1(elem!0)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[281])).
% 0.19/0.51 tff(283,plain,
% 0.19/0.51 (inv(pack1(elem!0)) = pack1(elem!0)),
% 0.19/0.51 inference(transitivity,[status(thm)],[186, 282, 9])).
% 0.19/0.51 tff(284,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[53, 283])).
% 0.19/0.51 tff(285,plain,(inv(pack1(inv(pack1(elem!0)))) = o), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(286,plain,
% 0.19/0.51 (inv(pack1(inv(pack1(elem!0)))) = pack1(pack1(elem!0))),
% 0.19/0.51 inference(transitivity,[status(thm)],[285, 190])).
% 0.19/0.51 tff(287,plain,
% 0.19/0.51 (unpack1(inv(pack1(elem!0)), inv(pack1(inv(pack1(elem!0))))) = unpack1(inv(pack1(elem!0)), pack1(pack1(elem!0)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[286])).
% 0.19/0.51 tff(288,plain,
% 0.19/0.51 (inv(pack1(elem!0)) = pack1(elem!0)),
% 0.19/0.51 inference(transitivity,[status(thm)],[43, 287, 9])).
% 0.19/0.51 tff(289,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[53, 288])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------