%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO070-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:05:30 AM UTC 2025
% Result : Unsatisfiable 128.74s 128.97s
% Output : Proof 129.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO070-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.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 14:12:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 128.74/128.97 % SZS status Unsatisfiable
% 128.74/128.97 % SZS output start Proof
% 128.74/128.97 tff(equidistant_type, type, (
% 128.74/128.97 equidistant: ( $i * $i * $i * $i ) > $o)).
% 128.74/128.97 tff(insertion_type, type, (
% 128.74/128.97 insertion: ( $i * $i * $i * $i ) > $i)).
% 128.74/128.97 tff(v_type, type, (
% 128.74/128.97 v: $i)).
% 128.74/128.97 tff(x_type, type, (
% 128.74/128.97 x: $i)).
% 128.74/128.97 tff(extension_type, type, (
% 128.74/128.97 extension: ( $i * $i * $i * $i ) > $i)).
% 128.74/128.97 tff(lower_dimension_point_2_type, type, (
% 128.74/128.97 lower_dimension_point_2: $i)).
% 128.74/128.97 tff(lower_dimension_point_1_type, type, (
% 128.74/128.97 lower_dimension_point_1: $i)).
% 128.74/128.97 tff(w_type, type, (
% 128.74/128.97 w: $i)).
% 128.74/128.97 tff(u_type, type, (
% 128.74/128.97 u: $i)).
% 128.74/128.97 tff(between_type, type, (
% 128.74/128.97 between: ( $i * $i * $i ) > $o)).
% 128.74/128.97 tff(y_type, type, (
% 128.74/128.97 y: $i)).
% 128.74/128.97 tff(colinear_type, type, (
% 128.74/128.97 colinear: ( $i * $i * $i ) > $o)).
% 128.74/128.97 tff(1,plain,
% 128.74/128.97 (^[V: $i, U: $i] : refl(between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)) <=> between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 128.74/128.97 inference(bind,[status(th)],[])).
% 128.74/128.97 tff(2,plain,
% 128.74/128.97 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)) <=> ![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(quant_intro,[status(thm)],[1])).
% 128.74/128.97 tff(3,plain,
% 128.74/128.97 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)) <=> ![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(rewrite,[status(thm)],[])).
% 128.74/128.97 tff(4,axiom,(![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e3_3')).
% 128.74/128.97 tff(5,plain,
% 128.74/128.97 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(modus_ponens,[status(thm)],[4, 3])).
% 128.74/128.97 tff(6,plain,(
% 128.74/128.97 ![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(skolemize,[status(sab)],[5])).
% 128.74/128.97 tff(7,plain,
% 128.74/128.97 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(modus_ponens,[status(thm)],[6, 2])).
% 128.74/128.97 tff(8,plain,
% 128.74/128.97 ((~![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))) | between(x, v, extension(x, v, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(quant_inst,[status(thm)],[])).
% 128.74/128.97 tff(9,plain,
% 128.74/128.97 (between(x, v, extension(x, v, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(unit_resolution,[status(thm)],[8, 7])).
% 128.74/128.97 tff(10,plain,
% 128.74/128.97 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ((~between(U, V, W)) | (V = insertion(U, W, U, V))))),
% 128.74/128.97 inference(bind,[status(th)],[])).
% 128.74/128.97 tff(11,plain,
% 128.74/128.97 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 128.74/128.97 inference(quant_intro,[status(thm)],[10])).
% 128.74/128.97 tff(12,plain,
% 128.74/128.97 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 128.74/128.97 inference(rewrite,[status(thm)],[])).
% 128.74/128.97 tff(13,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','i3')).
% 128.74/128.97 tff(14,plain,
% 128.74/128.97 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 128.74/128.97 inference(modus_ponens,[status(thm)],[13, 12])).
% 128.74/128.97 tff(15,plain,(
% 128.74/128.97 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 128.74/128.97 inference(skolemize,[status(sab)],[14])).
% 128.74/128.97 tff(16,plain,
% 128.74/128.97 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 128.74/128.97 inference(modus_ponens,[status(thm)],[15, 11])).
% 128.74/128.97 tff(17,plain,
% 128.74/128.97 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(x, v, extension(x, v, lower_dimension_point_1, lower_dimension_point_2))) | (v = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(x, v, extension(x, v, lower_dimension_point_1, lower_dimension_point_2))) | (v = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.74/128.97 inference(rewrite,[status(thm)],[])).
% 128.74/128.97 tff(18,plain,
% 128.74/128.97 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(x, v, extension(x, v, lower_dimension_point_1, lower_dimension_point_2))) | (v = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.74/128.97 inference(quant_inst,[status(thm)],[])).
% 128.74/128.97 tff(19,plain,
% 128.74/128.97 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(x, v, extension(x, v, lower_dimension_point_1, lower_dimension_point_2))) | (v = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.74/128.97 inference(modus_ponens,[status(thm)],[18, 17])).
% 128.74/128.97 tff(20,plain,
% 128.74/128.97 (v = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)),
% 128.74/128.97 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 128.74/128.97 tff(21,plain,
% 128.74/128.97 (insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = v),
% 128.74/128.97 inference(symmetry,[status(thm)],[20])).
% 128.74/128.97 tff(22,plain,
% 128.74/128.97 ((extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = u) <=> (u = extension(w, u, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(commutativity,[status(thm)],[])).
% 128.74/128.97 tff(23,plain,
% 128.74/128.97 ((~![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))) | between(w, u, extension(w, u, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(quant_inst,[status(thm)],[])).
% 128.74/128.97 tff(24,plain,
% 128.74/128.97 (between(w, u, extension(w, u, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(unit_resolution,[status(thm)],[23, 7])).
% 128.74/128.97 tff(25,plain,
% 128.74/128.97 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(w, u, extension(w, u, lower_dimension_point_1, lower_dimension_point_2))) | (u = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(w, u, extension(w, u, lower_dimension_point_1, lower_dimension_point_2))) | (u = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.74/128.97 inference(rewrite,[status(thm)],[])).
% 128.74/128.97 tff(26,plain,
% 128.74/128.97 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(w, u, extension(w, u, lower_dimension_point_1, lower_dimension_point_2))) | (u = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.74/128.97 inference(quant_inst,[status(thm)],[])).
% 128.74/128.97 tff(27,plain,
% 128.74/128.97 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(w, u, extension(w, u, lower_dimension_point_1, lower_dimension_point_2))) | (u = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.74/128.97 inference(modus_ponens,[status(thm)],[26, 25])).
% 128.74/128.97 tff(28,plain,
% 128.74/128.97 (u = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)),
% 128.74/128.97 inference(unit_resolution,[status(thm)],[27, 16, 24])).
% 128.74/128.97 tff(29,plain,
% 128.74/128.97 (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = u),
% 128.74/128.97 inference(symmetry,[status(thm)],[28])).
% 128.74/128.97 tff(30,plain,
% 128.74/128.97 ((extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> (extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = u)),
% 128.74/128.97 inference(monotonicity,[status(thm)],[29])).
% 128.74/128.97 tff(31,plain,
% 128.74/128.97 ((extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> (u = extension(w, u, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(transitivity,[status(thm)],[30, 22])).
% 128.74/128.97 tff(32,plain,
% 128.74/128.97 ((u = extension(w, u, lower_dimension_point_1, lower_dimension_point_2)) <=> (extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.74/128.97 inference(symmetry,[status(thm)],[31])).
% 128.74/128.97 tff(33,plain,
% 128.74/128.97 ((~(u = extension(w, u, lower_dimension_point_1, lower_dimension_point_2))) <=> (~(extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.74/128.97 inference(monotonicity,[status(thm)],[32])).
% 128.74/128.97 tff(34,plain,
% 128.74/128.97 (^[V: $i, U: $i] : refl((~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2))) <=> (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2))))),
% 128.74/128.97 inference(bind,[status(th)],[])).
% 128.74/128.97 tff(35,plain,
% 128.74/128.97 (![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2))) <=> ![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 128.74/128.97 inference(quant_intro,[status(thm)],[34])).
% 128.74/128.97 tff(36,plain,
% 128.74/128.97 (![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2))) <=> ![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 128.74/128.97 inference(rewrite,[status(thm)],[])).
% 128.74/128.97 tff(37,axiom,(![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e3_1')).
% 128.74/128.97 tff(38,plain,
% 128.74/128.97 (![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 128.74/128.97 inference(modus_ponens,[status(thm)],[37, 36])).
% 128.74/128.97 tff(39,plain,(
% 128.74/128.97 ![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 128.74/128.97 inference(skolemize,[status(sab)],[38])).
% 128.74/128.97 tff(40,plain,
% 128.74/128.97 (![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 128.74/128.97 inference(modus_ponens,[status(thm)],[39, 35])).
% 128.74/128.97 tff(41,plain,
% 128.74/128.97 ((~![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))) | (~(u = extension(w, u, lower_dimension_point_1, lower_dimension_point_2)))),
% 128.74/128.97 inference(quant_inst,[status(thm)],[])).
% 128.74/128.97 tff(42,plain,
% 128.74/128.97 (~(u = extension(w, u, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.97 inference(unit_resolution,[status(thm)],[41, 40])).
% 128.74/128.97 tff(43,plain,
% 128.74/128.97 (~(extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.74/128.97 inference(modus_ponens,[status(thm)],[42, 33])).
% 128.74/128.97 tff(44,plain,
% 128.74/128.97 (between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w) <=> between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), u, w)),
% 128.74/128.97 inference(monotonicity,[status(thm)],[29])).
% 128.74/128.97 tff(45,plain,
% 128.74/128.97 (between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), u, w) <=> between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)),
% 128.74/128.97 inference(symmetry,[status(thm)],[44])).
% 128.74/128.97 tff(46,plain,
% 128.74/128.97 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | between(W, V, U)) <=> ((~between(U, V, W)) | between(W, V, U)))),
% 128.74/128.97 inference(bind,[status(th)],[])).
% 128.74/128.97 tff(47,plain,
% 128.74/128.97 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U)) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 128.74/128.97 inference(quant_intro,[status(thm)],[46])).
% 128.74/128.97 tff(48,plain,
% 128.74/128.97 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U)) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 128.74/128.97 inference(rewrite,[status(thm)],[])).
% 128.74/128.97 tff(49,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1')).
% 128.74/128.97 tff(50,plain,
% 128.74/128.97 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[49, 48])).
% 128.74/128.98 tff(51,plain,(
% 128.74/128.98 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 128.74/128.98 inference(skolemize,[status(sab)],[50])).
% 128.74/128.98 tff(52,plain,
% 128.74/128.98 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[51, 47])).
% 128.74/128.98 tff(53,plain,
% 128.74/128.98 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(w, u, extension(w, u, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), u, w))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(w, u, extension(w, u, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), u, w))),
% 128.74/128.98 inference(rewrite,[status(thm)],[])).
% 128.74/128.98 tff(54,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(w, u, extension(w, u, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), u, w))),
% 128.74/128.98 inference(quant_inst,[status(thm)],[])).
% 128.74/128.98 tff(55,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(w, u, extension(w, u, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), u, w)),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[54, 53])).
% 128.74/128.98 tff(56,plain,
% 128.74/128.98 (between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), u, w)),
% 128.74/128.98 inference(unit_resolution,[status(thm)],[55, 52, 24])).
% 128.74/128.98 tff(57,plain,
% 128.74/128.98 (between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[56, 45])).
% 128.74/128.98 tff(58,plain,
% 128.74/128.98 (^[W: $i, V: $i, U: $i] : refl(((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))) <=> ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))))),
% 128.74/128.98 inference(bind,[status(th)],[])).
% 128.74/128.98 tff(59,plain,
% 128.74/128.98 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 128.74/128.98 inference(quant_intro,[status(thm)],[58])).
% 128.74/128.98 tff(60,plain,
% 128.74/128.98 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 128.74/128.98 inference(rewrite,[status(thm)],[])).
% 128.74/128.98 tff(61,plain,
% 128.74/128.98 (^[W: $i, V: $i, U: $i] : rewrite((((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W))) <=> ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))))),
% 128.74/128.98 inference(bind,[status(th)],[])).
% 128.74/128.98 tff(62,plain,
% 128.74/128.98 (![W: $i, V: $i, U: $i] : (((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 128.74/128.98 inference(quant_intro,[status(thm)],[61])).
% 128.74/128.98 tff(63,axiom,(![W: $i, V: $i, U: $i] : (((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_1')).
% 128.74/128.98 tff(64,plain,
% 128.74/128.98 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[63, 62])).
% 128.74/128.98 tff(65,plain,
% 128.74/128.98 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[64, 60])).
% 128.74/128.98 tff(66,plain,(
% 128.74/128.98 ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 128.74/128.98 inference(skolemize,[status(sab)],[65])).
% 128.74/128.98 tff(67,plain,
% 128.74/128.98 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[66, 59])).
% 128.74/128.98 tff(68,plain,
% 128.74/128.98 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (w = extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (w = extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)))),
% 128.74/128.98 inference(rewrite,[status(thm)],[])).
% 128.74/128.98 tff(69,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (w = extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)))),
% 128.74/128.98 inference(quant_inst,[status(thm)],[])).
% 128.74/128.98 tff(70,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (w = extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[69, 68])).
% 128.74/128.98 tff(71,plain,
% 128.74/128.98 ((extension(w, u, lower_dimension_point_1, lower_dimension_point_2) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (w = extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))),
% 128.74/128.98 inference(unit_resolution,[status(thm)],[70, 67])).
% 128.74/128.98 tff(72,plain,
% 128.74/128.98 (w = extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)),
% 128.74/128.98 inference(unit_resolution,[status(thm)],[71, 57, 43])).
% 128.74/128.98 tff(73,plain,
% 128.74/128.98 (extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w) = w),
% 128.74/128.98 inference(symmetry,[status(thm)],[72])).
% 128.74/128.98 tff(74,plain,
% 128.74/128.98 ((extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = v) <=> (v = extension(x, v, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.98 inference(commutativity,[status(thm)],[])).
% 128.74/128.98 tff(75,plain,
% 128.74/128.98 ((extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) <=> (extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = v)),
% 128.74/128.98 inference(monotonicity,[status(thm)],[21])).
% 128.74/128.98 tff(76,plain,
% 128.74/128.98 ((extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) <=> (v = extension(x, v, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.98 inference(transitivity,[status(thm)],[75, 74])).
% 128.74/128.98 tff(77,plain,
% 128.74/128.98 ((v = extension(x, v, lower_dimension_point_1, lower_dimension_point_2)) <=> (extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.74/128.98 inference(symmetry,[status(thm)],[76])).
% 128.74/128.98 tff(78,plain,
% 128.74/128.98 ((~(v = extension(x, v, lower_dimension_point_1, lower_dimension_point_2))) <=> (~(extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.74/128.98 inference(monotonicity,[status(thm)],[77])).
% 128.74/128.98 tff(79,plain,
% 128.74/128.98 ((~![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))) | (~(v = extension(x, v, lower_dimension_point_1, lower_dimension_point_2)))),
% 128.74/128.98 inference(quant_inst,[status(thm)],[])).
% 128.74/128.98 tff(80,plain,
% 128.74/128.98 (~(v = extension(x, v, lower_dimension_point_1, lower_dimension_point_2))),
% 128.74/128.98 inference(unit_resolution,[status(thm)],[79, 40])).
% 128.74/128.98 tff(81,plain,
% 128.74/128.98 (~(extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[80, 78])).
% 128.74/128.98 tff(82,plain,
% 128.74/128.98 (between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x) <=> between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), v, x)),
% 128.74/128.98 inference(monotonicity,[status(thm)],[21])).
% 128.74/128.98 tff(83,plain,
% 128.74/128.98 (between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), v, x) <=> between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)),
% 128.74/128.98 inference(symmetry,[status(thm)],[82])).
% 128.74/128.98 tff(84,plain,
% 128.74/128.98 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(x, v, extension(x, v, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), v, x))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(x, v, extension(x, v, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), v, x))),
% 128.74/128.98 inference(rewrite,[status(thm)],[])).
% 128.74/128.98 tff(85,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(x, v, extension(x, v, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), v, x))),
% 128.74/128.98 inference(quant_inst,[status(thm)],[])).
% 128.74/128.98 tff(86,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(x, v, extension(x, v, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), v, x)),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[85, 84])).
% 128.74/128.98 tff(87,plain,
% 128.74/128.98 (between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), v, x)),
% 128.74/128.98 inference(unit_resolution,[status(thm)],[86, 52, 9])).
% 128.74/128.98 tff(88,plain,
% 128.74/128.98 (between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[87, 83])).
% 128.74/128.98 tff(89,plain,
% 128.74/128.98 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (x = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (x = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.74/128.98 inference(rewrite,[status(thm)],[])).
% 128.74/128.98 tff(90,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (x = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.74/128.98 inference(quant_inst,[status(thm)],[])).
% 128.74/128.98 tff(91,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (x = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[90, 89])).
% 128.74/128.98 tff(92,plain,
% 128.74/128.98 ((extension(x, v, lower_dimension_point_1, lower_dimension_point_2) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (x = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.74/128.98 inference(unit_resolution,[status(thm)],[91, 67])).
% 128.74/128.98 tff(93,plain,
% 128.74/128.98 (x = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)),
% 128.74/128.98 inference(unit_resolution,[status(thm)],[92, 88, 81])).
% 128.74/128.98 tff(94,plain,
% 128.74/128.98 (extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x) = x),
% 128.74/128.98 inference(symmetry,[status(thm)],[93])).
% 128.74/128.98 tff(95,plain,
% 128.74/128.98 (equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) <=> equidistant(x, u, w, v)),
% 128.74/128.98 inference(monotonicity,[status(thm)],[94, 29, 73, 21])).
% 128.74/128.98 tff(96,plain,
% 128.74/128.98 (equidistant(x, u, w, v) <=> equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.74/128.98 inference(symmetry,[status(thm)],[95])).
% 128.74/128.98 tff(97,plain,
% 128.74/128.98 (equidistant(v, w, x, u) <=> equidistant(v, w, x, u)),
% 128.74/128.98 inference(rewrite,[status(thm)],[])).
% 128.74/128.98 tff(98,axiom,(equidistant(v, w, x, u)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','v_to_w_equals_x_to_u')).
% 128.74/128.98 tff(99,plain,
% 128.74/128.98 (equidistant(v, w, x, u)),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[98, 97])).
% 128.74/128.98 tff(100,plain,
% 128.74/128.98 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(W, X, V, U)) <=> ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U)))),
% 128.74/128.98 inference(bind,[status(th)],[])).
% 128.74/128.98 tff(101,plain,
% 128.74/128.98 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 128.74/128.98 inference(quant_intro,[status(thm)],[100])).
% 128.74/128.98 tff(102,plain,
% 128.74/128.98 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 128.74/128.98 inference(rewrite,[status(thm)],[])).
% 128.74/128.98 tff(103,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_3')).
% 128.74/128.98 tff(104,plain,
% 128.74/128.98 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[103, 102])).
% 128.74/128.98 tff(105,plain,(
% 128.74/128.98 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 128.74/128.98 inference(skolemize,[status(sab)],[104])).
% 128.74/128.98 tff(106,plain,
% 128.74/128.98 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[105, 101])).
% 128.74/128.98 tff(107,plain,
% 128.74/128.98 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(v, w, x, u)) | equidistant(x, u, w, v))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(v, w, x, u)) | equidistant(x, u, w, v))),
% 128.74/128.98 inference(rewrite,[status(thm)],[])).
% 128.74/128.98 tff(108,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(v, w, x, u)) | equidistant(x, u, w, v))),
% 128.74/128.98 inference(quant_inst,[status(thm)],[])).
% 128.74/128.98 tff(109,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(v, w, x, u)) | equidistant(x, u, w, v)),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[108, 107])).
% 128.74/128.98 tff(110,plain,
% 128.74/128.98 (equidistant(x, u, w, v)),
% 128.74/128.98 inference(unit_resolution,[status(thm)],[109, 106, 99])).
% 128.74/128.98 tff(111,plain,
% 128.74/128.98 (equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[110, 96])).
% 128.74/128.98 tff(112,assumption,(~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))), introduced(assumption)).
% 128.74/128.98 tff(113,plain,
% 128.74/128.98 (between(u, y, w) <=> between(u, y, w)),
% 128.74/128.98 inference(rewrite,[status(thm)],[])).
% 128.74/128.98 tff(114,axiom,(between(u, y, w)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','y_between_u_and_w')).
% 128.74/128.98 tff(115,plain,
% 128.74/128.98 (between(u, y, w)),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[114, 113])).
% 128.74/128.98 tff(116,plain,
% 128.74/128.98 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(u, y, w)) | (y = insertion(u, w, u, y)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(u, y, w)) | (y = insertion(u, w, u, y)))),
% 128.74/128.98 inference(rewrite,[status(thm)],[])).
% 128.74/128.98 tff(117,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(u, y, w)) | (y = insertion(u, w, u, y)))),
% 128.74/128.98 inference(quant_inst,[status(thm)],[])).
% 128.74/128.98 tff(118,plain,
% 128.74/128.98 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(u, y, w)) | (y = insertion(u, w, u, y))),
% 128.74/128.98 inference(modus_ponens,[status(thm)],[117, 116])).
% 128.74/128.98 tff(119,plain,
% 128.74/128.98 (y = insertion(u, w, u, y)),
% 128.74/128.98 inference(unit_resolution,[status(thm)],[118, 16, 115])).
% 128.74/128.98 tff(120,plain,
% 128.74/128.98 (insertion(u, w, u, y) = y),
% 128.74/128.98 inference(symmetry,[status(thm)],[119])).
% 128.74/128.98 tff(121,plain,
% 128.74/128.98 (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(u, w, u, y), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) <=> between(v, y, x)),
% 128.74/128.98 inference(monotonicity,[status(thm)],[21, 120, 94])).
% 128.74/128.98 tff(122,plain,
% 128.74/128.98 (between(v, y, x) <=> between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(u, w, u, y), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.74/128.98 inference(symmetry,[status(thm)],[121])).
% 128.74/128.98 tff(123,plain,
% 128.74/128.98 (between(v, y, x) <=> between(v, y, x)),
% 128.74/128.98 inference(rewrite,[status(thm)],[])).
% 128.74/128.98 tff(124,axiom,(between(v, y, x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','y_between_v_and_x')).
% 128.74/128.99 tff(125,plain,
% 128.74/128.99 (between(v, y, x)),
% 128.74/128.99 inference(modus_ponens,[status(thm)],[124, 123])).
% 128.74/128.99 tff(126,plain,
% 128.74/128.99 (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(u, w, u, y), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.74/128.99 inference(modus_ponens,[status(thm)],[125, 122])).
% 128.74/128.99 tff(127,plain,
% 128.74/128.99 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))) <=> ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))))),
% 128.74/128.99 inference(bind,[status(th)],[])).
% 128.74/128.99 tff(128,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 128.74/128.99 inference(quant_intro,[status(thm)],[127])).
% 128.74/128.99 tff(129,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 128.74/128.99 inference(rewrite,[status(thm)],[])).
% 128.74/128.99 tff(130,plain,
% 128.74/128.99 (^[W: $i, V: $i, U: $i, X: $i] : rewrite((((~between(U, V, X)) | (~between(V, W, X))) | between(U, W, X)) <=> ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))))),
% 128.74/128.99 inference(bind,[status(th)],[])).
% 128.74/128.99 tff(131,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, X)) | (~between(V, W, X))) | between(U, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 128.74/128.99 inference(quant_intro,[status(thm)],[130])).
% 128.74/128.99 tff(132,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, X)) | (~between(V, W, X))) | between(U, W, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b8')).
% 128.74/128.99 tff(133,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 128.74/128.99 inference(modus_ponens,[status(thm)],[132, 131])).
% 128.74/128.99 tff(134,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 128.74/128.99 inference(modus_ponens,[status(thm)],[133, 129])).
% 128.74/128.99 tff(135,plain,(
% 128.74/128.99 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 128.74/128.99 inference(skolemize,[status(sab)],[134])).
% 128.74/128.99 tff(136,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 128.74/128.99 inference(modus_ponens,[status(thm)],[135, 128])).
% 128.74/128.99 tff(137,plain,
% 128.74/128.99 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(u, w, u, y), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(u, w, u, y), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.74/128.99 inference(rewrite,[status(thm)],[])).
% 128.74/128.99 tff(138,plain,
% 128.74/128.99 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(u, w, u, y), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.74/128.99 inference(quant_inst,[status(thm)],[])).
% 128.74/128.99 tff(139,plain,
% 128.74/128.99 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(u, w, u, y), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.74/128.99 inference(modus_ponens,[status(thm)],[138, 137])).
% 128.74/128.99 tff(140,plain,
% 128.74/128.99 (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.74/128.99 inference(unit_resolution,[status(thm)],[139, 136, 126, 112])).
% 128.74/128.99 tff(141,plain,
% 128.74/128.99 (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> between(w, y, u)),
% 128.74/128.99 inference(monotonicity,[status(thm)],[73, 120, 29])).
% 128.74/128.99 tff(142,plain,
% 128.74/128.99 (between(w, y, u) <=> between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.74/128.99 inference(symmetry,[status(thm)],[141])).
% 128.74/128.99 tff(143,plain,
% 128.74/128.99 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, y, w)) | between(w, y, u))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, y, w)) | between(w, y, u))),
% 128.74/128.99 inference(rewrite,[status(thm)],[])).
% 128.74/128.99 tff(144,plain,
% 128.74/128.99 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, y, w)) | between(w, y, u))),
% 128.74/128.99 inference(quant_inst,[status(thm)],[])).
% 128.74/128.99 tff(145,plain,
% 128.74/128.99 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, y, w)) | between(w, y, u)),
% 128.74/128.99 inference(modus_ponens,[status(thm)],[144, 143])).
% 128.74/128.99 tff(146,plain,
% 128.74/128.99 (between(w, y, u)),
% 128.74/128.99 inference(unit_resolution,[status(thm)],[145, 52, 115])).
% 128.74/128.99 tff(147,plain,
% 128.74/128.99 (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.74/128.99 inference(modus_ponens,[status(thm)],[146, 142])).
% 128.74/128.99 tff(148,plain,
% 128.74/128.99 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))) <=> ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))))),
% 128.74/128.99 inference(bind,[status(th)],[])).
% 128.74/128.99 tff(149,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 128.74/128.99 inference(quant_intro,[status(thm)],[148])).
% 128.74/128.99 tff(150,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 128.74/128.99 inference(rewrite,[status(thm)],[])).
% 128.74/128.99 tff(151,plain,
% 128.74/128.99 (^[W: $i, V: $i, U: $i, X: $i] : rewrite((((~between(U, V, W)) | (~between(U, W, X))) | between(V, W, X)) <=> ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))))),
% 128.74/128.99 inference(bind,[status(th)],[])).
% 128.74/128.99 tff(152,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(V, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 128.74/128.99 inference(quant_intro,[status(thm)],[151])).
% 128.74/128.99 tff(153,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(V, W, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b5')).
% 128.74/128.99 tff(154,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 128.74/128.99 inference(modus_ponens,[status(thm)],[153, 152])).
% 128.74/128.99 tff(155,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 128.74/128.99 inference(modus_ponens,[status(thm)],[154, 150])).
% 128.74/128.99 tff(156,plain,(
% 128.74/128.99 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 128.74/128.99 inference(skolemize,[status(sab)],[155])).
% 128.74/128.99 tff(157,plain,
% 128.74/128.99 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 128.74/128.99 inference(modus_ponens,[status(thm)],[156, 149])).
% 128.74/128.99 tff(158,plain,
% 128.74/128.99 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.74/128.99 inference(rewrite,[status(thm)],[])).
% 128.74/128.99 tff(159,plain,
% 128.74/128.99 (((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))) <=> ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.74/128.99 inference(rewrite,[status(thm)],[])).
% 128.74/128.99 tff(160,plain,
% 128.74/128.99 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.74/128.99 inference(monotonicity,[status(thm)],[159])).
% 128.74/128.99 tff(161,plain,
% 128.74/128.99 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.74/128.99 inference(transitivity,[status(thm)],[160, 158])).
% 128.74/128.99 tff(162,plain,
% 128.74/129.00 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.74/129.00 inference(quant_inst,[status(thm)],[])).
% 128.74/129.00 tff(163,plain,
% 128.74/129.00 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.74/129.00 inference(modus_ponens,[status(thm)],[162, 161])).
% 128.74/129.00 tff(164,plain,
% 128.74/129.00 (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.74/129.00 inference(unit_resolution,[status(thm)],[163, 157, 147, 140])).
% 128.74/129.00 tff(165,plain,
% 128.74/129.00 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.74/129.00 inference(rewrite,[status(thm)],[])).
% 128.74/129.00 tff(166,plain,
% 128.74/129.00 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.74/129.00 inference(quant_inst,[status(thm)],[])).
% 128.74/129.00 tff(167,plain,
% 128.74/129.00 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.74/129.00 inference(modus_ponens,[status(thm)],[166, 165])).
% 128.74/129.00 tff(168,plain,
% 128.74/129.00 (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))),
% 128.74/129.00 inference(unit_resolution,[status(thm)],[167, 52, 164])).
% 128.74/129.00 tff(169,plain,
% 128.74/129.00 (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) <=> between(x, y, v)),
% 128.74/129.00 inference(monotonicity,[status(thm)],[94, 120, 21])).
% 128.74/129.00 tff(170,plain,
% 128.74/129.00 (between(x, y, v) <=> between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.74/129.00 inference(symmetry,[status(thm)],[169])).
% 128.74/129.00 tff(171,plain,
% 128.74/129.00 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(v, y, x)) | between(x, y, v))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(v, y, x)) | between(x, y, v))),
% 128.74/129.00 inference(rewrite,[status(thm)],[])).
% 128.74/129.00 tff(172,plain,
% 128.74/129.00 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(v, y, x)) | between(x, y, v))),
% 128.74/129.00 inference(quant_inst,[status(thm)],[])).
% 128.74/129.00 tff(173,plain,
% 128.74/129.00 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(v, y, x)) | between(x, y, v)),
% 128.74/129.00 inference(modus_ponens,[status(thm)],[172, 171])).
% 128.74/129.00 tff(174,plain,
% 128.74/129.00 (between(x, y, v)),
% 128.74/129.00 inference(unit_resolution,[status(thm)],[173, 52, 125])).
% 128.74/129.00 tff(175,plain,
% 128.74/129.00 (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.74/129.00 inference(modus_ponens,[status(thm)],[174, 170])).
% 128.74/129.00 tff(176,plain,
% 128.74/129.00 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.74/129.00 inference(rewrite,[status(thm)],[])).
% 128.74/129.00 tff(177,plain,
% 128.74/129.00 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.74/129.00 inference(quant_inst,[status(thm)],[])).
% 128.74/129.00 tff(178,plain,
% 128.74/129.00 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.74/129.00 inference(modus_ponens,[status(thm)],[177, 176])).
% 128.74/129.00 tff(179,plain,
% 128.74/129.00 (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.74/129.00 inference(unit_resolution,[status(thm)],[178, 52, 112])).
% 128.74/129.00 tff(180,plain,
% 128.74/129.00 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))),
% 128.74/129.00 inference(rewrite,[status(thm)],[])).
% 128.74/129.00 tff(181,plain,
% 128.74/129.00 (((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))) <=> (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))),
% 128.74/129.01 inference(rewrite,[status(thm)],[])).
% 128.74/129.01 tff(182,plain,
% 128.74/129.01 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))))),
% 128.74/129.01 inference(monotonicity,[status(thm)],[181])).
% 128.74/129.01 tff(183,plain,
% 128.74/129.01 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))),
% 128.74/129.01 inference(transitivity,[status(thm)],[182, 180])).
% 128.74/129.01 tff(184,plain,
% 128.74/129.01 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))),
% 128.74/129.01 inference(quant_inst,[status(thm)],[])).
% 128.74/129.01 tff(185,plain,
% 128.74/129.01 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(u, w, u, y), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.74/129.01 inference(modus_ponens,[status(thm)],[184, 183])).
% 128.74/129.01 tff(186,plain,
% 128.74/129.01 (~between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.74/129.01 inference(unit_resolution,[status(thm)],[185, 136, 179, 175])).
% 128.74/129.01 tff(187,plain,
% 128.74/129.01 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.74/129.01 inference(rewrite,[status(thm)],[])).
% 128.74/129.01 tff(188,plain,
% 128.74/129.01 (((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))) <=> ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.74/129.01 inference(rewrite,[status(thm)],[])).
% 128.74/129.01 tff(189,plain,
% 128.74/129.01 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))),
% 128.74/129.01 inference(monotonicity,[status(thm)],[188])).
% 128.74/129.01 tff(190,plain,
% 128.74/129.01 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.74/129.01 inference(transitivity,[status(thm)],[189, 187])).
% 128.74/129.01 tff(191,plain,
% 128.74/129.01 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))),
% 128.74/129.01 inference(quant_inst,[status(thm)],[])).
% 128.74/129.01 tff(192,plain,
% 128.74/129.01 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(u, w, u, y), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.74/129.01 inference(modus_ponens,[status(thm)],[191, 190])).
% 128.74/129.01 tff(193,plain,
% 128.74/129.01 (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.74/129.01 inference(unit_resolution,[status(thm)],[192, 157, 147, 186])).
% 128.74/129.01 tff(194,plain,
% 128.74/129.01 (equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> equidistant(u, w, w, u)),
% 128.74/129.02 inference(monotonicity,[status(thm)],[29, 73, 73, 29])).
% 128.74/129.02 tff(195,plain,
% 128.74/129.02 (equidistant(u, w, w, u) <=> equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.74/129.02 inference(symmetry,[status(thm)],[194])).
% 128.74/129.02 tff(196,plain,
% 128.74/129.02 (equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> equidistant(u, w, w, u)),
% 128.74/129.02 inference(monotonicity,[status(thm)],[29, 29])).
% 128.74/129.02 tff(197,plain,
% 128.74/129.02 (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)),
% 128.74/129.02 inference(monotonicity,[status(thm)],[29])).
% 128.74/129.02 tff(198,plain,
% 128.74/129.02 (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.74/129.02 inference(symmetry,[status(thm)],[197])).
% 128.74/129.02 tff(199,plain,
% 128.74/129.02 (equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.74/129.02 inference(monotonicity,[status(thm)],[198])).
% 128.74/129.02 tff(200,plain,
% 128.74/129.02 (equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) <=> equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.74/129.02 inference(symmetry,[status(thm)],[199])).
% 128.74/129.02 tff(201,plain,
% 128.74/129.02 (^[V: $i, W1: $i, U: $i, U1: $i] : refl(equidistant(U, V, U1, insertion(U1, W1, U, V)) <=> equidistant(U, V, U1, insertion(U1, W1, U, V)))),
% 128.74/129.02 inference(bind,[status(th)],[])).
% 128.74/129.02 tff(202,plain,
% 128.74/129.02 (![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V)) <=> ![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V))),
% 128.74/129.02 inference(quant_intro,[status(thm)],[201])).
% 128.74/129.02 tff(203,plain,
% 128.74/129.02 (![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V)) <=> ![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V))),
% 128.74/129.02 inference(rewrite,[status(thm)],[])).
% 128.74/129.02 tff(204,axiom,(![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','i2_1')).
% 128.74/129.02 tff(205,plain,
% 128.74/129.02 (![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V))),
% 128.74/129.02 inference(modus_ponens,[status(thm)],[204, 203])).
% 128.74/129.02 tff(206,plain,(
% 128.74/129.02 ![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V))),
% 128.85/129.02 inference(skolemize,[status(sab)],[205])).
% 128.85/129.02 tff(207,plain,
% 128.85/129.02 (![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[206, 202])).
% 128.85/129.02 tff(208,plain,
% 128.85/129.02 ((~![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V))) | equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.85/129.02 inference(quant_inst,[status(thm)],[])).
% 128.85/129.02 tff(209,plain,
% 128.85/129.02 (equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.85/129.02 inference(unit_resolution,[status(thm)],[208, 207])).
% 128.85/129.02 tff(210,plain,
% 128.85/129.02 (equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[209, 200])).
% 128.85/129.02 tff(211,plain,
% 128.85/129.02 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(X, W, U, V)) <=> ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V)))),
% 128.85/129.02 inference(bind,[status(th)],[])).
% 128.85/129.02 tff(212,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 128.85/129.02 inference(quant_intro,[status(thm)],[211])).
% 128.85/129.02 tff(213,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 128.85/129.02 inference(rewrite,[status(thm)],[])).
% 128.85/129.02 tff(214,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_4')).
% 128.85/129.02 tff(215,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[214, 213])).
% 128.85/129.02 tff(216,plain,(
% 128.85/129.02 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 128.85/129.02 inference(skolemize,[status(sab)],[215])).
% 128.85/129.02 tff(217,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[216, 212])).
% 128.85/129.02 tff(218,plain,
% 128.85/129.02 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.85/129.02 inference(rewrite,[status(thm)],[])).
% 128.85/129.02 tff(219,plain,
% 128.85/129.02 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.85/129.02 inference(quant_inst,[status(thm)],[])).
% 128.85/129.02 tff(220,plain,
% 128.85/129.02 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[219, 218])).
% 128.85/129.02 tff(221,plain,
% 128.85/129.02 ((~equidistant(w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.85/129.02 inference(unit_resolution,[status(thm)],[220, 217])).
% 128.85/129.02 tff(222,plain,
% 128.85/129.02 (equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w, w, insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.85/129.02 inference(unit_resolution,[status(thm)],[221, 210])).
% 128.85/129.02 tff(223,plain,
% 128.85/129.02 (equidistant(u, w, w, u)),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[222, 196])).
% 128.85/129.02 tff(224,plain,
% 128.85/129.02 (equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[223, 195])).
% 128.85/129.02 tff(225,plain,
% 128.85/129.02 (equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) <=> equidistant(u, x, w, v)),
% 128.85/129.02 inference(monotonicity,[status(thm)],[29, 94, 73, 21])).
% 128.85/129.02 tff(226,plain,
% 128.85/129.02 (equidistant(u, x, w, v) <=> equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.02 inference(symmetry,[status(thm)],[225])).
% 128.85/129.02 tff(227,plain,
% 128.85/129.02 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)) <=> ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)))),
% 128.85/129.02 inference(bind,[status(th)],[])).
% 128.85/129.02 tff(228,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 128.85/129.02 inference(quant_intro,[status(thm)],[227])).
% 128.85/129.02 tff(229,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 128.85/129.02 inference(rewrite,[status(thm)],[])).
% 128.85/129.02 tff(230,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_5')).
% 128.85/129.02 tff(231,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[230, 229])).
% 128.85/129.02 tff(232,plain,(
% 128.85/129.02 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 128.85/129.02 inference(skolemize,[status(sab)],[231])).
% 128.85/129.02 tff(233,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[232, 228])).
% 128.85/129.02 tff(234,plain,
% 128.85/129.02 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(v, w, x, u)) | equidistant(u, x, w, v))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(v, w, x, u)) | equidistant(u, x, w, v))),
% 128.85/129.02 inference(rewrite,[status(thm)],[])).
% 128.85/129.02 tff(235,plain,
% 128.85/129.02 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(v, w, x, u)) | equidistant(u, x, w, v))),
% 128.85/129.02 inference(quant_inst,[status(thm)],[])).
% 128.85/129.02 tff(236,plain,
% 128.85/129.02 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(v, w, x, u)) | equidistant(u, x, w, v)),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[235, 234])).
% 128.85/129.02 tff(237,plain,
% 128.85/129.02 (equidistant(u, x, w, v)),
% 128.85/129.02 inference(unit_resolution,[status(thm)],[236, 233, 99])).
% 128.85/129.02 tff(238,plain,
% 128.85/129.02 (equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[237, 226])).
% 128.85/129.02 tff(239,plain,
% 128.85/129.02 (equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) <=> equidistant(w, x, u, v)),
% 128.85/129.02 inference(monotonicity,[status(thm)],[73, 94, 29, 21])).
% 128.85/129.02 tff(240,plain,
% 128.85/129.02 (equidistant(w, x, u, v) <=> equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.02 inference(symmetry,[status(thm)],[239])).
% 128.85/129.02 tff(241,plain,
% 128.85/129.02 (equidistant(u, v, w, x) <=> equidistant(u, v, w, x)),
% 128.85/129.02 inference(rewrite,[status(thm)],[])).
% 128.85/129.02 tff(242,axiom,(equidistant(u, v, w, x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','u_to_v_equals_w_to_x')).
% 128.85/129.02 tff(243,plain,
% 128.85/129.02 (equidistant(u, v, w, x)),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[242, 241])).
% 128.85/129.02 tff(244,plain,
% 128.85/129.02 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)))),
% 128.85/129.02 inference(bind,[status(th)],[])).
% 128.85/129.02 tff(245,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 128.85/129.02 inference(quant_intro,[status(thm)],[244])).
% 128.85/129.02 tff(246,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 128.85/129.02 inference(rewrite,[status(thm)],[])).
% 128.85/129.02 tff(247,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2')).
% 128.85/129.02 tff(248,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[247, 246])).
% 128.85/129.02 tff(249,plain,(
% 128.85/129.02 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 128.85/129.02 inference(skolemize,[status(sab)],[248])).
% 128.85/129.02 tff(250,plain,
% 128.85/129.02 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[249, 245])).
% 128.85/129.02 tff(251,plain,
% 128.85/129.02 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(u, v, w, x)) | equidistant(w, x, u, v))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(u, v, w, x)) | equidistant(w, x, u, v))),
% 128.85/129.02 inference(rewrite,[status(thm)],[])).
% 128.85/129.02 tff(252,plain,
% 128.85/129.02 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(u, v, w, x)) | equidistant(w, x, u, v))),
% 128.85/129.02 inference(quant_inst,[status(thm)],[])).
% 128.85/129.02 tff(253,plain,
% 128.85/129.02 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(u, v, w, x)) | equidistant(w, x, u, v)),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[252, 251])).
% 128.85/129.02 tff(254,plain,
% 128.85/129.02 (equidistant(w, x, u, v)),
% 128.85/129.02 inference(unit_resolution,[status(thm)],[253, 250, 243])).
% 128.85/129.02 tff(255,plain,
% 128.85/129.02 (equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[254, 240])).
% 128.85/129.02 tff(256,plain,
% 128.85/129.02 (^[W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : refl((between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) <=> (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))))),
% 128.85/129.02 inference(bind,[status(th)],[])).
% 128.85/129.02 tff(257,plain,
% 128.85/129.02 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))),
% 128.85/129.02 inference(quant_intro,[status(thm)],[256])).
% 128.85/129.02 tff(258,plain,
% 128.85/129.02 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))),
% 128.85/129.02 inference(rewrite,[status(thm)],[])).
% 128.85/129.02 tff(259,plain,
% 128.85/129.02 (^[W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) <=> ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~between(U, V, W))) <=> (((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~between(U, V, W))))), rewrite((((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~between(U, V, W))) <=> ((~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~between(U, V, W))) <=> ((~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))))), ((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~between(U, V, W))) | between(U1, V1, W1)) <=> (((~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | between(U1, V1, W1)))), rewrite((((~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | between(U1, V1, W1)) <=> (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))), ((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~between(U, V, W))) | between(U1, V1, W1)) <=> (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))))),
% 128.85/129.02 inference(bind,[status(th)],[])).
% 128.85/129.02 tff(260,plain,
% 128.85/129.02 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~between(U, V, W))) | between(U1, V1, W1)) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))),
% 128.85/129.02 inference(quant_intro,[status(thm)],[259])).
% 128.85/129.02 tff(261,axiom,(![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~between(U, V, W))) | between(U1, V1, W1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b11')).
% 128.85/129.02 tff(262,plain,
% 128.85/129.02 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[261, 260])).
% 128.85/129.02 tff(263,plain,
% 128.85/129.02 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))),
% 128.85/129.02 inference(modus_ponens,[status(thm)],[262, 258])).
% 128.85/129.03 tff(264,plain,(
% 128.85/129.03 ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))),
% 128.85/129.03 inference(skolemize,[status(sab)],[263])).
% 128.85/129.03 tff(265,plain,
% 128.85/129.03 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))),
% 128.85/129.03 inference(modus_ponens,[status(thm)],[264, 257])).
% 128.85/129.03 tff(266,plain,
% 128.85/129.03 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | ((~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.85/129.03 inference(rewrite,[status(thm)],[])).
% 128.85/129.03 tff(267,plain,
% 128.85/129.03 ((between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))) <=> ((~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.85/129.03 inference(rewrite,[status(thm)],[])).
% 128.85/129.03 tff(268,plain,
% 128.85/129.03 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | ((~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))),
% 128.85/129.03 inference(monotonicity,[status(thm)],[267])).
% 128.85/129.03 tff(269,plain,
% 128.85/129.03 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.85/129.04 inference(transitivity,[status(thm)],[268, 266])).
% 128.85/129.04 tff(270,plain,
% 128.85/129.04 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))),
% 128.85/129.04 inference(quant_inst,[status(thm)],[])).
% 128.85/129.04 tff(271,plain,
% 128.85/129.04 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.04 inference(modus_ponens,[status(thm)],[270, 269])).
% 128.85/129.04 tff(272,plain,
% 128.85/129.04 ((~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.04 inference(unit_resolution,[status(thm)],[271, 265, 255, 238, 224])).
% 128.85/129.04 tff(273,plain,
% 128.85/129.04 (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.04 inference(unit_resolution,[status(thm)],[272, 193])).
% 128.85/129.04 tff(274,plain,
% 128.85/129.04 (colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> colinear(w, x, u)),
% 128.85/129.04 inference(monotonicity,[status(thm)],[73, 94, 29])).
% 128.85/129.04 tff(275,plain,
% 128.85/129.04 (colinear(w, x, u) <=> colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.85/129.04 inference(symmetry,[status(thm)],[274])).
% 128.85/129.04 tff(276,plain,
% 128.85/129.04 (colinear(u, v, w) <=> colinear(u, v, w)),
% 128.85/129.04 inference(rewrite,[status(thm)],[])).
% 128.85/129.04 tff(277,axiom,(colinear(u, v, w)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_uvw_not_colinear')).
% 128.85/129.04 tff(278,plain,
% 128.85/129.04 (colinear(u, v, w)),
% 128.85/129.04 inference(modus_ponens,[status(thm)],[277, 276])).
% 128.85/129.04 tff(279,plain,
% 128.85/129.04 (^[W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : refl(((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W))) <=> ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W))))),
% 128.85/129.04 inference(bind,[status(th)],[])).
% 128.85/129.04 tff(280,plain,
% 128.85/129.04 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W))) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))),
% 128.85/129.04 inference(quant_intro,[status(thm)],[279])).
% 128.85/129.04 tff(281,plain,
% 128.85/129.04 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W))) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))),
% 128.85/129.04 inference(rewrite,[status(thm)],[])).
% 128.85/129.04 tff(282,plain,
% 128.85/129.04 (^[W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) <=> ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~colinear(U, V, W))) <=> (((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~colinear(U, V, W))))), rewrite((((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~colinear(U, V, W))) <=> ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | (~colinear(U, V, W)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~colinear(U, V, W))) <=> ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | (~colinear(U, V, W))))), ((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~colinear(U, V, W))) | colinear(U1, V1, W1)) <=> (((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | (~colinear(U, V, W))) | colinear(U1, V1, W1)))), rewrite((((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | (~colinear(U, V, W))) | colinear(U1, V1, W1)) <=> ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))), ((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~colinear(U, V, W))) | colinear(U1, V1, W1)) <=> ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))))),
% 128.85/129.04 inference(bind,[status(th)],[])).
% 128.85/129.04 tff(283,plain,
% 128.85/129.04 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~colinear(U, V, W))) | colinear(U1, V1, W1)) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))),
% 128.85/129.04 inference(quant_intro,[status(thm)],[282])).
% 128.85/129.04 tff(284,axiom,(![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, W, U1, W1))) | (~colinear(U, V, W))) | colinear(U1, V1, W1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c4')).
% 128.85/129.04 tff(285,plain,
% 128.85/129.04 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))),
% 128.85/129.04 inference(modus_ponens,[status(thm)],[284, 283])).
% 128.85/129.04 tff(286,plain,
% 128.85/129.04 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))),
% 128.85/129.04 inference(modus_ponens,[status(thm)],[285, 281])).
% 128.85/129.04 tff(287,plain,(
% 128.85/129.04 ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))),
% 128.85/129.04 inference(skolemize,[status(sab)],[286])).
% 128.85/129.04 tff(288,plain,
% 128.85/129.04 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))),
% 128.85/129.04 inference(modus_ponens,[status(thm)],[287, 280])).
% 128.85/129.04 tff(289,plain,
% 128.85/129.04 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))) | ((~equidistant(u, v, w, x)) | (~equidistant(v, w, x, u)) | (~equidistant(u, w, w, u)) | colinear(w, x, u) | (~colinear(u, v, w)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))) | (~equidistant(u, v, w, x)) | (~equidistant(v, w, x, u)) | (~equidistant(u, w, w, u)) | colinear(w, x, u) | (~colinear(u, v, w)))),
% 128.85/129.04 inference(rewrite,[status(thm)],[])).
% 128.85/129.04 tff(290,plain,
% 128.85/129.04 (((~equidistant(v, w, x, u)) | (~equidistant(u, v, w, x)) | (~equidistant(u, w, w, u)) | colinear(w, x, u) | (~colinear(u, v, w))) <=> ((~equidistant(u, v, w, x)) | (~equidistant(v, w, x, u)) | (~equidistant(u, w, w, u)) | colinear(w, x, u) | (~colinear(u, v, w)))),
% 128.85/129.04 inference(rewrite,[status(thm)],[])).
% 128.85/129.04 tff(291,plain,
% 128.85/129.04 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))) | ((~equidistant(v, w, x, u)) | (~equidistant(u, v, w, x)) | (~equidistant(u, w, w, u)) | colinear(w, x, u) | (~colinear(u, v, w)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))) | ((~equidistant(u, v, w, x)) | (~equidistant(v, w, x, u)) | (~equidistant(u, w, w, u)) | colinear(w, x, u) | (~colinear(u, v, w))))),
% 128.85/129.04 inference(monotonicity,[status(thm)],[290])).
% 128.85/129.04 tff(292,plain,
% 128.85/129.04 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))) | ((~equidistant(v, w, x, u)) | (~equidistant(u, v, w, x)) | (~equidistant(u, w, w, u)) | colinear(w, x, u) | (~colinear(u, v, w)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))) | (~equidistant(u, v, w, x)) | (~equidistant(v, w, x, u)) | (~equidistant(u, w, w, u)) | colinear(w, x, u) | (~colinear(u, v, w)))),
% 128.85/129.05 inference(transitivity,[status(thm)],[291, 289])).
% 128.85/129.05 tff(293,plain,
% 128.85/129.05 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))) | ((~equidistant(v, w, x, u)) | (~equidistant(u, v, w, x)) | (~equidistant(u, w, w, u)) | colinear(w, x, u) | (~colinear(u, v, w)))),
% 128.85/129.05 inference(quant_inst,[status(thm)],[])).
% 128.85/129.05 tff(294,plain,
% 128.85/129.05 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : ((~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)) | colinear(U1, V1, W1) | (~colinear(U, V, W)))) | (~equidistant(u, v, w, x)) | (~equidistant(v, w, x, u)) | (~equidistant(u, w, w, u)) | colinear(w, x, u) | (~colinear(u, v, w))),
% 128.85/129.05 inference(modus_ponens,[status(thm)],[293, 292])).
% 128.85/129.05 tff(295,plain,
% 128.85/129.05 ((~equidistant(u, w, w, u)) | colinear(w, x, u)),
% 128.85/129.05 inference(unit_resolution,[status(thm)],[294, 288, 243, 99, 278])).
% 128.85/129.05 tff(296,plain,
% 128.85/129.05 (colinear(w, x, u)),
% 128.85/129.05 inference(unit_resolution,[status(thm)],[295, 223])).
% 128.85/129.05 tff(297,plain,
% 128.85/129.05 (colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.85/129.05 inference(modus_ponens,[status(thm)],[296, 275])).
% 128.85/129.05 tff(298,plain,
% 128.85/129.05 (^[Z: $i, Y: $i, X: $i] : refl((between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) <=> (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))))),
% 128.85/129.05 inference(bind,[status(th)],[])).
% 128.85/129.05 tff(299,plain,
% 128.85/129.05 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 128.85/129.05 inference(quant_intro,[status(thm)],[298])).
% 128.85/129.05 tff(300,plain,
% 128.85/129.05 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 128.85/129.05 inference(rewrite,[status(thm)],[])).
% 128.85/129.05 tff(301,plain,
% 128.85/129.05 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) <=> (between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))), (((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) <=> ((between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) | between(Z, X, Y)))), rewrite(((between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) | between(Z, X, Y)) <=> (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))), (((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) <=> (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))))),
% 128.85/129.05 inference(bind,[status(th)],[])).
% 128.85/129.05 tff(302,plain,
% 128.85/129.05 (![Z: $i, Y: $i, X: $i] : ((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) <=> ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 128.85/129.05 inference(quant_intro,[status(thm)],[301])).
% 128.85/129.05 tff(303,axiom,(![Z: $i, Y: $i, X: $i] : ((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax','colinearity4')).
% 128.85/129.05 tff(304,plain,
% 128.85/129.05 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 128.85/129.05 inference(modus_ponens,[status(thm)],[303, 302])).
% 128.85/129.05 tff(305,plain,
% 128.85/129.05 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 128.85/129.05 inference(modus_ponens,[status(thm)],[304, 300])).
% 128.85/129.05 tff(306,plain,(
% 128.85/129.05 ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 128.85/129.05 inference(skolemize,[status(sab)],[305])).
% 128.85/129.05 tff(307,plain,
% 128.85/129.05 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 128.85/129.05 inference(modus_ponens,[status(thm)],[306, 299])).
% 128.85/129.05 tff(308,plain,
% 128.85/129.05 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))),
% 128.85/129.05 inference(rewrite,[status(thm)],[])).
% 128.85/129.05 tff(309,plain,
% 128.85/129.05 ((between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))) <=> (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))),
% 128.85/129.05 inference(rewrite,[status(thm)],[])).
% 128.85/129.05 tff(310,plain,
% 128.85/129.05 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))))),
% 128.85/129.05 inference(monotonicity,[status(thm)],[309])).
% 128.85/129.05 tff(311,plain,
% 128.85/129.05 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))),
% 128.85/129.06 inference(transitivity,[status(thm)],[310, 308])).
% 128.85/129.06 tff(312,plain,
% 128.85/129.06 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))),
% 128.85/129.06 inference(quant_inst,[status(thm)],[])).
% 128.85/129.06 tff(313,plain,
% 128.85/129.06 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.85/129.06 inference(modus_ponens,[status(thm)],[312, 311])).
% 128.85/129.06 tff(314,plain,
% 128.85/129.06 (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~colinear(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.85/129.06 inference(unit_resolution,[status(thm)],[313, 307])).
% 128.85/129.06 tff(315,plain,
% 128.85/129.06 (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.06 inference(unit_resolution,[status(thm)],[314, 297])).
% 128.85/129.06 tff(316,plain,
% 128.85/129.06 (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.85/129.06 inference(unit_resolution,[status(thm)],[315, 273, 168])).
% 128.85/129.06 tff(317,plain,
% 128.85/129.06 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x) = insertion(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x) = insertion(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.85/129.06 inference(rewrite,[status(thm)],[])).
% 128.85/129.06 tff(318,plain,
% 128.85/129.06 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x) = insertion(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.85/129.06 inference(quant_inst,[status(thm)],[])).
% 128.85/129.06 tff(319,plain,
% 128.85/129.06 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x) = insertion(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.85/129.07 inference(modus_ponens,[status(thm)],[318, 317])).
% 128.85/129.07 tff(320,plain,
% 128.85/129.07 (extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x) = insertion(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.07 inference(unit_resolution,[status(thm)],[319, 16, 316])).
% 128.85/129.07 tff(321,plain,
% 128.85/129.07 (insertion(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)),
% 128.85/129.07 inference(symmetry,[status(thm)],[320])).
% 128.85/129.07 tff(322,plain,
% 128.85/129.07 (equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) <=> equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.07 inference(monotonicity,[status(thm)],[321])).
% 128.85/129.07 tff(323,plain,
% 128.85/129.07 ((~![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V))) | equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.85/129.07 inference(quant_inst,[status(thm)],[])).
% 128.85/129.07 tff(324,plain,
% 128.85/129.07 (equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.85/129.07 inference(unit_resolution,[status(thm)],[323, 207])).
% 128.85/129.07 tff(325,plain,
% 128.85/129.07 (equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.07 inference(modus_ponens,[status(thm)],[324, 322])).
% 128.85/129.07 tff(326,plain,
% 128.85/129.07 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.85/129.07 inference(rewrite,[status(thm)],[])).
% 128.85/129.07 tff(327,plain,
% 128.85/129.07 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.85/129.07 inference(quant_inst,[status(thm)],[])).
% 128.85/129.07 tff(328,plain,
% 128.85/129.07 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.07 inference(modus_ponens,[status(thm)],[327, 326])).
% 128.85/129.07 tff(329,plain,
% 128.85/129.07 (equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.08 inference(unit_resolution,[status(thm)],[328, 217, 325])).
% 128.85/129.08 tff(330,plain,
% 128.85/129.08 (equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) <=> equidistant(u, x, v, w)),
% 128.85/129.08 inference(monotonicity,[status(thm)],[29, 94, 21, 73])).
% 128.85/129.08 tff(331,plain,
% 128.85/129.08 (equidistant(u, x, v, w) <=> equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))),
% 128.85/129.08 inference(symmetry,[status(thm)],[330])).
% 128.85/129.08 tff(332,plain,
% 128.85/129.08 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(v, w, x, u)) | equidistant(u, x, v, w))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(v, w, x, u)) | equidistant(u, x, v, w))),
% 128.85/129.08 inference(rewrite,[status(thm)],[])).
% 128.85/129.08 tff(333,plain,
% 128.85/129.08 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(v, w, x, u)) | equidistant(u, x, v, w))),
% 128.85/129.08 inference(quant_inst,[status(thm)],[])).
% 128.85/129.08 tff(334,plain,
% 128.85/129.08 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(v, w, x, u)) | equidistant(u, x, v, w)),
% 128.85/129.08 inference(modus_ponens,[status(thm)],[333, 332])).
% 128.85/129.08 tff(335,plain,
% 128.85/129.08 (equidistant(u, x, v, w)),
% 128.85/129.08 inference(unit_resolution,[status(thm)],[334, 217, 99])).
% 128.85/129.08 tff(336,plain,
% 128.85/129.08 (equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))),
% 128.85/129.08 inference(modus_ponens,[status(thm)],[335, 331])).
% 128.85/129.08 tff(337,plain,
% 128.85/129.08 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)))),
% 128.85/129.08 inference(rewrite,[status(thm)],[])).
% 128.85/129.08 tff(338,plain,
% 128.85/129.08 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)))),
% 128.85/129.08 inference(quant_inst,[status(thm)],[])).
% 128.85/129.08 tff(339,plain,
% 128.85/129.08 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))),
% 128.85/129.08 inference(modus_ponens,[status(thm)],[338, 337])).
% 128.85/129.08 tff(340,plain,
% 128.85/129.08 (between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))),
% 128.85/129.08 inference(unit_resolution,[status(thm)],[339, 52, 316])).
% 128.85/129.08 tff(341,plain,
% 128.85/129.08 (equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) <=> equidistant(u, w, v, x)),
% 128.85/129.08 inference(monotonicity,[status(thm)],[29, 73, 21, 94])).
% 128.85/129.08 tff(342,plain,
% 128.85/129.08 (equidistant(u, w, v, x) <=> equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.08 inference(symmetry,[status(thm)],[341])).
% 128.85/129.08 tff(343,plain,
% 128.85/129.08 (equidistant(u, w, v, x) <=> equidistant(u, w, v, x)),
% 128.85/129.08 inference(rewrite,[status(thm)],[])).
% 128.85/129.08 tff(344,axiom,(equidistant(u, w, v, x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','u_to_w_equals_v_to_x')).
% 128.85/129.08 tff(345,plain,
% 128.85/129.08 (equidistant(u, w, v, x)),
% 128.85/129.08 inference(modus_ponens,[status(thm)],[344, 343])).
% 128.85/129.08 tff(346,plain,
% 128.85/129.08 (equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.08 inference(modus_ponens,[status(thm)],[345, 342])).
% 128.85/129.08 tff(347,plain,
% 128.85/129.08 (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) <=> between(x, w, v)),
% 128.85/129.08 inference(monotonicity,[status(thm)],[94, 73, 21])).
% 128.85/129.08 tff(348,plain,
% 128.85/129.08 (between(x, w, v) <=> between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.08 inference(symmetry,[status(thm)],[347])).
% 128.85/129.08 tff(349,plain,
% 128.85/129.08 ((~between(x, w, v)) <=> (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.85/129.08 inference(monotonicity,[status(thm)],[348])).
% 128.85/129.08 tff(350,plain,
% 128.85/129.08 (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) <=> between(v, u, x)),
% 128.85/129.08 inference(monotonicity,[status(thm)],[21, 29, 94])).
% 128.85/129.08 tff(351,plain,
% 128.85/129.08 ((~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) <=> (~between(v, u, x))),
% 128.85/129.08 inference(monotonicity,[status(thm)],[350])).
% 128.85/129.08 tff(352,plain,
% 128.85/129.08 (~between(v, u, x)),
% 128.85/129.08 inference(modus_ponens,[status(thm)],[112, 351])).
% 128.85/129.08 tff(353,plain,
% 128.85/129.08 (equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x) <=> equidistant(x, v, v, x)),
% 128.85/129.08 inference(monotonicity,[status(thm)],[21, 21])).
% 128.85/129.08 tff(354,plain,
% 128.85/129.08 (insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)),
% 128.85/129.08 inference(monotonicity,[status(thm)],[21])).
% 128.85/129.08 tff(355,plain,
% 128.85/129.08 (insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.08 inference(symmetry,[status(thm)],[354])).
% 128.85/129.08 tff(356,plain,
% 128.85/129.08 (equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) <=> equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.85/129.08 inference(monotonicity,[status(thm)],[355])).
% 128.85/129.08 tff(357,plain,
% 128.85/129.08 (equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) <=> equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.08 inference(symmetry,[status(thm)],[356])).
% 128.85/129.08 tff(358,plain,
% 128.85/129.08 ((~![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V))) | equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.85/129.08 inference(quant_inst,[status(thm)],[])).
% 128.85/129.08 tff(359,plain,
% 128.85/129.08 (equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.85/129.08 inference(unit_resolution,[status(thm)],[358, 207])).
% 128.85/129.08 tff(360,plain,
% 128.85/129.08 (equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.08 inference(modus_ponens,[status(thm)],[359, 357])).
% 128.85/129.08 tff(361,plain,
% 128.85/129.08 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.09 inference(rewrite,[status(thm)],[])).
% 128.85/129.09 tff(362,plain,
% 128.85/129.09 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.09 inference(quant_inst,[status(thm)],[])).
% 128.85/129.09 tff(363,plain,
% 128.85/129.09 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)),
% 128.85/129.09 inference(modus_ponens,[status(thm)],[362, 361])).
% 128.85/129.09 tff(364,plain,
% 128.85/129.09 ((~equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)),
% 128.85/129.09 inference(unit_resolution,[status(thm)],[363, 106])).
% 128.85/129.09 tff(365,plain,
% 128.85/129.09 (equidistant(x, insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)),
% 128.85/129.09 inference(unit_resolution,[status(thm)],[364, 360])).
% 128.85/129.09 tff(366,plain,
% 128.85/129.09 (equidistant(x, v, v, x)),
% 128.85/129.09 inference(modus_ponens,[status(thm)],[365, 353])).
% 128.85/129.09 tff(367,plain,
% 128.85/129.09 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)) <=> ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)))),
% 128.85/129.09 inference(bind,[status(th)],[])).
% 128.85/129.09 tff(368,plain,
% 128.85/129.09 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 128.85/129.09 inference(quant_intro,[status(thm)],[367])).
% 128.85/129.09 tff(369,plain,
% 128.85/129.09 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 128.85/129.09 inference(rewrite,[status(thm)],[])).
% 128.85/129.09 tff(370,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_2')).
% 128.85/129.09 tff(371,plain,
% 128.85/129.09 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 128.85/129.09 inference(modus_ponens,[status(thm)],[370, 369])).
% 128.85/129.09 tff(372,plain,(
% 128.85/129.09 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 128.85/129.09 inference(skolemize,[status(sab)],[371])).
% 128.85/129.09 tff(373,plain,
% 128.85/129.09 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 128.85/129.09 inference(modus_ponens,[status(thm)],[372, 368])).
% 128.85/129.09 tff(374,plain,
% 128.85/129.09 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | ((~equidistant(v, w, x, u)) | equidistant(w, v, u, x))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | (~equidistant(v, w, x, u)) | equidistant(w, v, u, x))),
% 128.85/129.09 inference(rewrite,[status(thm)],[])).
% 128.85/129.09 tff(375,plain,
% 128.85/129.09 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | ((~equidistant(v, w, x, u)) | equidistant(w, v, u, x))),
% 128.85/129.09 inference(quant_inst,[status(thm)],[])).
% 128.85/129.09 tff(376,plain,
% 128.85/129.09 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | (~equidistant(v, w, x, u)) | equidistant(w, v, u, x)),
% 128.85/129.09 inference(modus_ponens,[status(thm)],[375, 374])).
% 128.85/129.09 tff(377,plain,
% 128.85/129.09 (equidistant(w, v, u, x)),
% 128.85/129.09 inference(unit_resolution,[status(thm)],[376, 373, 99])).
% 128.85/129.09 tff(378,plain,
% 128.85/129.09 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(u, v, w, x)) | equidistant(x, w, v, u))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(u, v, w, x)) | equidistant(x, w, v, u))),
% 128.85/129.09 inference(rewrite,[status(thm)],[])).
% 128.85/129.09 tff(379,plain,
% 128.85/129.09 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(u, v, w, x)) | equidistant(x, w, v, u))),
% 128.85/129.09 inference(quant_inst,[status(thm)],[])).
% 128.85/129.09 tff(380,plain,
% 128.85/129.09 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(u, v, w, x)) | equidistant(x, w, v, u)),
% 128.85/129.09 inference(modus_ponens,[status(thm)],[379, 378])).
% 128.85/129.09 tff(381,plain,
% 128.85/129.09 (equidistant(x, w, v, u)),
% 128.85/129.09 inference(unit_resolution,[status(thm)],[380, 233, 243])).
% 128.85/129.09 tff(382,plain,
% 128.85/129.09 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | ((~equidistant(x, w, v, u)) | (~equidistant(w, v, u, x)) | (~equidistant(x, v, v, x)) | between(v, u, x) | (~between(x, w, v)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (~equidistant(x, w, v, u)) | (~equidistant(w, v, u, x)) | (~equidistant(x, v, v, x)) | between(v, u, x) | (~between(x, w, v)))),
% 128.85/129.09 inference(rewrite,[status(thm)],[])).
% 128.85/129.09 tff(383,plain,
% 128.85/129.09 ((between(v, u, x) | (~between(x, w, v)) | (~equidistant(w, v, u, x)) | (~equidistant(x, w, v, u)) | (~equidistant(x, v, v, x))) <=> ((~equidistant(x, w, v, u)) | (~equidistant(w, v, u, x)) | (~equidistant(x, v, v, x)) | between(v, u, x) | (~between(x, w, v)))),
% 128.85/129.09 inference(rewrite,[status(thm)],[])).
% 128.85/129.09 tff(384,plain,
% 128.85/129.09 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(v, u, x) | (~between(x, w, v)) | (~equidistant(w, v, u, x)) | (~equidistant(x, w, v, u)) | (~equidistant(x, v, v, x)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | ((~equidistant(x, w, v, u)) | (~equidistant(w, v, u, x)) | (~equidistant(x, v, v, x)) | between(v, u, x) | (~between(x, w, v))))),
% 128.85/129.09 inference(monotonicity,[status(thm)],[383])).
% 128.85/129.09 tff(385,plain,
% 128.85/129.09 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(v, u, x) | (~between(x, w, v)) | (~equidistant(w, v, u, x)) | (~equidistant(x, w, v, u)) | (~equidistant(x, v, v, x)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (~equidistant(x, w, v, u)) | (~equidistant(w, v, u, x)) | (~equidistant(x, v, v, x)) | between(v, u, x) | (~between(x, w, v)))),
% 128.85/129.09 inference(transitivity,[status(thm)],[384, 382])).
% 128.85/129.09 tff(386,plain,
% 128.85/129.09 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(v, u, x) | (~between(x, w, v)) | (~equidistant(w, v, u, x)) | (~equidistant(x, w, v, u)) | (~equidistant(x, v, v, x)))),
% 128.85/129.09 inference(quant_inst,[status(thm)],[])).
% 128.85/129.09 tff(387,plain,
% 128.85/129.09 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (~equidistant(x, w, v, u)) | (~equidistant(w, v, u, x)) | (~equidistant(x, v, v, x)) | between(v, u, x) | (~between(x, w, v))),
% 128.85/129.09 inference(modus_ponens,[status(thm)],[386, 385])).
% 128.85/129.09 tff(388,plain,
% 128.85/129.09 ((~equidistant(x, v, v, x)) | between(v, u, x) | (~between(x, w, v))),
% 128.85/129.09 inference(unit_resolution,[status(thm)],[387, 265, 381, 377])).
% 128.85/129.09 tff(389,plain,
% 128.85/129.09 (between(v, u, x) | (~between(x, w, v))),
% 128.85/129.09 inference(unit_resolution,[status(thm)],[388, 366])).
% 128.85/129.09 tff(390,plain,
% 128.85/129.09 (~between(x, w, v)),
% 128.85/129.09 inference(unit_resolution,[status(thm)],[389, 352])).
% 128.85/129.09 tff(391,plain,
% 128.85/129.09 (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.09 inference(modus_ponens,[status(thm)],[390, 349])).
% 128.85/129.09 tff(392,plain,
% 128.85/129.09 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.85/129.09 inference(rewrite,[status(thm)],[])).
% 128.85/129.09 tff(393,plain,
% 128.85/129.09 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.85/129.09 inference(quant_inst,[status(thm)],[])).
% 128.85/129.09 tff(394,plain,
% 128.85/129.09 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.85/129.09 inference(modus_ponens,[status(thm)],[393, 392])).
% 128.85/129.09 tff(395,plain,
% 128.85/129.09 (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.85/129.09 inference(unit_resolution,[status(thm)],[394, 52, 391])).
% 128.85/129.09 tff(396,plain,
% 128.85/129.09 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.92/129.10 inference(rewrite,[status(thm)],[])).
% 128.92/129.10 tff(397,plain,
% 128.92/129.10 ((between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))) <=> (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.92/129.10 inference(rewrite,[status(thm)],[])).
% 128.92/129.10 tff(398,plain,
% 128.92/129.10 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))))),
% 128.92/129.10 inference(monotonicity,[status(thm)],[397])).
% 128.92/129.10 tff(399,plain,
% 128.92/129.10 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.92/129.11 inference(transitivity,[status(thm)],[398, 396])).
% 128.92/129.11 tff(400,plain,
% 128.92/129.11 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.92/129.11 inference(quant_inst,[status(thm)],[])).
% 128.92/129.11 tff(401,plain,
% 128.92/129.11 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.92/129.11 inference(modus_ponens,[status(thm)],[400, 399])).
% 128.92/129.11 tff(402,plain,
% 128.92/129.11 ($false),
% 128.92/129.11 inference(unit_resolution,[status(thm)],[401, 265, 395, 346, 340, 336, 329])).
% 128.92/129.11 tff(403,plain,(between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))), inference(lemma,lemma(discharge,[]))).
% 128.92/129.11 tff(404,plain,
% 128.92/129.11 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))),
% 128.92/129.11 inference(rewrite,[status(thm)],[])).
% 128.92/129.11 tff(405,plain,
% 128.92/129.11 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))),
% 128.92/129.11 inference(quant_inst,[status(thm)],[])).
% 128.92/129.11 tff(406,plain,
% 128.92/129.11 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.92/129.11 inference(modus_ponens,[status(thm)],[405, 404])).
% 128.92/129.11 tff(407,plain,
% 128.92/129.11 (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.11 inference(unit_resolution,[status(thm)],[406, 16, 403])).
% 128.92/129.11 tff(408,plain,
% 128.92/129.11 (insertion(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)),
% 128.92/129.11 inference(symmetry,[status(thm)],[407])).
% 128.92/129.11 tff(409,plain,
% 128.92/129.11 (equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) <=> equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.12 inference(monotonicity,[status(thm)],[408])).
% 128.92/129.12 tff(410,plain,
% 128.92/129.12 ((~![V: $i, W1: $i, U: $i, U1: $i] : equidistant(U, V, U1, insertion(U1, W1, U, V))) | equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.92/129.12 inference(quant_inst,[status(thm)],[])).
% 128.92/129.12 tff(411,plain,
% 128.92/129.12 (equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.92/129.12 inference(unit_resolution,[status(thm)],[410, 207])).
% 128.92/129.12 tff(412,plain,
% 128.92/129.12 (equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[411, 409])).
% 128.92/129.12 tff(413,plain,
% 128.92/129.12 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.92/129.12 inference(rewrite,[status(thm)],[])).
% 128.92/129.12 tff(414,plain,
% 128.92/129.12 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.92/129.12 inference(quant_inst,[status(thm)],[])).
% 128.92/129.12 tff(415,plain,
% 128.92/129.12 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[414, 413])).
% 128.92/129.12 tff(416,plain,
% 128.92/129.12 (equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.12 inference(unit_resolution,[status(thm)],[415, 217, 412])).
% 128.92/129.12 tff(417,plain,
% 128.92/129.12 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.92/129.12 inference(rewrite,[status(thm)],[])).
% 128.92/129.12 tff(418,plain,
% 128.92/129.12 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.92/129.12 inference(quant_inst,[status(thm)],[])).
% 128.92/129.12 tff(419,plain,
% 128.92/129.12 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[418, 417])).
% 128.92/129.12 tff(420,plain,
% 128.92/129.12 (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.92/129.12 inference(unit_resolution,[status(thm)],[419, 52, 403])).
% 128.92/129.12 tff(421,plain,
% 128.92/129.12 (equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> equidistant(x, v, w, u)),
% 128.92/129.12 inference(monotonicity,[status(thm)],[94, 21, 73, 29])).
% 128.92/129.12 tff(422,plain,
% 128.92/129.12 (equidistant(x, v, w, u) <=> equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.12 inference(symmetry,[status(thm)],[421])).
% 128.92/129.12 tff(423,plain,
% 128.92/129.12 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(u, w, v, x)) | equidistant(x, v, w, u))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(u, w, v, x)) | equidistant(x, v, w, u))),
% 128.92/129.12 inference(rewrite,[status(thm)],[])).
% 128.92/129.12 tff(424,plain,
% 128.92/129.12 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(u, w, v, x)) | equidistant(x, v, w, u))),
% 128.92/129.12 inference(quant_inst,[status(thm)],[])).
% 128.92/129.12 tff(425,plain,
% 128.92/129.12 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(u, w, v, x)) | equidistant(x, v, w, u)),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[424, 423])).
% 128.92/129.12 tff(426,plain,
% 128.92/129.12 (equidistant(x, v, w, u)),
% 128.92/129.12 inference(unit_resolution,[status(thm)],[425, 233, 345])).
% 128.92/129.12 tff(427,plain,
% 128.92/129.12 (equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[426, 422])).
% 128.92/129.12 tff(428,plain,
% 128.92/129.12 ((insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) <=> (u = v)),
% 128.92/129.12 inference(monotonicity,[status(thm)],[29, 21])).
% 128.92/129.12 tff(429,plain,
% 128.92/129.12 ((u = v) <=> (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.92/129.12 inference(symmetry,[status(thm)],[428])).
% 128.92/129.12 tff(430,plain,
% 128.92/129.12 ((~(u = v)) <=> (~(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.92/129.12 inference(monotonicity,[status(thm)],[429])).
% 128.92/129.12 tff(431,plain,
% 128.92/129.12 ((~(u = v)) <=> (~(u = v))),
% 128.92/129.12 inference(rewrite,[status(thm)],[])).
% 128.92/129.12 tff(432,axiom,(~(u = v)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','u_not_v')).
% 128.92/129.12 tff(433,plain,
% 128.92/129.12 (~(u = v)),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[432, 431])).
% 128.92/129.12 tff(434,plain,
% 128.92/129.12 (~(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[433, 430])).
% 128.92/129.12 tff(435,plain,
% 128.92/129.12 ((v = u) <=> (u = v)),
% 128.92/129.12 inference(commutativity,[status(thm)],[])).
% 128.92/129.12 tff(436,plain,
% 128.92/129.12 ((insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> (v = u)),
% 128.92/129.12 inference(monotonicity,[status(thm)],[21, 29])).
% 128.92/129.12 tff(437,plain,
% 128.92/129.12 ((insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> (u = v)),
% 128.92/129.12 inference(transitivity,[status(thm)],[436, 435])).
% 128.92/129.12 tff(438,plain,
% 128.92/129.12 ((u = v) <=> (insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.12 inference(symmetry,[status(thm)],[437])).
% 128.92/129.12 tff(439,plain,
% 128.92/129.12 ((~(u = v)) <=> (~(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.92/129.12 inference(monotonicity,[status(thm)],[438])).
% 128.92/129.12 tff(440,plain,
% 128.92/129.12 (~(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[433, 439])).
% 128.92/129.12 tff(441,plain,
% 128.92/129.12 ((u = x) <=> (x = u)),
% 128.92/129.12 inference(commutativity,[status(thm)],[])).
% 128.92/129.12 tff(442,plain,
% 128.92/129.12 ((insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) <=> (u = x)),
% 128.92/129.12 inference(monotonicity,[status(thm)],[29, 94])).
% 128.92/129.12 tff(443,plain,
% 128.92/129.12 ((insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) <=> (x = u)),
% 128.92/129.12 inference(transitivity,[status(thm)],[442, 441])).
% 128.92/129.12 tff(444,plain,
% 128.92/129.12 ((x = u) <=> (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.92/129.12 inference(symmetry,[status(thm)],[443])).
% 128.92/129.12 tff(445,plain,
% 128.92/129.12 ((~(x = u)) <=> (~(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.92/129.12 inference(monotonicity,[status(thm)],[444])).
% 128.92/129.12 tff(446,plain,
% 128.92/129.12 ((~(x = u)) <=> (~(x = u))),
% 128.92/129.12 inference(rewrite,[status(thm)],[])).
% 128.92/129.12 tff(447,axiom,(~(x = u)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x_not_u')).
% 128.92/129.12 tff(448,plain,
% 128.92/129.12 (~(x = u)),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[447, 446])).
% 128.92/129.12 tff(449,plain,
% 128.92/129.12 (~(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[448, 445])).
% 128.92/129.12 tff(450,plain,
% 128.92/129.12 (^[W: $i, V: $i, U: $i] : refl(((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V))) <=> ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V))))),
% 128.92/129.12 inference(bind,[status(th)],[])).
% 128.92/129.12 tff(451,plain,
% 128.92/129.12 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))),
% 128.92/129.12 inference(quant_intro,[status(thm)],[450])).
% 128.92/129.12 tff(452,plain,
% 128.92/129.12 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))),
% 128.92/129.12 inference(rewrite,[status(thm)],[])).
% 128.92/129.12 tff(453,plain,
% 128.92/129.12 (^[W: $i, V: $i, U: $i] : trans(monotonicity(rewrite((((~between(U, V, W)) | (~between(U, W, V))) | (U = V)) <=> ((U = V) | (~between(U, V, W)) | (~between(U, W, V)))), (((((~between(U, V, W)) | (~between(U, W, V))) | (U = V)) | (V = W)) <=> (((U = V) | (~between(U, V, W)) | (~between(U, W, V))) | (V = W)))), rewrite((((U = V) | (~between(U, V, W)) | (~between(U, W, V))) | (V = W)) <=> ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))), (((((~between(U, V, W)) | (~between(U, W, V))) | (U = V)) | (V = W)) <=> ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))))),
% 128.92/129.12 inference(bind,[status(th)],[])).
% 128.92/129.12 tff(454,plain,
% 128.92/129.12 (![W: $i, V: $i, U: $i] : ((((~between(U, V, W)) | (~between(U, W, V))) | (U = V)) | (V = W)) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))),
% 128.92/129.12 inference(quant_intro,[status(thm)],[453])).
% 128.92/129.12 tff(455,axiom,(![W: $i, V: $i, U: $i] : ((((~between(U, V, W)) | (~between(U, W, V))) | (U = V)) | (V = W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t6_2')).
% 128.92/129.12 tff(456,plain,
% 128.92/129.12 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[455, 454])).
% 128.92/129.12 tff(457,plain,
% 128.92/129.12 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[456, 452])).
% 128.92/129.12 tff(458,plain,(
% 128.92/129.12 ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))),
% 128.92/129.12 inference(skolemize,[status(sab)],[457])).
% 128.92/129.12 tff(459,plain,
% 128.92/129.12 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))),
% 128.92/129.12 inference(modus_ponens,[status(thm)],[458, 451])).
% 128.92/129.12 tff(460,plain,
% 128.92/129.12 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))) | ((insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.92/129.13 inference(rewrite,[status(thm)],[])).
% 128.92/129.13 tff(461,plain,
% 128.92/129.13 (((insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))) <=> ((insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.92/129.13 inference(rewrite,[status(thm)],[])).
% 128.92/129.13 tff(462,plain,
% 128.92/129.13 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))) | ((insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))) | ((insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))))),
% 128.92/129.13 inference(monotonicity,[status(thm)],[461])).
% 128.92/129.13 tff(463,plain,
% 128.92/129.13 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))) | ((insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))))),
% 128.92/129.13 inference(transitivity,[status(thm)],[462, 460])).
% 128.92/129.13 tff(464,plain,
% 128.92/129.13 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))) | ((insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))),
% 128.92/129.13 inference(quant_inst,[status(thm)],[])).
% 128.92/129.13 tff(465,plain,
% 128.92/129.13 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (V = W) | (~between(U, W, V)))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) | (insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v) = insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)))),
% 128.92/129.13 inference(modus_ponens,[status(thm)],[464, 463])).
% 128.92/129.13 tff(466,plain,
% 128.92/129.13 (~between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.13 inference(unit_resolution,[status(thm)],[465, 459, 449, 440, 403])).
% 128.92/129.13 tff(467,plain,
% 128.92/129.13 (equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x)) <=> equidistant(x, v, v, x)),
% 128.92/129.13 inference(monotonicity,[status(thm)],[94, 21, 21, 94])).
% 128.92/129.13 tff(468,plain,
% 128.92/129.13 (equidistant(x, v, v, x) <=> equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.92/129.13 inference(symmetry,[status(thm)],[467])).
% 128.92/129.13 tff(469,plain,
% 128.92/129.13 (equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))),
% 128.92/129.13 inference(modus_ponens,[status(thm)],[366, 468])).
% 128.92/129.13 tff(470,plain,
% 128.92/129.13 (equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> equidistant(x, w, v, u)),
% 128.92/129.13 inference(monotonicity,[status(thm)],[94, 73, 21, 29])).
% 128.92/129.13 tff(471,plain,
% 128.92/129.13 (equidistant(x, w, v, u) <=> equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.13 inference(symmetry,[status(thm)],[470])).
% 128.92/129.13 tff(472,plain,
% 128.92/129.13 (equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.13 inference(modus_ponens,[status(thm)],[381, 471])).
% 128.92/129.13 tff(473,plain,
% 128.92/129.13 (equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) <=> equidistant(v, w, x, u)),
% 128.92/129.13 inference(monotonicity,[status(thm)],[21, 73, 94, 29])).
% 128.92/129.13 tff(474,plain,
% 128.92/129.13 (equidistant(v, w, x, u) <=> equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.13 inference(symmetry,[status(thm)],[473])).
% 128.92/129.13 tff(475,plain,
% 128.92/129.13 (equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.14 inference(modus_ponens,[status(thm)],[99, 474])).
% 128.92/129.14 tff(476,plain,
% 128.92/129.14 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | ((~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.92/129.14 inference(rewrite,[status(thm)],[])).
% 128.92/129.14 tff(477,plain,
% 128.92/129.14 ((between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))) <=> ((~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.92/129.14 inference(rewrite,[status(thm)],[])).
% 128.92/129.14 tff(478,plain,
% 128.92/129.14 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | ((~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))),
% 128.92/129.14 inference(monotonicity,[status(thm)],[477])).
% 128.92/129.14 tff(479,plain,
% 128.92/129.14 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))),
% 128.92/129.15 inference(transitivity,[status(thm)],[478, 476])).
% 128.92/129.15 tff(480,plain,
% 128.92/129.15 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))),
% 128.92/129.15 inference(quant_inst,[status(thm)],[])).
% 128.92/129.15 tff(481,plain,
% 128.92/129.15 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (~equidistant(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.15 inference(modus_ponens,[status(thm)],[480, 479])).
% 128.92/129.15 tff(482,plain,
% 128.92/129.15 ((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | between(insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.15 inference(unit_resolution,[status(thm)],[481, 265, 475, 472, 469])).
% 128.92/129.15 tff(483,plain,
% 128.92/129.15 (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))),
% 128.92/129.15 inference(unit_resolution,[status(thm)],[482, 466])).
% 128.92/129.15 tff(484,plain,
% 128.92/129.15 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W)) <=> ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W)))),
% 128.92/129.15 inference(bind,[status(th)],[])).
% 128.92/129.15 tff(485,plain,
% 128.92/129.15 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 128.92/129.15 inference(quant_intro,[status(thm)],[484])).
% 128.92/129.15 tff(486,plain,
% 128.92/129.15 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 128.92/129.15 inference(rewrite,[status(thm)],[])).
% 128.92/129.15 tff(487,plain,
% 128.92/129.15 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~between(U, V, W)) | (~between(V, W, X))) | between(U, W, X)) <=> ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)))), (((((~between(U, V, W)) | (~between(V, W, X))) | between(U, W, X)) | (V = W)) <=> (((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X))) | (V = W)))), rewrite((((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X))) | (V = W)) <=> ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))), (((((~between(U, V, W)) | (~between(V, W, X))) | between(U, W, X)) | (V = W)) <=> ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))))),
% 128.92/129.15 inference(bind,[status(th)],[])).
% 128.92/129.15 tff(488,plain,
% 128.92/129.15 (![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, W)) | (~between(V, W, X))) | between(U, W, X)) | (V = W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 128.92/129.15 inference(quant_intro,[status(thm)],[487])).
% 128.92/129.15 tff(489,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, W)) | (~between(V, W, X))) | between(U, W, X)) | (V = W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b6')).
% 128.92/129.15 tff(490,plain,
% 128.92/129.15 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 128.92/129.15 inference(modus_ponens,[status(thm)],[489, 488])).
% 128.92/129.15 tff(491,plain,
% 128.92/129.15 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 128.92/129.15 inference(modus_ponens,[status(thm)],[490, 486])).
% 128.92/129.15 tff(492,plain,(
% 128.92/129.15 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 128.92/129.15 inference(skolemize,[status(sab)],[491])).
% 128.92/129.15 tff(493,plain,
% 128.92/129.15 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 128.92/129.15 inference(modus_ponens,[status(thm)],[492, 485])).
% 128.92/129.15 tff(494,plain,
% 128.92/129.15 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))))),
% 128.92/129.16 inference(rewrite,[status(thm)],[])).
% 128.92/129.16 tff(495,plain,
% 128.92/129.16 (((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) <=> (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))))),
% 128.92/129.16 inference(rewrite,[status(thm)],[])).
% 128.92/129.16 tff(496,plain,
% 128.92/129.16 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | (between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)))))),
% 128.92/129.16 inference(monotonicity,[status(thm)],[495])).
% 128.92/129.16 tff(497,plain,
% 128.92/129.16 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))))),
% 128.92/129.16 inference(transitivity,[status(thm)],[496, 494])).
% 128.92/129.16 tff(498,plain,
% 128.92/129.16 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 128.92/129.16 inference(quant_inst,[status(thm)],[])).
% 128.92/129.16 tff(499,plain,
% 128.92/129.16 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u) = insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)) | (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)))),
% 128.92/129.16 inference(modus_ponens,[status(thm)],[498, 497])).
% 128.92/129.16 tff(500,plain,
% 128.92/129.16 (~between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))),
% 128.92/129.16 inference(unit_resolution,[status(thm)],[499, 493, 483, 420, 434])).
% 128.92/129.16 tff(501,plain,
% 128.92/129.16 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)))),
% 128.92/129.16 inference(rewrite,[status(thm)],[])).
% 128.92/129.16 tff(502,plain,
% 128.92/129.16 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w)))),
% 128.92/129.16 inference(quant_inst,[status(thm)],[])).
% 128.92/129.16 tff(503,plain,
% 128.92/129.16 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | between(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w))),
% 128.92/129.16 inference(modus_ponens,[status(thm)],[502, 501])).
% 128.92/129.16 tff(504,plain,
% 128.92/129.16 (~between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))),
% 128.92/129.16 inference(unit_resolution,[status(thm)],[503, 52, 500])).
% 128.92/129.16 tff(505,plain,
% 128.92/129.16 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))),
% 128.92/129.17 inference(rewrite,[status(thm)],[])).
% 128.92/129.17 tff(506,plain,
% 128.92/129.17 ((between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)))) <=> (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))),
% 128.92/129.17 inference(rewrite,[status(thm)],[])).
% 128.92/129.17 tff(507,plain,
% 128.92/129.17 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))))),
% 128.92/129.17 inference(monotonicity,[status(thm)],[506])).
% 128.92/129.17 tff(508,plain,
% 128.92/129.17 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))))),
% 129.00/129.18 inference(transitivity,[status(thm)],[507, 505])).
% 129.00/129.18 tff(509,plain,
% 129.00/129.18 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | (between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))))),
% 129.02/129.21 inference(quant_inst,[status(thm)],[])).
% 129.02/129.21 tff(510,plain,
% 129.02/129.21 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (between(U1, V1, W1) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1)))) | between(extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u)) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~between(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v))) | (~equidistant(insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u))) | (~equidistant(extension(extension(x, v, lower_dimension_point_1, lower_dimension_point_2), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v), x), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), extension(extension(w, u, lower_dimension_point_1, lower_dimension_point_2), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), insertion(w, extension(w, u, lower_dimension_point_1, lower_dimension_point_2), w, u), w), insertion(x, extension(x, v, lower_dimension_point_1, lower_dimension_point_2), x, v)))),
% 129.02/129.21 inference(modus_ponens,[status(thm)],[509, 508])).
% 129.02/129.21 tff(511,plain,
% 129.02/129.21 ($false),
% 129.02/129.21 inference(unit_resolution,[status(thm)],[510, 265, 504, 427, 420, 416, 111])).
% 129.02/129.21 % SZS output end Proof
% 129.02/129.22 % E exiting
%------------------------------------------------------------------------------