%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV052-1.002.001 : TPTP v9.0.0. Released v4.1.0.
% 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 05:10:35 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : HWV052-1.002.001 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.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 : Thu Jun 19 17:29:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(elem_0_type, type, (
% 0.20/0.45 elem_0: $i)).
% 0.20/0.45 tff(inv_type, type, (
% 0.20/0.45 inv: $i > $i)).
% 0.20/0.45 tff(unpack2_type, type, (
% 0.20/0.45 unpack2: ( $i * $i * $i ) > $i)).
% 0.20/0.45 tff(pack1_type, type, (
% 0.20/0.45 pack1: ( $i * $i ) > $i)).
% 0.20/0.45 tff(i_type, type, (
% 0.20/0.45 i: $i)).
% 0.20/0.45 tff(o_type, type, (
% 0.20/0.45 o: $i)).
% 0.20/0.45 tff(1,plain,
% 0.20/0.45 (^[X2: $i, X1: $i] : refl((unpack2(X1, X2, inv(pack1(X1, X2))) = X2) <=> (unpack2(X1, X2, inv(pack1(X1, X2))) = X2))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, X2, inv(pack1(X1, X2))) = X2) <=> ![X2: $i, X1: $i] : (unpack2(X1, X2, inv(pack1(X1, X2))) = X2)),
% 0.20/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, X2, inv(pack1(X1, X2))) = X2) <=> ![X2: $i, X1: $i] : (unpack2(X1, X2, inv(pack1(X1, X2))) = X2)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(4,axiom,(![X2: $i, X1: $i] : (unpack2(X1, X2, inv(pack1(X1, X2))) = X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unpack2_06')).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, X2, inv(pack1(X1, X2))) = X2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.45 tff(6,plain,(
% 0.20/0.45 ![X2: $i, X1: $i] : (unpack2(X1, X2, inv(pack1(X1, X2))) = X2)),
% 0.20/0.45 inference(skolemize,[status(sab)],[5])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, X2, inv(pack1(X1, X2))) = X2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 ((~![X2: $i, X1: $i] : (unpack2(X1, X2, inv(pack1(X1, X2))) = X2)) | (unpack2(elem!0, elem!0, inv(pack1(elem!0, elem!0))) = elem!0)),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (unpack2(elem!0, elem!0, inv(pack1(elem!0, elem!0))) = elem!0),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 ((o = pack1(elem!0, elem!0)) <=> (pack1(elem!0, elem!0) = o)),
% 0.20/0.45 inference(commutativity,[status(thm)],[])).
% 0.20/0.45 tff(11,assumption,(elem!0 = o), introduced(assumption)).
% 0.20/0.45 tff(12,assumption,(inv(pack1(elem!0, elem!0)) = i), introduced(assumption)).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 (i = inv(pack1(elem!0, elem!0))),
% 0.20/0.45 inference(symmetry,[status(thm)],[12])).
% 0.20/0.45 tff(14,plain,
% 0.20/0.45 ((i = pack1(elem!0, elem!0)) <=> (pack1(elem!0, elem!0) = i)),
% 0.20/0.45 inference(commutativity,[status(thm)],[])).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 ((inv(pack1(elem!0, elem!0)) = pack1(elem!0, elem!0)) <=> (i = pack1(elem!0, elem!0))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[12])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 ((inv(pack1(elem!0, elem!0)) = pack1(elem!0, elem!0)) <=> (pack1(elem!0, elem!0) = i)),
% 0.20/0.45 inference(transitivity,[status(thm)],[15, 14])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 ((~(inv(pack1(elem!0, elem!0)) = pack1(elem!0, elem!0))) <=> (~(pack1(elem!0, elem!0) = i))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (^[X: $i] : refl((~(inv(X) = X)) <=> (~(inv(X) = X)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 (![X: $i] : (~(inv(X) = X)) <=> ![X: $i] : (~(inv(X) = X))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 (![X: $i] : (~(inv(X) = X)) <=> ![X: $i] : (~(inv(X) = X))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(21,axiom,(![X: $i] : (~(inv(X) = X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bit_inverse')).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (![X: $i] : (~(inv(X) = X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.45 tff(23,plain,(
% 0.20/0.45 ![X: $i] : (~(inv(X) = X))),
% 0.20/0.45 inference(skolemize,[status(sab)],[22])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (![X: $i] : (~(inv(X) = X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 ((~![X: $i] : (~(inv(X) = X))) | (~(inv(pack1(elem!0, elem!0)) = pack1(elem!0, elem!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (~(inv(pack1(elem!0, elem!0)) = pack1(elem!0, elem!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (~(pack1(elem!0, elem!0) = i)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[26, 17])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (![X: $i] : ((X = i) | (X = o)) <=> ![X: $i] : ((X = i) | (X = o))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (^[X: $i] : rewrite(((X = o) | (X = i)) <=> ((X = i) | (X = o)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (![X: $i] : ((X = o) | (X = i)) <=> ![X: $i] : ((X = i) | (X = o))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.45 tff(31,axiom,(![X: $i] : ((X = o) | (X = i))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bit_domain')).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (![X: $i] : ((X = i) | (X = o))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (![X: $i] : ((X = i) | (X = o))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.45 tff(34,plain,(
% 0.20/0.45 ![X: $i] : ((X = i) | (X = o))),
% 0.20/0.45 inference(skolemize,[status(sab)],[33])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (((~![X: $i] : ((X = i) | (X = o))) | ((pack1(elem!0, elem!0) = i) | (pack1(elem!0, elem!0) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (pack1(elem!0, elem!0) = i) | (pack1(elem!0, elem!0) = o))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 ((~![X: $i] : ((X = i) | (X = o))) | ((pack1(elem!0, elem!0) = i) | (pack1(elem!0, elem!0) = o))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 ((~![X: $i] : ((X = i) | (X = o))) | (pack1(elem!0, elem!0) = i) | (pack1(elem!0, elem!0) = o)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 ((pack1(elem!0, elem!0) = i) | (pack1(elem!0, elem!0) = o)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (pack1(elem!0, elem!0) = o),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[38, 27])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (^[X2: $i, X1: $i] : refl((unpack2(X1, X2, pack1(X1, X2)) = X2) <=> (unpack2(X1, X2, pack1(X1, X2)) = X2))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, X2, pack1(X1, X2)) = X2) <=> ![X2: $i, X1: $i] : (unpack2(X1, X2, pack1(X1, X2)) = X2)),
% 0.20/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, X2, pack1(X1, X2)) = X2) <=> ![X2: $i, X1: $i] : (unpack2(X1, X2, pack1(X1, X2)) = X2)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(43,axiom,(![X2: $i, X1: $i] : (unpack2(X1, X2, pack1(X1, X2)) = X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unpack2')).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, X2, pack1(X1, X2)) = X2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.45 tff(45,plain,(
% 0.20/0.45 ![X2: $i, X1: $i] : (unpack2(X1, X2, pack1(X1, X2)) = X2)),
% 0.20/0.45 inference(skolemize,[status(sab)],[44])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, X2, pack1(X1, X2)) = X2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 ((~![X2: $i, X1: $i] : (unpack2(X1, X2, pack1(X1, X2)) = X2)) | (unpack2(elem!0, elem!0, pack1(elem!0, elem!0)) = elem!0)),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (unpack2(elem!0, elem!0, pack1(elem!0, elem!0)) = elem!0),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.45 tff(49,assumption,(pack1(elem!0, elem!0) = o), introduced(assumption)).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (o = pack1(elem!0, elem!0)),
% 0.20/0.45 inference(symmetry,[status(thm)],[49])).
% 0.20/0.45 tff(51,assumption,(pack1(elem!0, inv(elem!0)) = o), introduced(assumption)).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (o = elem!0),
% 0.20/0.45 inference(symmetry,[status(thm)],[11])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (pack1(elem!0, elem!0) = elem!0),
% 0.20/0.45 inference(transitivity,[status(thm)],[49, 52])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 (pack1(pack1(elem!0, elem!0), inv(elem!0)) = pack1(elem!0, inv(elem!0))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (pack1(pack1(elem!0, elem!0), inv(elem!0)) = pack1(elem!0, elem!0)),
% 0.20/0.45 inference(transitivity,[status(thm)],[54, 51, 50])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 ((inv(elem!0) = o) <=> (inv(elem!0) = elem!0)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 ((inv(elem!0) = elem!0) <=> (inv(elem!0) = o)),
% 0.20/0.45 inference(symmetry,[status(thm)],[56])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 ((~(inv(elem!0) = elem!0)) <=> (~(inv(elem!0) = o))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 ((~![X: $i] : (~(inv(X) = X))) | (~(inv(elem!0) = elem!0))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (~(inv(elem!0) = elem!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[59, 24])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (~(inv(elem!0) = o)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[60, 58])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (((~![X: $i] : ((X = i) | (X = o))) | ((inv(elem!0) = i) | (inv(elem!0) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (inv(elem!0) = i) | (inv(elem!0) = o))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 ((~![X: $i] : ((X = i) | (X = o))) | ((inv(elem!0) = i) | (inv(elem!0) = o))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 ((~![X: $i] : ((X = i) | (X = o))) | (inv(elem!0) = i) | (inv(elem!0) = o)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 ((inv(elem!0) = i) | (inv(elem!0) = o)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[64, 34])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (inv(elem!0) = i),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[65, 61])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (i = inv(elem!0)),
% 0.20/0.45 inference(symmetry,[status(thm)],[66])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 ((inv(inv(elem!0)) = i) <=> (inv(inv(elem!0)) = inv(elem!0))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 ((inv(inv(elem!0)) = inv(elem!0)) <=> (inv(inv(elem!0)) = i)),
% 0.20/0.45 inference(symmetry,[status(thm)],[68])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 ((~(inv(inv(elem!0)) = inv(elem!0))) <=> (~(inv(inv(elem!0)) = i))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 ((~![X: $i] : (~(inv(X) = X))) | (~(inv(inv(elem!0)) = inv(elem!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (~(inv(inv(elem!0)) = inv(elem!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[71, 24])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (~(inv(inv(elem!0)) = i)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[72, 70])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (((~![X: $i] : ((X = i) | (X = o))) | ((inv(inv(elem!0)) = i) | (inv(inv(elem!0)) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (inv(inv(elem!0)) = i) | (inv(inv(elem!0)) = o))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 ((~![X: $i] : ((X = i) | (X = o))) | ((inv(inv(elem!0)) = i) | (inv(inv(elem!0)) = o))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 ((~![X: $i] : ((X = i) | (X = o))) | (inv(inv(elem!0)) = i) | (inv(inv(elem!0)) = o)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 ((inv(inv(elem!0)) = i) | (inv(inv(elem!0)) = o)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[76, 34])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (inv(inv(elem!0)) = o),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[77, 73])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 (inv(inv(elem!0)) = elem!0),
% 0.20/0.45 inference(transitivity,[status(thm)],[78, 52])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (unpack2(pack1(elem!0, elem!0), inv(inv(elem!0)), pack1(pack1(elem!0, elem!0), inv(elem!0))) = unpack2(elem!0, elem!0, pack1(elem!0, elem!0))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[53, 79, 55])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (^[X2: $i, X1: $i] : refl((unpack2(X1, inv(X2), pack1(X1, X2)) = X2) <=> (unpack2(X1, inv(X2), pack1(X1, X2)) = X2))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, inv(X2), pack1(X1, X2)) = X2) <=> ![X2: $i, X1: $i] : (unpack2(X1, inv(X2), pack1(X1, X2)) = X2)),
% 0.20/0.45 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, inv(X2), pack1(X1, X2)) = X2) <=> ![X2: $i, X1: $i] : (unpack2(X1, inv(X2), pack1(X1, X2)) = X2)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(84,axiom,(![X2: $i, X1: $i] : (unpack2(X1, inv(X2), pack1(X1, X2)) = X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unpack2_05')).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, inv(X2), pack1(X1, X2)) = X2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.45 tff(86,plain,(
% 0.20/0.45 ![X2: $i, X1: $i] : (unpack2(X1, inv(X2), pack1(X1, X2)) = X2)),
% 0.20/0.45 inference(skolemize,[status(sab)],[85])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (![X2: $i, X1: $i] : (unpack2(X1, inv(X2), pack1(X1, X2)) = X2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 ((~![X2: $i, X1: $i] : (unpack2(X1, inv(X2), pack1(X1, X2)) = X2)) | (unpack2(pack1(elem!0, elem!0), inv(inv(elem!0)), pack1(pack1(elem!0, elem!0), inv(elem!0))) = inv(elem!0))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.46 (unpack2(pack1(elem!0, elem!0), inv(inv(elem!0)), pack1(pack1(elem!0, elem!0), inv(elem!0))) = inv(elem!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (inv(elem!0) = unpack2(pack1(elem!0, elem!0), inv(inv(elem!0)), pack1(pack1(elem!0, elem!0), inv(elem!0)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[89])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (inv(elem!0) = elem!0),
% 0.20/0.46 inference(transitivity,[status(thm)],[90, 80, 48])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[60, 91])).
% 0.20/0.46 tff(93,plain,((~(pack1(elem!0, inv(elem!0)) = o)) | (~(pack1(elem!0, elem!0) = o)) | (~(elem!0 = o))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (~(pack1(elem!0, inv(elem!0)) = o)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[93, 39, 11])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 (((~![X: $i] : ((X = i) | (X = o))) | ((pack1(elem!0, inv(elem!0)) = i) | (pack1(elem!0, inv(elem!0)) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (pack1(elem!0, inv(elem!0)) = i) | (pack1(elem!0, inv(elem!0)) = o))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 ((~![X: $i] : ((X = i) | (X = o))) | ((pack1(elem!0, inv(elem!0)) = i) | (pack1(elem!0, inv(elem!0)) = o))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 ((~![X: $i] : ((X = i) | (X = o))) | (pack1(elem!0, inv(elem!0)) = i) | (pack1(elem!0, inv(elem!0)) = o)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 ((pack1(elem!0, inv(elem!0)) = i) | (pack1(elem!0, inv(elem!0)) = o)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[97, 34])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (pack1(elem!0, inv(elem!0)) = i),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[98, 94])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (pack1(elem!0, elem!0) = elem!0),
% 0.20/0.46 inference(transitivity,[status(thm)],[39, 52])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (pack1(pack1(elem!0, elem!0), inv(elem!0)) = pack1(elem!0, inv(elem!0))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (pack1(pack1(elem!0, elem!0), inv(elem!0)) = inv(pack1(elem!0, elem!0))),
% 0.20/0.46 inference(transitivity,[status(thm)],[101, 99, 13])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (unpack2(pack1(elem!0, elem!0), inv(inv(elem!0)), pack1(pack1(elem!0, elem!0), inv(elem!0))) = unpack2(elem!0, elem!0, inv(pack1(elem!0, elem!0)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[100, 79, 102])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (inv(elem!0) = elem!0),
% 0.20/0.46 inference(transitivity,[status(thm)],[90, 103, 9])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[60, 104])).
% 0.20/0.46 tff(106,plain,((~(inv(pack1(elem!0, elem!0)) = i)) | (~(elem!0 = o))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (~(inv(pack1(elem!0, elem!0)) = i)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[106, 11])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (((~![X: $i] : ((X = i) | (X = o))) | ((inv(pack1(elem!0, elem!0)) = i) | (inv(pack1(elem!0, elem!0)) = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (inv(pack1(elem!0, elem!0)) = i) | (inv(pack1(elem!0, elem!0)) = o))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 ((~![X: $i] : ((X = i) | (X = o))) | ((inv(pack1(elem!0, elem!0)) = i) | (inv(pack1(elem!0, elem!0)) = o))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 ((~![X: $i] : ((X = i) | (X = o))) | (inv(pack1(elem!0, elem!0)) = i) | (inv(pack1(elem!0, elem!0)) = o)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 ((inv(pack1(elem!0, elem!0)) = i) | (inv(pack1(elem!0, elem!0)) = o)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[110, 34])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (inv(pack1(elem!0, elem!0)) = o),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[111, 107])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 ((inv(pack1(elem!0, elem!0)) = pack1(elem!0, elem!0)) <=> (o = pack1(elem!0, elem!0))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 ((inv(pack1(elem!0, elem!0)) = pack1(elem!0, elem!0)) <=> (pack1(elem!0, elem!0) = o)),
% 0.20/0.46 inference(transitivity,[status(thm)],[113, 10])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 ((~(inv(pack1(elem!0, elem!0)) = pack1(elem!0, elem!0))) <=> (~(pack1(elem!0, elem!0) = o))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[114])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 (~(pack1(elem!0, elem!0) = o)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[26, 115])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (pack1(elem!0, elem!0) = i),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[38, 116])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 ((~![X2: $i, X1: $i] : (unpack2(X1, inv(X2), pack1(X1, X2)) = X2)) | (unpack2(elem!0, inv(elem!0), pack1(elem!0, elem!0)) = elem!0)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 (unpack2(elem!0, inv(elem!0), pack1(elem!0, elem!0)) = elem!0),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[118, 87])).
% 0.20/0.46 tff(120,assumption,(pack1(elem!0, inv(elem!0)) = i), introduced(assumption)).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (i = pack1(elem!0, inv(elem!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[120])).
% 0.20/0.46 tff(122,assumption,(pack1(elem!0, elem!0) = i), introduced(assumption)).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (pack1(elem!0, elem!0) = pack1(elem!0, inv(elem!0))),
% 0.20/0.46 inference(transitivity,[status(thm)],[122, 121])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (unpack2(elem!0, inv(elem!0), pack1(elem!0, elem!0)) = unpack2(elem!0, inv(elem!0), pack1(elem!0, inv(elem!0)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[123])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 (unpack2(elem!0, inv(elem!0), pack1(elem!0, inv(elem!0))) = unpack2(elem!0, inv(elem!0), pack1(elem!0, elem!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[124])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 ((~![X2: $i, X1: $i] : (unpack2(X1, X2, pack1(X1, X2)) = X2)) | (unpack2(elem!0, inv(elem!0), pack1(elem!0, inv(elem!0))) = inv(elem!0))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (unpack2(elem!0, inv(elem!0), pack1(elem!0, inv(elem!0))) = inv(elem!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[126, 46])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 (inv(elem!0) = unpack2(elem!0, inv(elem!0), pack1(elem!0, inv(elem!0)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[127])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (inv(elem!0) = elem!0),
% 0.20/0.46 inference(transitivity,[status(thm)],[128, 125, 119])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[60, 129])).
% 0.20/0.46 tff(131,plain,((~(pack1(elem!0, inv(elem!0)) = i)) | (~(pack1(elem!0, elem!0) = i))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (~(pack1(elem!0, inv(elem!0)) = i)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[131, 117])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 (pack1(elem!0, inv(elem!0)) = o),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[98, 132])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 (o = pack1(elem!0, inv(elem!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[133])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (inv(pack1(elem!0, elem!0)) = pack1(elem!0, inv(elem!0))),
% 0.20/0.46 inference(transitivity,[status(thm)],[112, 134])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (o = inv(inv(elem!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[78])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 (elem!0 = inv(inv(elem!0))),
% 0.20/0.46 inference(transitivity,[status(thm)],[11, 136])).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 (unpack2(elem!0, elem!0, inv(pack1(elem!0, elem!0))) = unpack2(elem!0, inv(inv(elem!0)), pack1(elem!0, inv(elem!0)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[137, 135])).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (unpack2(elem!0, inv(inv(elem!0)), pack1(elem!0, inv(elem!0))) = unpack2(elem!0, elem!0, inv(pack1(elem!0, elem!0)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[138])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 ((~![X2: $i, X1: $i] : (unpack2(X1, inv(X2), pack1(X1, X2)) = X2)) | (unpack2(elem!0, inv(inv(elem!0)), pack1(elem!0, inv(elem!0))) = inv(elem!0))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 (unpack2(elem!0, inv(inv(elem!0)), pack1(elem!0, inv(elem!0))) = inv(elem!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[140, 87])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (inv(elem!0) = unpack2(elem!0, inv(inv(elem!0)), pack1(elem!0, inv(elem!0)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[141])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 (inv(elem!0) = elem!0),
% 0.20/0.46 inference(transitivity,[status(thm)],[142, 139, 9])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[60, 143])).
% 0.20/0.46 tff(145,plain,(~(elem!0 = o)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 (((~![X: $i] : ((X = i) | (X = o))) | ((elem!0 = i) | (elem!0 = o))) <=> ((~![X: $i] : ((X = i) | (X = o))) | (elem!0 = i) | (elem!0 = o))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(147,plain,
% 0.20/0.46 ((~![X: $i] : ((X = i) | (X = o))) | ((elem!0 = i) | (elem!0 = o))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(148,plain,
% 0.20/0.46 ((~![X: $i] : ((X = i) | (X = o))) | (elem!0 = i) | (elem!0 = o)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 ((elem!0 = i) | (elem!0 = o)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[148, 34])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 (elem!0 = i),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[149, 145])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 (i = elem!0),
% 0.20/0.46 inference(symmetry,[status(thm)],[150])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 (o = pack1(elem!0, inv(elem!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[51])).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 (pack1(elem!0, elem!0) = pack1(elem!0, inv(elem!0))),
% 0.20/0.46 inference(transitivity,[status(thm)],[49, 152])).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 (unpack2(elem!0, inv(elem!0), pack1(elem!0, elem!0)) = unpack2(elem!0, inv(elem!0), pack1(elem!0, inv(elem!0)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[153])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (unpack2(elem!0, inv(elem!0), pack1(elem!0, inv(elem!0))) = unpack2(elem!0, inv(elem!0), pack1(elem!0, elem!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[154])).
% 0.20/0.46 tff(156,plain,
% 0.20/0.46 (inv(elem!0) = elem!0),
% 0.20/0.46 inference(transitivity,[status(thm)],[128, 155, 119])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[60, 156])).
% 0.20/0.46 tff(158,plain,((~(pack1(elem!0, inv(elem!0)) = o)) | (~(pack1(elem!0, elem!0) = o))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 (~(pack1(elem!0, inv(elem!0)) = o)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[158, 49])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 (pack1(elem!0, inv(elem!0)) = i),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[98, 159])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (i = pack1(elem!0, inv(elem!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[160])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 ((inv(elem!0) = i) <=> (inv(elem!0) = elem!0)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 ((inv(elem!0) = elem!0) <=> (inv(elem!0) = i)),
% 0.20/0.46 inference(symmetry,[status(thm)],[162])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 ((~(inv(elem!0) = elem!0)) <=> (~(inv(elem!0) = i))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[163])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 (~(inv(elem!0) = i)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[60, 164])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 (inv(elem!0) = o),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[65, 165])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 (o = inv(elem!0)),
% 0.20/0.46 inference(symmetry,[status(thm)],[166])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 ((inv(inv(elem!0)) = o) <=> (inv(inv(elem!0)) = inv(elem!0))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[167])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 ((inv(inv(elem!0)) = inv(elem!0)) <=> (inv(inv(elem!0)) = o)),
% 0.20/0.46 inference(symmetry,[status(thm)],[168])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 ((~(inv(inv(elem!0)) = inv(elem!0))) <=> (~(inv(inv(elem!0)) = o))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[169])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 (~(inv(inv(elem!0)) = o)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[72, 170])).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (inv(inv(elem!0)) = i),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[77, 171])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (pack1(elem!0, elem!0) = inv(elem!0)),
% 0.20/0.46 inference(transitivity,[status(thm)],[49, 167])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (inv(pack1(elem!0, elem!0)) = inv(inv(elem!0))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[173])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (inv(pack1(elem!0, elem!0)) = pack1(elem!0, inv(elem!0))),
% 0.20/0.46 inference(transitivity,[status(thm)],[174, 172, 161])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (i = inv(inv(elem!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[172])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (elem!0 = inv(inv(elem!0))),
% 0.20/0.46 inference(transitivity,[status(thm)],[150, 176])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (unpack2(elem!0, elem!0, inv(pack1(elem!0, elem!0))) = unpack2(elem!0, inv(inv(elem!0)), pack1(elem!0, inv(elem!0)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[177, 175])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (unpack2(elem!0, inv(inv(elem!0)), pack1(elem!0, inv(elem!0))) = unpack2(elem!0, elem!0, inv(pack1(elem!0, elem!0)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[178])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 (inv(elem!0) = elem!0),
% 0.20/0.46 inference(transitivity,[status(thm)],[142, 179, 9])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[60, 180])).
% 0.20/0.46 tff(182,plain,(~(pack1(elem!0, elem!0) = o)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 (pack1(elem!0, elem!0) = i),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[38, 182])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 (pack1(elem!0, elem!0) = elem!0),
% 0.20/0.46 inference(transitivity,[status(thm)],[183, 151])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 (inv(pack1(elem!0, elem!0)) = inv(elem!0)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[184])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 (inv(elem!0) = inv(pack1(elem!0, elem!0))),
% 0.20/0.46 inference(symmetry,[status(thm)],[185])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 (~(pack1(elem!0, inv(elem!0)) = i)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[131, 183])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (pack1(elem!0, inv(elem!0)) = o),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[98, 187])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 (pack1(elem!0, inv(elem!0)) = inv(pack1(elem!0, elem!0))),
% 0.20/0.46 inference(transitivity,[status(thm)],[188, 167, 186])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 (inv(inv(elem!0)) = elem!0),
% 0.20/0.46 inference(transitivity,[status(thm)],[172, 151])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 (unpack2(elem!0, inv(inv(elem!0)), pack1(elem!0, inv(elem!0))) = unpack2(elem!0, elem!0, inv(pack1(elem!0, elem!0)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[190, 189])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 (inv(elem!0) = elem!0),
% 0.20/0.46 inference(transitivity,[status(thm)],[142, 191, 9])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[60, 192])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------