%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO034-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:05:23 AM UTC 2025
% Result : Unsatisfiable 17.09s 17.24s
% Output : Proof 17.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO034-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:10:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 17.09/17.24 % SZS status Unsatisfiable
% 17.09/17.24 % SZS output start Proof
% 17.09/17.24 tff(between_type, type, (
% 17.09/17.24 between: ( $i * $i * $i ) > $o)).
% 17.09/17.24 tff(extension_type, type, (
% 17.09/17.24 extension: ( $i * $i * $i * $i ) > $i)).
% 17.09/17.24 tff(u_type, type, (
% 17.09/17.24 u: $i)).
% 17.09/17.24 tff(v_type, type, (
% 17.09/17.24 v: $i)).
% 17.09/17.24 tff(w_type, type, (
% 17.09/17.24 w: $i)).
% 17.09/17.24 tff(equidistant_type, type, (
% 17.09/17.24 equidistant: ( $i * $i * $i * $i ) > $o)).
% 17.09/17.24 tff(x_type, type, (
% 17.09/17.24 x: $i)).
% 17.09/17.24 tff(reflection_type, type, (
% 17.09/17.24 reflection: ( $i * $i ) > $i)).
% 17.09/17.24 tff(1,assumption,(u = v), introduced(assumption)).
% 17.09/17.24 tff(2,assumption,(w = v), introduced(assumption)).
% 17.09/17.24 tff(3,plain,
% 17.09/17.24 (v = w),
% 17.09/17.24 inference(symmetry,[status(thm)],[2])).
% 17.09/17.24 tff(4,plain,
% 17.09/17.24 (equidistant(v, x, v, v) <=> equidistant(w, x, v, w)),
% 17.09/17.24 inference(monotonicity,[status(thm)],[3, 3])).
% 17.09/17.24 tff(5,plain,
% 17.09/17.24 (equidistant(w, x, v, w) <=> equidistant(v, x, v, v)),
% 17.09/17.24 inference(symmetry,[status(thm)],[4])).
% 17.09/17.24 tff(6,plain,
% 17.09/17.24 (equidistant(w, v, w, x) <=> equidistant(w, v, w, x)),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(7,axiom,(equidistant(w, v, w, x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','w_to_v_equals_w_to_x')).
% 17.09/17.24 tff(8,plain,
% 17.09/17.24 (equidistant(w, v, w, x)),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[7, 6])).
% 17.09/17.24 tff(9,plain,
% 17.09/17.24 (^[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)))),
% 17.09/17.24 inference(bind,[status(th)],[])).
% 17.09/17.24 tff(10,plain,
% 17.09/17.24 (![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))),
% 17.09/17.24 inference(quant_intro,[status(thm)],[9])).
% 17.09/17.24 tff(11,plain,
% 17.09/17.24 (![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))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(12,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_3')).
% 17.09/17.24 tff(13,plain,
% 17.09/17.24 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[12, 11])).
% 17.09/17.24 tff(14,plain,(
% 17.09/17.24 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 17.09/17.24 inference(skolemize,[status(sab)],[13])).
% 17.09/17.24 tff(15,plain,
% 17.09/17.24 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[14, 10])).
% 17.09/17.24 tff(16,plain,
% 17.09/17.24 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(w, v, w, x)) | equidistant(w, x, v, w))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(w, v, w, x)) | equidistant(w, x, v, w))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(17,plain,
% 17.09/17.24 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(w, v, w, x)) | equidistant(w, x, v, w))),
% 17.09/17.24 inference(quant_inst,[status(thm)],[])).
% 17.09/17.24 tff(18,plain,
% 17.09/17.24 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(w, v, w, x)) | equidistant(w, x, v, w)),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[17, 16])).
% 17.09/17.24 tff(19,plain,
% 17.09/17.24 (equidistant(w, x, v, w)),
% 17.09/17.24 inference(unit_resolution,[status(thm)],[18, 15, 8])).
% 17.09/17.24 tff(20,plain,
% 17.09/17.24 (equidistant(v, x, v, v)),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[19, 5])).
% 17.09/17.24 tff(21,plain,
% 17.09/17.24 ((~(v = x)) <=> (~(v = x))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(22,axiom,(~(v = x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_v_is_x')).
% 17.09/17.24 tff(23,plain,
% 17.09/17.24 (~(v = x)),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[22, 21])).
% 17.09/17.24 tff(24,plain,
% 17.09/17.24 (^[Z: $i, Y: $i, X: $i] : refl(((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ((~equidistant(X, Y, Z, Z)) | (X = Y)))),
% 17.09/17.24 inference(bind,[status(th)],[])).
% 17.09/17.24 tff(25,plain,
% 17.09/17.24 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 17.09/17.24 inference(quant_intro,[status(thm)],[24])).
% 17.09/17.24 tff(26,plain,
% 17.09/17.24 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(27,axiom,(![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax','identity_for_equidistance')).
% 17.09/17.24 tff(28,plain,
% 17.09/17.24 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[27, 26])).
% 17.09/17.24 tff(29,plain,(
% 17.09/17.24 ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 17.09/17.24 inference(skolemize,[status(sab)],[28])).
% 17.09/17.24 tff(30,plain,
% 17.09/17.24 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[29, 25])).
% 17.09/17.24 tff(31,plain,
% 17.09/17.24 (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(v, x, v, v)) | (v = x))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(v, x, v, v)) | (v = x))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(32,plain,
% 17.09/17.24 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(v, x, v, v)) | (v = x))),
% 17.09/17.24 inference(quant_inst,[status(thm)],[])).
% 17.09/17.24 tff(33,plain,
% 17.09/17.24 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(v, x, v, v)) | (v = x)),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[32, 31])).
% 17.09/17.24 tff(34,plain,
% 17.09/17.24 (~equidistant(v, x, v, v)),
% 17.09/17.24 inference(unit_resolution,[status(thm)],[33, 30, 23])).
% 17.09/17.24 tff(35,plain,
% 17.09/17.24 ($false),
% 17.09/17.24 inference(unit_resolution,[status(thm)],[34, 20])).
% 17.09/17.24 tff(36,plain,(~(w = v)), inference(lemma,lemma(discharge,[]))).
% 17.09/17.24 tff(37,plain,
% 17.09/17.24 (between(u, v, w) <=> between(u, v, w)),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(38,axiom,(between(u, v, w)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v_between_u_and_w')).
% 17.09/17.24 tff(39,plain,
% 17.09/17.24 (between(u, v, w)),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[38, 37])).
% 17.09/17.24 tff(40,plain,
% 17.09/17.24 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | between(W, V, U)) <=> ((~between(U, V, W)) | between(W, V, U)))),
% 17.09/17.24 inference(bind,[status(th)],[])).
% 17.09/17.24 tff(41,plain,
% 17.09/17.24 (![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))),
% 17.09/17.24 inference(quant_intro,[status(thm)],[40])).
% 17.09/17.24 tff(42,plain,
% 17.09/17.24 (![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))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(43,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1')).
% 17.09/17.24 tff(44,plain,
% 17.09/17.24 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[43, 42])).
% 17.09/17.24 tff(45,plain,(
% 17.09/17.24 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 17.09/17.24 inference(skolemize,[status(sab)],[44])).
% 17.09/17.24 tff(46,plain,
% 17.09/17.24 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[45, 41])).
% 17.09/17.24 tff(47,plain,
% 17.09/17.24 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, v, w)) | between(w, v, u))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, v, w)) | between(w, v, u))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(48,plain,
% 17.09/17.24 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, v, w)) | between(w, v, u))),
% 17.09/17.24 inference(quant_inst,[status(thm)],[])).
% 17.09/17.24 tff(49,plain,
% 17.09/17.24 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, v, w)) | between(w, v, u)),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[48, 47])).
% 17.09/17.24 tff(50,plain,
% 17.09/17.24 (between(w, v, u)),
% 17.09/17.24 inference(unit_resolution,[status(thm)],[49, 46, 39])).
% 17.09/17.24 tff(51,plain,
% 17.09/17.24 (^[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))))),
% 17.09/17.24 inference(bind,[status(th)],[])).
% 17.09/17.24 tff(52,plain,
% 17.09/17.24 (![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)))),
% 17.09/17.24 inference(quant_intro,[status(thm)],[51])).
% 17.09/17.24 tff(53,plain,
% 17.09/17.24 (![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)))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(54,plain,
% 17.09/17.24 (^[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))))),
% 17.09/17.24 inference(bind,[status(th)],[])).
% 17.09/17.24 tff(55,plain,
% 17.09/17.24 (![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)))),
% 17.09/17.24 inference(quant_intro,[status(thm)],[54])).
% 17.09/17.24 tff(56,axiom,(![W: $i, V: $i, U: $i] : (((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_1')).
% 17.09/17.24 tff(57,plain,
% 17.09/17.24 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[56, 55])).
% 17.09/17.24 tff(58,plain,
% 17.09/17.24 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[57, 53])).
% 17.09/17.24 tff(59,plain,(
% 17.09/17.24 ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 17.09/17.24 inference(skolemize,[status(sab)],[58])).
% 17.09/17.24 tff(60,plain,
% 17.09/17.24 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[59, 52])).
% 17.09/17.24 tff(61,plain,
% 17.09/17.24 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((w = v) | (~between(w, v, u)) | (u = extension(w, v, v, u)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (w = v) | (~between(w, v, u)) | (u = extension(w, v, v, u)))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(62,plain,
% 17.09/17.24 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((w = v) | (~between(w, v, u)) | (u = extension(w, v, v, u)))),
% 17.09/17.24 inference(quant_inst,[status(thm)],[])).
% 17.09/17.24 tff(63,plain,
% 17.09/17.24 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (w = v) | (~between(w, v, u)) | (u = extension(w, v, v, u))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[62, 61])).
% 17.09/17.24 tff(64,plain,
% 17.09/17.24 ((w = v) | (u = extension(w, v, v, u))),
% 17.09/17.24 inference(unit_resolution,[status(thm)],[63, 60, 50])).
% 17.09/17.24 tff(65,plain,
% 17.09/17.24 (u = extension(w, v, v, u)),
% 17.09/17.24 inference(unit_resolution,[status(thm)],[64, 36])).
% 17.09/17.24 tff(66,plain,
% 17.09/17.24 (extension(w, v, v, u) = u),
% 17.09/17.24 inference(symmetry,[status(thm)],[65])).
% 17.09/17.24 tff(67,plain,
% 17.09/17.24 (extension(w, v, v, u) = v),
% 17.09/17.24 inference(transitivity,[status(thm)],[66, 1])).
% 17.09/17.24 tff(68,plain,
% 17.09/17.24 (equidistant(w, extension(w, v, v, u), w, x) <=> equidistant(w, v, w, x)),
% 17.09/17.24 inference(monotonicity,[status(thm)],[67])).
% 17.09/17.24 tff(69,plain,
% 17.09/17.24 (equidistant(w, v, w, x) <=> equidistant(w, extension(w, v, v, u), w, x)),
% 17.09/17.24 inference(symmetry,[status(thm)],[68])).
% 17.09/17.24 tff(70,plain,
% 17.09/17.24 (equidistant(w, extension(w, v, v, u), w, x)),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[8, 69])).
% 17.09/17.24 tff(71,plain,
% 17.09/17.24 ((extension(w, v, v, u) = x) <=> (v = x)),
% 17.09/17.24 inference(monotonicity,[status(thm)],[67])).
% 17.09/17.24 tff(72,plain,
% 17.09/17.24 ((v = x) <=> (extension(w, v, v, u) = x)),
% 17.09/17.24 inference(symmetry,[status(thm)],[71])).
% 17.09/17.24 tff(73,plain,
% 17.09/17.24 ((~(v = x)) <=> (~(extension(w, v, v, u) = x))),
% 17.09/17.24 inference(monotonicity,[status(thm)],[72])).
% 17.09/17.24 tff(74,plain,
% 17.09/17.24 (~(extension(w, v, v, u) = x)),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[23, 73])).
% 17.09/17.24 tff(75,plain,
% 17.09/17.24 (equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x) <=> equidistant(u, v, u, x)),
% 17.09/17.24 inference(monotonicity,[status(thm)],[66, 67, 66])).
% 17.09/17.24 tff(76,plain,
% 17.09/17.24 (equidistant(u, v, u, x) <=> equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)),
% 17.09/17.24 inference(symmetry,[status(thm)],[75])).
% 17.09/17.24 tff(77,plain,
% 17.09/17.24 (equidistant(u, v, u, x) <=> equidistant(u, v, u, x)),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(78,axiom,(equidistant(u, v, u, x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','u_to_v_equals_u_to_x')).
% 17.09/17.24 tff(79,plain,
% 17.09/17.24 (equidistant(u, v, u, x)),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[78, 77])).
% 17.09/17.24 tff(80,plain,
% 17.09/17.24 (equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[79, 76])).
% 17.09/17.24 tff(81,plain,
% 17.09/17.24 ((w = u) <=> (u = w)),
% 17.09/17.24 inference(commutativity,[status(thm)],[])).
% 17.09/17.24 tff(82,plain,
% 17.09/17.24 ((w = extension(w, v, v, u)) <=> (w = u)),
% 17.09/17.24 inference(monotonicity,[status(thm)],[66])).
% 17.09/17.24 tff(83,plain,
% 17.09/17.24 ((w = extension(w, v, v, u)) <=> (u = w)),
% 17.09/17.24 inference(transitivity,[status(thm)],[82, 81])).
% 17.09/17.24 tff(84,plain,
% 17.09/17.24 ((u = w) <=> (w = extension(w, v, v, u))),
% 17.09/17.24 inference(symmetry,[status(thm)],[83])).
% 17.09/17.24 tff(85,plain,
% 17.09/17.24 (v = u),
% 17.09/17.24 inference(symmetry,[status(thm)],[1])).
% 17.09/17.24 tff(86,plain,
% 17.09/17.24 ((w = v) <=> (w = u)),
% 17.09/17.24 inference(monotonicity,[status(thm)],[85])).
% 17.09/17.24 tff(87,plain,
% 17.09/17.24 ((w = v) <=> (u = w)),
% 17.09/17.24 inference(transitivity,[status(thm)],[86, 81])).
% 17.09/17.24 tff(88,plain,
% 17.09/17.24 ((w = v) <=> (w = extension(w, v, v, u))),
% 17.09/17.24 inference(transitivity,[status(thm)],[87, 84])).
% 17.09/17.24 tff(89,plain,
% 17.09/17.24 ((~(w = v)) <=> (~(w = extension(w, v, v, u)))),
% 17.09/17.24 inference(monotonicity,[status(thm)],[88])).
% 17.09/17.24 tff(90,plain,
% 17.09/17.24 (~(w = extension(w, v, v, u))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[36, 89])).
% 17.09/17.24 tff(91,plain,
% 17.09/17.24 (between(w, extension(w, v, v, u), extension(w, v, v, u)) <=> between(w, v, u)),
% 17.09/17.24 inference(monotonicity,[status(thm)],[67, 66])).
% 17.09/17.24 tff(92,plain,
% 17.09/17.24 (between(w, v, u) <=> between(w, extension(w, v, v, u), extension(w, v, v, u))),
% 17.09/17.24 inference(symmetry,[status(thm)],[91])).
% 17.09/17.24 tff(93,plain,
% 17.09/17.24 (between(w, extension(w, v, v, u), extension(w, v, v, u))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[50, 92])).
% 17.09/17.24 tff(94,plain,
% 17.09/17.24 (^[W: $i, V: $i, W1: $i, U: $i] : refl(((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W))) <=> ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W))))),
% 17.09/17.24 inference(bind,[status(th)],[])).
% 17.09/17.24 tff(95,plain,
% 17.09/17.24 (![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W))) <=> ![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))),
% 17.09/17.24 inference(quant_intro,[status(thm)],[94])).
% 17.09/17.24 tff(96,plain,
% 17.09/17.24 (![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W))) <=> ![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(97,plain,
% 17.09/17.24 (^[W: $i, V: $i, W1: $i, U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~between(U, V, W)) | (~equidistant(U, W, U, W1))) | (~equidistant(V, W, V, W1))) <=> ((~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))), (((((~between(U, V, W)) | (~equidistant(U, W, U, W1))) | (~equidistant(V, W, V, W1))) | (U = V)) <=> (((~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W))) | (U = V)))), rewrite((((~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W))) | (U = V)) <=> ((U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))), (((((~between(U, V, W)) | (~equidistant(U, W, U, W1))) | (~equidistant(V, W, V, W1))) | (U = V)) <=> ((U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W))))), ((((((~between(U, V, W)) | (~equidistant(U, W, U, W1))) | (~equidistant(V, W, V, W1))) | (U = V)) | (W = W1)) <=> (((U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W))) | (W = W1)))), rewrite((((U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W))) | (W = W1)) <=> ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))), ((((((~between(U, V, W)) | (~equidistant(U, W, U, W1))) | (~equidistant(V, W, V, W1))) | (U = V)) | (W = W1)) <=> ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))))),
% 17.09/17.24 inference(bind,[status(th)],[])).
% 17.09/17.24 tff(98,plain,
% 17.09/17.24 (![W: $i, V: $i, W1: $i, U: $i] : (((((~between(U, V, W)) | (~equidistant(U, W, U, W1))) | (~equidistant(V, W, V, W1))) | (U = V)) | (W = W1)) <=> ![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))),
% 17.09/17.24 inference(quant_intro,[status(thm)],[97])).
% 17.09/17.24 tff(99,axiom,(![W: $i, V: $i, W1: $i, U: $i] : (((((~between(U, V, W)) | (~equidistant(U, W, U, W1))) | (~equidistant(V, W, V, W1))) | (U = V)) | (W = W1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d11')).
% 17.09/17.24 tff(100,plain,
% 17.09/17.24 (![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[99, 98])).
% 17.09/17.24 tff(101,plain,
% 17.09/17.24 (![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[100, 96])).
% 17.09/17.24 tff(102,plain,(
% 17.09/17.24 ![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))),
% 17.09/17.24 inference(skolemize,[status(sab)],[101])).
% 17.09/17.24 tff(103,plain,
% 17.09/17.24 (![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))),
% 17.09/17.24 inference(modus_ponens,[status(thm)],[102, 95])).
% 17.09/17.24 tff(104,plain,
% 17.09/17.24 (((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | ((w = extension(w, v, v, u)) | (~between(w, extension(w, v, v, u), extension(w, v, v, u))) | (extension(w, v, v, u) = x) | (~equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)) | (~equidistant(w, extension(w, v, v, u), w, x)))) <=> ((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | (w = extension(w, v, v, u)) | (~between(w, extension(w, v, v, u), extension(w, v, v, u))) | (extension(w, v, v, u) = x) | (~equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)) | (~equidistant(w, extension(w, v, v, u), w, x)))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(105,plain,
% 17.09/17.24 (((extension(w, v, v, u) = x) | (w = extension(w, v, v, u)) | (~equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)) | (~equidistant(w, extension(w, v, v, u), w, x)) | (~between(w, extension(w, v, v, u), extension(w, v, v, u)))) <=> ((w = extension(w, v, v, u)) | (~between(w, extension(w, v, v, u), extension(w, v, v, u))) | (extension(w, v, v, u) = x) | (~equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)) | (~equidistant(w, extension(w, v, v, u), w, x)))),
% 17.09/17.24 inference(rewrite,[status(thm)],[])).
% 17.09/17.24 tff(106,plain,
% 17.09/17.24 (((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | ((extension(w, v, v, u) = x) | (w = extension(w, v, v, u)) | (~equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)) | (~equidistant(w, extension(w, v, v, u), w, x)) | (~between(w, extension(w, v, v, u), extension(w, v, v, u))))) <=> ((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | ((w = extension(w, v, v, u)) | (~between(w, extension(w, v, v, u), extension(w, v, v, u))) | (extension(w, v, v, u) = x) | (~equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)) | (~equidistant(w, extension(w, v, v, u), w, x))))),
% 17.09/17.25 inference(monotonicity,[status(thm)],[105])).
% 17.09/17.25 tff(107,plain,
% 17.09/17.25 (((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | ((extension(w, v, v, u) = x) | (w = extension(w, v, v, u)) | (~equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)) | (~equidistant(w, extension(w, v, v, u), w, x)) | (~between(w, extension(w, v, v, u), extension(w, v, v, u))))) <=> ((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | (w = extension(w, v, v, u)) | (~between(w, extension(w, v, v, u), extension(w, v, v, u))) | (extension(w, v, v, u) = x) | (~equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)) | (~equidistant(w, extension(w, v, v, u), w, x)))),
% 17.09/17.25 inference(transitivity,[status(thm)],[106, 104])).
% 17.09/17.25 tff(108,plain,
% 17.09/17.25 ((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | ((extension(w, v, v, u) = x) | (w = extension(w, v, v, u)) | (~equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)) | (~equidistant(w, extension(w, v, v, u), w, x)) | (~between(w, extension(w, v, v, u), extension(w, v, v, u))))),
% 17.09/17.25 inference(quant_inst,[status(thm)],[])).
% 17.09/17.25 tff(109,plain,
% 17.09/17.25 ((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | (w = extension(w, v, v, u)) | (~between(w, extension(w, v, v, u), extension(w, v, v, u))) | (extension(w, v, v, u) = x) | (~equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)) | (~equidistant(w, extension(w, v, v, u), w, x))),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[108, 107])).
% 17.09/17.25 tff(110,plain,
% 17.09/17.25 ((extension(w, v, v, u) = x) | (~equidistant(extension(w, v, v, u), extension(w, v, v, u), extension(w, v, v, u), x)) | (~equidistant(w, extension(w, v, v, u), w, x))),
% 17.09/17.25 inference(unit_resolution,[status(thm)],[109, 103, 93, 90])).
% 17.09/17.25 tff(111,plain,
% 17.09/17.25 ($false),
% 17.09/17.25 inference(unit_resolution,[status(thm)],[110, 80, 74, 70])).
% 17.09/17.25 tff(112,plain,(~(u = v)), inference(lemma,lemma(discharge,[]))).
% 17.09/17.25 tff(113,plain,
% 17.09/17.25 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~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)))) | (~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))),
% 17.09/17.25 inference(rewrite,[status(thm)],[])).
% 17.09/17.25 tff(114,plain,
% 17.09/17.25 (((u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w))) <=> ((~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))),
% 17.09/17.25 inference(rewrite,[status(thm)],[])).
% 17.09/17.25 tff(115,plain,
% 17.09/17.25 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((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)))) | ((~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w))))),
% 17.09/17.25 inference(monotonicity,[status(thm)],[114])).
% 17.09/17.25 tff(116,plain,
% 17.09/17.25 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((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)))) | (~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))),
% 17.09/17.25 inference(transitivity,[status(thm)],[115, 113])).
% 17.09/17.25 tff(117,plain,
% 17.09/17.25 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w)))),
% 17.09/17.25 inference(quant_inst,[status(thm)],[])).
% 17.09/17.25 tff(118,plain,
% 17.09/17.25 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w))),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[117, 116])).
% 17.09/17.25 tff(119,plain,
% 17.09/17.25 ((u = v) | (w = extension(u, v, v, w))),
% 17.09/17.25 inference(unit_resolution,[status(thm)],[118, 60, 39])).
% 17.09/17.25 tff(120,plain,
% 17.09/17.25 (w = extension(u, v, v, w)),
% 17.09/17.25 inference(unit_resolution,[status(thm)],[119, 112])).
% 17.09/17.25 tff(121,plain,
% 17.09/17.25 (extension(u, v, v, w) = w),
% 17.09/17.25 inference(symmetry,[status(thm)],[120])).
% 17.09/17.25 tff(122,plain,
% 17.09/17.25 ((extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = w) <=> (w = extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.09/17.25 inference(commutativity,[status(thm)],[])).
% 17.09/17.25 tff(123,plain,
% 17.09/17.25 ((extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(u, v, v, w)) <=> (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = w)),
% 17.09/17.25 inference(monotonicity,[status(thm)],[121])).
% 17.09/17.25 tff(124,plain,
% 17.09/17.25 ((extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(u, v, v, w)) <=> (w = extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.09/17.25 inference(transitivity,[status(thm)],[123, 122])).
% 17.09/17.25 tff(125,plain,
% 17.09/17.25 ((w = extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) <=> (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(u, v, v, w))),
% 17.09/17.25 inference(symmetry,[status(thm)],[124])).
% 17.09/17.25 tff(126,plain,
% 17.09/17.25 ((extension(u, v, v, w) = extension(w, v, v, u)) <=> (extension(w, v, v, u) = extension(u, v, v, w))),
% 17.09/17.25 inference(commutativity,[status(thm)],[])).
% 17.09/17.25 tff(127,assumption,(~between(extension(extension(w, v, v, u), v, v, v), x, x)), introduced(assumption)).
% 17.09/17.25 tff(128,plain,
% 17.09/17.25 (^[V: $i, U: $i] : refl(between(U, V, V) <=> between(U, V, V))),
% 17.09/17.25 inference(bind,[status(th)],[])).
% 17.09/17.25 tff(129,plain,
% 17.09/17.25 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 17.09/17.25 inference(quant_intro,[status(thm)],[128])).
% 17.09/17.25 tff(130,plain,
% 17.09/17.25 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 17.09/17.25 inference(rewrite,[status(thm)],[])).
% 17.09/17.25 tff(131,axiom,(![V: $i, U: $i] : between(U, V, V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3')).
% 17.09/17.25 tff(132,plain,
% 17.09/17.25 (![V: $i, U: $i] : between(U, V, V)),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[131, 130])).
% 17.09/17.25 tff(133,plain,(
% 17.09/17.25 ![V: $i, U: $i] : between(U, V, V)),
% 17.09/17.25 inference(skolemize,[status(sab)],[132])).
% 17.09/17.25 tff(134,plain,
% 17.09/17.25 (![V: $i, U: $i] : between(U, V, V)),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[133, 129])).
% 17.09/17.25 tff(135,plain,
% 17.09/17.25 ((~![V: $i, U: $i] : between(U, V, V)) | between(extension(extension(w, v, v, u), v, v, v), x, x)),
% 17.09/17.25 inference(quant_inst,[status(thm)],[])).
% 17.09/17.25 tff(136,plain,
% 17.09/17.25 ($false),
% 17.09/17.25 inference(unit_resolution,[status(thm)],[135, 134, 127])).
% 17.09/17.25 tff(137,plain,(between(extension(extension(w, v, v, u), v, v, v), x, x)), inference(lemma,lemma(discharge,[]))).
% 17.09/17.25 tff(138,plain,
% 17.09/17.25 ((extension(w, v, v, u) = v) <=> (u = v)),
% 17.09/17.25 inference(monotonicity,[status(thm)],[66])).
% 17.09/17.25 tff(139,plain,
% 17.09/17.25 ((u = v) <=> (extension(w, v, v, u) = v)),
% 17.09/17.25 inference(symmetry,[status(thm)],[138])).
% 17.09/17.25 tff(140,plain,
% 17.09/17.25 ((~(u = v)) <=> (~(extension(w, v, v, u) = v))),
% 17.09/17.25 inference(monotonicity,[status(thm)],[139])).
% 17.09/17.25 tff(141,plain,
% 17.09/17.25 (~(extension(w, v, v, u) = v)),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[112, 140])).
% 17.09/17.25 tff(142,plain,
% 17.09/17.25 ((~![V: $i, U: $i] : between(U, V, V)) | between(extension(w, v, v, u), v, v)),
% 17.09/17.25 inference(quant_inst,[status(thm)],[])).
% 17.09/17.25 tff(143,plain,
% 17.09/17.25 (between(extension(w, v, v, u), v, v)),
% 17.09/17.25 inference(unit_resolution,[status(thm)],[142, 134])).
% 17.09/17.25 tff(144,plain,
% 17.09/17.25 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w, v, v, u) = v) | (v = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(w, v, v, u), v, v)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (extension(w, v, v, u) = v) | (v = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(w, v, v, u), v, v)))),
% 17.09/17.25 inference(rewrite,[status(thm)],[])).
% 17.09/17.25 tff(145,plain,
% 17.09/17.25 (((extension(w, v, v, u) = v) | (~between(extension(w, v, v, u), v, v)) | (v = extension(extension(w, v, v, u), v, v, v))) <=> ((extension(w, v, v, u) = v) | (v = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(w, v, v, u), v, v)))),
% 17.09/17.25 inference(rewrite,[status(thm)],[])).
% 17.09/17.25 tff(146,plain,
% 17.09/17.25 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w, v, v, u) = v) | (~between(extension(w, v, v, u), v, v)) | (v = extension(extension(w, v, v, u), v, v, v)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w, v, v, u) = v) | (v = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(w, v, v, u), v, v))))),
% 17.09/17.25 inference(monotonicity,[status(thm)],[145])).
% 17.09/17.25 tff(147,plain,
% 17.09/17.25 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w, v, v, u) = v) | (~between(extension(w, v, v, u), v, v)) | (v = extension(extension(w, v, v, u), v, v, v)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (extension(w, v, v, u) = v) | (v = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(w, v, v, u), v, v)))),
% 17.09/17.25 inference(transitivity,[status(thm)],[146, 144])).
% 17.09/17.25 tff(148,plain,
% 17.09/17.25 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w, v, v, u) = v) | (~between(extension(w, v, v, u), v, v)) | (v = extension(extension(w, v, v, u), v, v, v)))),
% 17.09/17.25 inference(quant_inst,[status(thm)],[])).
% 17.09/17.25 tff(149,plain,
% 17.09/17.25 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (extension(w, v, v, u) = v) | (v = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(w, v, v, u), v, v))),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[148, 147])).
% 17.09/17.25 tff(150,plain,
% 17.09/17.25 ((extension(w, v, v, u) = v) | (v = extension(extension(w, v, v, u), v, v, v))),
% 17.09/17.25 inference(unit_resolution,[status(thm)],[149, 60, 143])).
% 17.09/17.25 tff(151,plain,
% 17.09/17.25 (v = extension(extension(w, v, v, u), v, v, v)),
% 17.09/17.25 inference(unit_resolution,[status(thm)],[150, 141])).
% 17.09/17.25 tff(152,plain,
% 17.09/17.25 (extension(extension(w, v, v, u), v, v, v) = v),
% 17.09/17.25 inference(symmetry,[status(thm)],[151])).
% 17.09/17.25 tff(153,plain,
% 17.09/17.25 ((extension(extension(w, v, v, u), v, v, v) = x) <=> (v = x)),
% 17.09/17.25 inference(monotonicity,[status(thm)],[152])).
% 17.09/17.25 tff(154,plain,
% 17.09/17.25 ((v = x) <=> (extension(extension(w, v, v, u), v, v, v) = x)),
% 17.09/17.25 inference(symmetry,[status(thm)],[153])).
% 17.09/17.25 tff(155,plain,
% 17.09/17.25 ((~(v = x)) <=> (~(extension(extension(w, v, v, u), v, v, v) = x))),
% 17.09/17.25 inference(monotonicity,[status(thm)],[154])).
% 17.09/17.25 tff(156,plain,
% 17.09/17.25 (~(extension(extension(w, v, v, u), v, v, v) = x)),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[23, 155])).
% 17.09/17.25 tff(157,plain,
% 17.09/17.25 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(extension(w, v, v, u), v, v, v) = x) | (~between(extension(extension(w, v, v, u), v, v, v), x, x)) | (x = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (extension(extension(w, v, v, u), v, v, v) = x) | (~between(extension(extension(w, v, v, u), v, v, v), x, x)) | (x = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)))),
% 17.09/17.25 inference(rewrite,[status(thm)],[])).
% 17.09/17.25 tff(158,plain,
% 17.09/17.25 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(extension(w, v, v, u), v, v, v) = x) | (~between(extension(extension(w, v, v, u), v, v, v), x, x)) | (x = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)))),
% 17.09/17.25 inference(quant_inst,[status(thm)],[])).
% 17.09/17.25 tff(159,plain,
% 17.09/17.25 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (extension(extension(w, v, v, u), v, v, v) = x) | (~between(extension(extension(w, v, v, u), v, v, v), x, x)) | (x = extension(extension(extension(w, v, v, u), v, v, v), x, x, x))),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[158, 157])).
% 17.09/17.25 tff(160,plain,
% 17.09/17.25 (x = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)),
% 17.09/17.25 inference(unit_resolution,[status(thm)],[159, 60, 156, 137])).
% 17.09/17.25 tff(161,plain,
% 17.09/17.25 (extension(extension(extension(w, v, v, u), v, v, v), x, x, x) = x),
% 17.09/17.25 inference(symmetry,[status(thm)],[160])).
% 17.09/17.25 tff(162,plain,
% 17.09/17.25 ((extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) <=> (v = x)),
% 17.09/17.25 inference(monotonicity,[status(thm)],[152, 161])).
% 17.09/17.25 tff(163,plain,
% 17.09/17.25 ((v = x) <=> (extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x))),
% 17.09/17.25 inference(symmetry,[status(thm)],[162])).
% 17.09/17.25 tff(164,plain,
% 17.09/17.25 ((~(v = x)) <=> (~(extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)))),
% 17.09/17.25 inference(monotonicity,[status(thm)],[163])).
% 17.09/17.25 tff(165,plain,
% 17.09/17.25 (~(extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x))),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[23, 164])).
% 17.09/17.25 tff(166,plain,
% 17.09/17.25 (equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) <=> equidistant(u, v, u, x)),
% 17.09/17.25 inference(monotonicity,[status(thm)],[66, 152, 66, 161])).
% 17.09/17.25 tff(167,plain,
% 17.09/17.25 (equidistant(u, v, u, x) <=> equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))),
% 17.09/17.25 inference(symmetry,[status(thm)],[166])).
% 17.09/17.25 tff(168,plain,
% 17.09/17.25 (equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[79, 167])).
% 17.09/17.25 tff(169,assumption,(~(extension(u, v, v, w) = extension(w, v, v, u))), introduced(assumption)).
% 17.09/17.25 tff(170,plain,
% 17.09/17.25 (equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) <=> equidistant(w, v, w, x)),
% 17.09/17.25 inference(monotonicity,[status(thm)],[121, 152, 121, 161])).
% 17.09/17.25 tff(171,plain,
% 17.09/17.25 (equidistant(w, v, w, x) <=> equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))),
% 17.09/17.25 inference(symmetry,[status(thm)],[170])).
% 17.09/17.25 tff(172,plain,
% 17.09/17.25 (equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[8, 171])).
% 17.09/17.25 tff(173,plain,
% 17.09/17.25 ((v = u) <=> (u = v)),
% 17.09/17.25 inference(commutativity,[status(thm)],[])).
% 17.09/17.25 tff(174,plain,
% 17.09/17.25 ((extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) <=> (v = u)),
% 17.09/17.25 inference(monotonicity,[status(thm)],[152, 66])).
% 17.09/17.25 tff(175,plain,
% 17.09/17.25 ((extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) <=> (u = v)),
% 17.09/17.25 inference(transitivity,[status(thm)],[174, 173])).
% 17.09/17.25 tff(176,plain,
% 17.09/17.25 ((u = v) <=> (extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u))),
% 17.09/17.25 inference(symmetry,[status(thm)],[175])).
% 17.09/17.25 tff(177,plain,
% 17.09/17.25 ((~(u = v)) <=> (~(extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)))),
% 17.09/17.25 inference(monotonicity,[status(thm)],[176])).
% 17.09/17.25 tff(178,plain,
% 17.09/17.25 (~(extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u))),
% 17.09/17.25 inference(modus_ponens,[status(thm)],[112, 177])).
% 17.09/17.25 tff(179,assumption,(~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))), introduced(assumption)).
% 17.09/17.25 tff(180,plain,
% 17.09/17.25 (between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) <=> between(w, v, u)),
% 17.09/17.25 inference(monotonicity,[status(thm)],[121, 152, 66])).
% 17.09/17.25 tff(181,plain,
% 17.09/17.25 (between(w, v, u) <=> between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))),
% 17.09/17.26 inference(symmetry,[status(thm)],[180])).
% 17.09/17.26 tff(182,plain,
% 17.09/17.26 (between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))),
% 17.09/17.26 inference(modus_ponens,[status(thm)],[50, 181])).
% 17.09/17.26 tff(183,plain,
% 17.09/17.26 (between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) <=> between(w, extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.09/17.26 inference(monotonicity,[status(thm)],[121])).
% 17.09/17.26 tff(184,plain,
% 17.09/17.26 (between(w, extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) <=> between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.09/17.26 inference(symmetry,[status(thm)],[183])).
% 17.09/17.26 tff(185,plain,
% 17.09/17.26 (^[W: $i, V: $i, U: $i, X: $i] : refl(between(U, V, extension(U, V, W, X)) <=> between(U, V, extension(U, V, W, X)))),
% 17.09/17.26 inference(bind,[status(th)],[])).
% 17.09/17.26 tff(186,plain,
% 17.09/17.26 (![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 17.09/17.26 inference(quant_intro,[status(thm)],[185])).
% 17.09/17.26 tff(187,plain,
% 17.09/17.26 (![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 17.09/17.26 inference(rewrite,[status(thm)],[])).
% 17.09/17.26 tff(188,plain,
% 17.09/17.26 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 17.09/17.26 inference(elim_unused_vars,[status(thm)],[])).
% 17.09/17.26 tff(189,plain,
% 17.09/17.26 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~(Y = extension(U, V, W, X))) | between(U, V, Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 17.09/17.26 inference(destructive_equality_resolution,[status(thm)],[])).
% 17.09/17.26 tff(190,plain,
% 17.09/17.26 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~(Y = extension(U, V, W, X))) | between(U, V, Y)) <=> ![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 17.09/17.26 inference(transitivity,[status(thm)],[189, 188])).
% 17.09/17.26 tff(191,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~(Y = extension(U, V, W, X))) | between(U, V, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b0')).
% 17.09/17.26 tff(192,plain,
% 17.09/17.26 (![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 17.09/17.26 inference(modus_ponens,[status(thm)],[191, 190])).
% 17.09/17.26 tff(193,plain,
% 17.09/17.26 (![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 17.09/17.26 inference(modus_ponens,[status(thm)],[192, 187])).
% 17.09/17.26 tff(194,plain,(
% 17.09/17.26 ![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 17.09/17.26 inference(skolemize,[status(sab)],[193])).
% 17.09/17.26 tff(195,plain,
% 17.09/17.26 (![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 17.09/17.26 inference(modus_ponens,[status(thm)],[194, 186])).
% 17.09/17.26 tff(196,plain,
% 17.09/17.26 ((~![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))) | between(w, extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.09/17.26 inference(quant_inst,[status(thm)],[])).
% 17.09/17.26 tff(197,plain,
% 17.09/17.26 (between(w, extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.09/17.26 inference(unit_resolution,[status(thm)],[196, 195])).
% 17.09/17.26 tff(198,plain,
% 17.09/17.26 (between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.09/17.26 inference(modus_ponens,[status(thm)],[197, 184])).
% 17.09/17.26 tff(199,plain,
% 17.09/17.26 (^[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))))),
% 17.09/17.26 inference(bind,[status(th)],[])).
% 17.09/17.26 tff(200,plain,
% 17.09/17.26 (![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)))),
% 17.09/17.26 inference(quant_intro,[status(thm)],[199])).
% 17.09/17.26 tff(201,plain,
% 17.09/17.26 (![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)))),
% 17.12/17.26 inference(rewrite,[status(thm)],[])).
% 17.12/17.26 tff(202,plain,
% 17.12/17.26 (^[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))))),
% 17.12/17.26 inference(bind,[status(th)],[])).
% 17.12/17.26 tff(203,plain,
% 17.12/17.26 (![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)))),
% 17.12/17.26 inference(quant_intro,[status(thm)],[202])).
% 17.12/17.26 tff(204,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(V, W, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b5')).
% 17.12/17.26 tff(205,plain,
% 17.12/17.26 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 17.12/17.26 inference(modus_ponens,[status(thm)],[204, 203])).
% 17.12/17.26 tff(206,plain,
% 17.12/17.26 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 17.12/17.26 inference(modus_ponens,[status(thm)],[205, 201])).
% 17.12/17.26 tff(207,plain,(
% 17.12/17.26 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 17.12/17.26 inference(skolemize,[status(sab)],[206])).
% 17.12/17.26 tff(208,plain,
% 17.12/17.26 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 17.12/17.26 inference(modus_ponens,[status(thm)],[207, 200])).
% 17.12/17.26 tff(209,plain,
% 17.12/17.26 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))),
% 17.12/17.26 inference(rewrite,[status(thm)],[])).
% 17.12/17.26 tff(210,plain,
% 17.12/17.26 (((~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))) <=> ((~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))),
% 17.12/17.26 inference(rewrite,[status(thm)],[])).
% 17.12/17.26 tff(211,plain,
% 17.12/17.26 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))),
% 17.12/17.26 inference(monotonicity,[status(thm)],[210])).
% 17.12/17.26 tff(212,plain,
% 17.12/17.26 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))),
% 17.12/17.26 inference(transitivity,[status(thm)],[211, 209])).
% 17.12/17.26 tff(213,plain,
% 17.12/17.26 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))),
% 17.12/17.26 inference(quant_inst,[status(thm)],[])).
% 17.12/17.26 tff(214,plain,
% 17.12/17.26 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.26 inference(modus_ponens,[status(thm)],[213, 212])).
% 17.12/17.26 tff(215,plain,
% 17.12/17.26 ($false),
% 17.12/17.26 inference(unit_resolution,[status(thm)],[214, 208, 198, 182, 179])).
% 17.12/17.26 tff(216,plain,(between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))), inference(lemma,lemma(discharge,[]))).
% 17.12/17.26 tff(217,plain,
% 17.12/17.26 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))),
% 17.12/17.26 inference(rewrite,[status(thm)],[])).
% 17.12/17.26 tff(218,plain,
% 17.12/17.26 (((extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))) <=> ((~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))),
% 17.12/17.26 inference(rewrite,[status(thm)],[])).
% 17.12/17.26 tff(219,plain,
% 17.12/17.26 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))))),
% 17.12/17.26 inference(monotonicity,[status(thm)],[218])).
% 17.12/17.26 tff(220,plain,
% 17.12/17.26 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))),
% 17.12/17.26 inference(transitivity,[status(thm)],[219, 217])).
% 17.12/17.26 tff(221,plain,
% 17.12/17.26 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))),
% 17.12/17.26 inference(quant_inst,[status(thm)],[])).
% 17.12/17.26 tff(222,plain,
% 17.12/17.26 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (extension(extension(w, v, v, u), v, v, v) = extension(w, v, v, u)) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))),
% 17.12/17.26 inference(modus_ponens,[status(thm)],[221, 220])).
% 17.12/17.26 tff(223,plain,
% 17.12/17.27 (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.27 inference(unit_resolution,[status(thm)],[222, 60, 216, 178])).
% 17.12/17.27 tff(224,plain,
% 17.12/17.27 (equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) <=> equidistant(extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.27 inference(monotonicity,[status(thm)],[223])).
% 17.12/17.27 tff(225,plain,
% 17.12/17.27 (equidistant(extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) <=> equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.27 inference(symmetry,[status(thm)],[224])).
% 17.12/17.27 tff(226,plain,
% 17.12/17.27 (^[W: $i, V: $i, Y: $i, X: $i] : refl(equidistant(Y, extension(X, Y, W, V), W, V) <=> equidistant(Y, extension(X, Y, W, V), W, V))),
% 17.12/17.27 inference(bind,[status(th)],[])).
% 17.12/17.27 tff(227,plain,
% 17.12/17.27 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V) <=> ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 17.12/17.27 inference(quant_intro,[status(thm)],[226])).
% 17.12/17.27 tff(228,plain,
% 17.12/17.27 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V) <=> ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 17.12/17.27 inference(rewrite,[status(thm)],[])).
% 17.12/17.27 tff(229,axiom,(![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax','segment_construction2')).
% 17.12/17.27 tff(230,plain,
% 17.12/17.27 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 17.12/17.27 inference(modus_ponens,[status(thm)],[229, 228])).
% 17.12/17.27 tff(231,plain,(
% 17.12/17.27 ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 17.12/17.27 inference(skolemize,[status(sab)],[230])).
% 17.12/17.27 tff(232,plain,
% 17.12/17.27 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 17.12/17.27 inference(modus_ponens,[status(thm)],[231, 227])).
% 17.12/17.27 tff(233,plain,
% 17.12/17.27 ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.27 inference(quant_inst,[status(thm)],[])).
% 17.12/17.27 tff(234,plain,
% 17.12/17.27 (equidistant(extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.27 inference(unit_resolution,[status(thm)],[233, 232])).
% 17.12/17.27 tff(235,plain,
% 17.12/17.27 (equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.27 inference(modus_ponens,[status(thm)],[234, 225])).
% 17.12/17.27 tff(236,assumption,(~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))), introduced(assumption)).
% 17.12/17.27 tff(237,plain,
% 17.12/17.27 (extension(w, v, v, extension(w, v, v, u)) = extension(w, v, v, u)),
% 17.12/17.27 inference(monotonicity,[status(thm)],[66])).
% 17.12/17.27 tff(238,plain,
% 17.12/17.27 (extension(w, v, v, u) = extension(w, v, v, extension(w, v, v, u))),
% 17.12/17.27 inference(symmetry,[status(thm)],[237])).
% 17.12/17.27 tff(239,plain,
% 17.12/17.27 (equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) <=> equidistant(v, extension(w, v, v, extension(w, v, v, u)), v, extension(w, v, v, u))),
% 17.12/17.27 inference(monotonicity,[status(thm)],[152, 238, 152])).
% 17.12/17.27 tff(240,plain,
% 17.12/17.27 (equidistant(v, extension(w, v, v, extension(w, v, v, u)), v, extension(w, v, v, u)) <=> equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))),
% 17.12/17.27 inference(symmetry,[status(thm)],[239])).
% 17.12/17.27 tff(241,plain,
% 17.12/17.27 ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(v, extension(w, v, v, extension(w, v, v, u)), v, extension(w, v, v, u))),
% 17.12/17.27 inference(quant_inst,[status(thm)],[])).
% 17.12/17.27 tff(242,plain,
% 17.12/17.27 (equidistant(v, extension(w, v, v, extension(w, v, v, u)), v, extension(w, v, v, u))),
% 17.12/17.27 inference(unit_resolution,[status(thm)],[241, 232])).
% 17.12/17.27 tff(243,plain,
% 17.12/17.27 (equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))),
% 17.12/17.27 inference(modus_ponens,[status(thm)],[242, 240])).
% 17.12/17.27 tff(244,assumption,(~equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u))), introduced(assumption)).
% 17.12/17.27 tff(245,plain,
% 17.12/17.27 (extension(extension(w, v, v, u), v, v, extension(u, v, v, w)) = extension(u, v, v, w)),
% 17.12/17.27 inference(monotonicity,[status(thm)],[66, 121])).
% 17.12/17.27 tff(246,plain,
% 17.12/17.27 (extension(u, v, v, w) = extension(extension(w, v, v, u), v, v, extension(u, v, v, w))),
% 17.12/17.27 inference(symmetry,[status(thm)],[245])).
% 17.12/17.27 tff(247,plain,
% 17.12/17.27 (equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w)) <=> equidistant(v, extension(extension(w, v, v, u), v, v, extension(u, v, v, w)), v, extension(u, v, v, w))),
% 17.12/17.27 inference(monotonicity,[status(thm)],[152, 246, 152])).
% 17.12/17.27 tff(248,plain,
% 17.12/17.27 (equidistant(v, extension(extension(w, v, v, u), v, v, extension(u, v, v, w)), v, extension(u, v, v, w)) <=> equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))),
% 17.12/17.27 inference(symmetry,[status(thm)],[247])).
% 17.12/17.27 tff(249,plain,
% 17.12/17.27 ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(v, extension(extension(w, v, v, u), v, v, extension(u, v, v, w)), v, extension(u, v, v, w))),
% 17.12/17.27 inference(quant_inst,[status(thm)],[])).
% 17.12/17.27 tff(250,plain,
% 17.12/17.27 (equidistant(v, extension(extension(w, v, v, u), v, v, extension(u, v, v, w)), v, extension(u, v, v, w))),
% 17.12/17.27 inference(unit_resolution,[status(thm)],[249, 232])).
% 17.12/17.27 tff(251,plain,
% 17.12/17.27 (equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))),
% 17.12/17.27 inference(modus_ponens,[status(thm)],[250, 248])).
% 17.12/17.27 tff(252,plain,
% 17.12/17.27 (^[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)))),
% 17.12/17.27 inference(bind,[status(th)],[])).
% 17.12/17.27 tff(253,plain,
% 17.12/17.27 (![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))),
% 17.12/17.27 inference(quant_intro,[status(thm)],[252])).
% 17.12/17.27 tff(254,plain,
% 17.12/17.27 (![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))),
% 17.12/17.27 inference(rewrite,[status(thm)],[])).
% 17.12/17.27 tff(255,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_5')).
% 17.12/17.27 tff(256,plain,
% 17.12/17.27 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 17.12/17.27 inference(modus_ponens,[status(thm)],[255, 254])).
% 17.12/17.27 tff(257,plain,(
% 17.12/17.27 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 17.12/17.27 inference(skolemize,[status(sab)],[256])).
% 17.12/17.27 tff(258,plain,
% 17.12/17.27 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 17.12/17.27 inference(modus_ponens,[status(thm)],[257, 253])).
% 17.12/17.27 tff(259,plain,
% 17.12/17.27 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v)))),
% 17.12/17.27 inference(rewrite,[status(thm)],[])).
% 17.12/17.27 tff(260,plain,
% 17.12/17.27 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v)))),
% 17.12/17.27 inference(quant_inst,[status(thm)],[])).
% 17.12/17.27 tff(261,plain,
% 17.12/17.27 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))),
% 17.12/17.27 inference(modus_ponens,[status(thm)],[260, 259])).
% 17.12/17.27 tff(262,plain,
% 17.12/17.27 ((~equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))),
% 17.12/17.27 inference(unit_resolution,[status(thm)],[261, 258])).
% 17.12/17.27 tff(263,plain,
% 17.12/17.27 (equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))),
% 17.12/17.27 inference(unit_resolution,[status(thm)],[262, 251])).
% 17.12/17.27 tff(264,plain,
% 17.12/17.27 (^[W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : refl((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) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))))),
% 17.12/17.27 inference(bind,[status(th)],[])).
% 17.12/17.27 tff(265,plain,
% 17.12/17.27 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 17.12/17.27 inference(quant_intro,[status(thm)],[264])).
% 17.12/17.27 tff(266,plain,
% 17.12/17.27 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 17.12/17.27 inference(rewrite,[status(thm)],[])).
% 17.12/17.27 tff(267,plain,
% 17.12/17.27 (^[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))) | (~between(U, V, W))) <=> ((~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) <=> (((~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))) | (~between(U1, V1, W1))))), rewrite((((~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))) | (~between(U1, V1, W1))) <=> ((~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, 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, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | 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)))), rewrite((((~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, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))), ((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | equidistant(U, W, U1, W1)) <=> (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))))),
% 17.12/17.27 inference(bind,[status(th)],[])).
% 17.12/17.27 tff(268,plain,
% 17.12/17.27 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | equidistant(U, W, U1, W1)) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 17.12/17.27 inference(quant_intro,[status(thm)],[267])).
% 17.12/17.27 tff(269,axiom,(![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | equidistant(U, W, U1, W1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8')).
% 17.12/17.27 tff(270,plain,
% 17.12/17.27 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 17.12/17.27 inference(modus_ponens,[status(thm)],[269, 268])).
% 17.12/17.27 tff(271,plain,
% 17.12/17.27 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 17.12/17.27 inference(modus_ponens,[status(thm)],[270, 266])).
% 17.12/17.27 tff(272,plain,(
% 17.12/17.27 ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 17.12/17.27 inference(skolemize,[status(sab)],[271])).
% 17.12/17.27 tff(273,plain,
% 17.12/17.27 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 17.12/17.27 inference(modus_ponens,[status(thm)],[272, 265])).
% 17.12/17.27 tff(274,plain,
% 17.12/17.27 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | ((~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))) | equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u)) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))) | equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u)) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))))),
% 17.12/17.28 inference(rewrite,[status(thm)],[])).
% 17.12/17.28 tff(275,plain,
% 17.12/17.28 ((equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v)))) <=> ((~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))) | equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u)) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))))),
% 17.12/17.28 inference(rewrite,[status(thm)],[])).
% 17.12/17.28 tff(276,plain,
% 17.12/17.28 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | ((~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))) | equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u)) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)))))),
% 17.12/17.28 inference(monotonicity,[status(thm)],[275])).
% 17.12/17.28 tff(277,plain,
% 17.12/17.28 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))) | equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u)) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))))),
% 17.12/17.28 inference(transitivity,[status(thm)],[276, 274])).
% 17.12/17.28 tff(278,plain,
% 17.12/17.28 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))))),
% 17.12/17.28 inference(quant_inst,[status(thm)],[])).
% 17.12/17.28 tff(279,plain,
% 17.12/17.28 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | (~between(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v))) | equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u)) | (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)))),
% 17.12/17.28 inference(modus_ponens,[status(thm)],[278, 277])).
% 17.12/17.28 tff(280,plain,
% 17.12/17.28 ($false),
% 17.12/17.28 inference(unit_resolution,[status(thm)],[279, 273, 263, 182, 244, 243])).
% 17.12/17.28 tff(281,plain,(equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u))), inference(lemma,lemma(discharge,[]))).
% 17.12/17.28 tff(282,plain,
% 17.12/17.28 (^[V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : refl((equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) <=> (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))),
% 17.12/17.28 inference(bind,[status(th)],[])).
% 17.12/17.28 tff(283,plain,
% 17.12/17.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) <=> ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 17.12/17.28 inference(quant_intro,[status(thm)],[282])).
% 17.12/17.28 tff(284,plain,
% 17.12/17.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) <=> ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 17.12/17.28 inference(rewrite,[status(thm)],[])).
% 17.12/17.28 tff(285,plain,
% 17.12/17.28 (^[V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) <=> ((~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) <=> (((~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~equidistant(Y, V, Y1, V1))))), rewrite((((~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~equidistant(Y, V, Y1, V1))) <=> ((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) <=> ((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), ((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) <=> (((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X, Y, Z))))), rewrite((((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X, Y, Z))) <=> ((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), ((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) <=> ((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), (((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) <=> (((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X1, Y1, Z1))))), rewrite((((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X1, Y1, Z1))) <=> ((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) <=> ((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) <=> (((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (X = Y)))), rewrite((((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (X = Y)) <=> ((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) <=> ((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), (((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1)) <=> (((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | equidistant(Z, V, Z1, V1)))), rewrite((((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | equidistant(Z, V, Z1, V1)) <=> (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1)) <=> (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))))),
% 17.12/17.28 inference(bind,[status(th)],[])).
% 17.12/17.28 tff(286,plain,
% 17.12/17.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1)) <=> ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 17.12/17.28 inference(quant_intro,[status(thm)],[285])).
% 17.12/17.28 tff(287,axiom,(![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax','outer_five_segment')).
% 17.12/17.28 tff(288,plain,
% 17.12/17.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 17.12/17.28 inference(modus_ponens,[status(thm)],[287, 286])).
% 17.12/17.28 tff(289,plain,
% 17.12/17.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 17.12/17.28 inference(modus_ponens,[status(thm)],[288, 284])).
% 17.12/17.28 tff(290,plain,(
% 17.12/17.28 ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 17.12/17.28 inference(skolemize,[status(sab)],[289])).
% 17.12/17.28 tff(291,plain,
% 17.12/17.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 17.12/17.28 inference(modus_ponens,[status(thm)],[290, 283])).
% 17.12/17.28 tff(292,plain,
% 17.12/17.28 (((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | ((extension(u, v, v, w) = extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u))) | (~equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))))) <=> ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (extension(u, v, v, w) = extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u))) | (~equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))))),
% 17.12/17.28 inference(rewrite,[status(thm)],[])).
% 17.12/17.28 tff(293,plain,
% 17.12/17.28 ((equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (extension(u, v, v, w) = extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u)))) <=> ((extension(u, v, v, w) = extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u))) | (~equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))))),
% 17.12/17.29 inference(rewrite,[status(thm)],[])).
% 17.12/17.29 tff(294,plain,
% 17.12/17.29 (((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (extension(u, v, v, w) = extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u))))) <=> ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | ((extension(u, v, v, w) = extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u))) | (~equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)))))),
% 17.12/17.29 inference(monotonicity,[status(thm)],[293])).
% 17.12/17.29 tff(295,plain,
% 17.12/17.29 (((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (extension(u, v, v, w) = extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u))))) <=> ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (extension(u, v, v, w) = extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u))) | (~equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))))),
% 17.12/17.29 inference(transitivity,[status(thm)],[294, 292])).
% 17.12/17.29 tff(296,plain,
% 17.12/17.29 ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (extension(u, v, v, w) = extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u))))),
% 17.12/17.29 inference(quant_inst,[status(thm)],[])).
% 17.12/17.29 tff(297,plain,
% 17.12/17.29 ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (extension(u, v, v, w) = extension(w, v, v, u)) | (~between(extension(u, v, v, w), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~equidistant(extension(u, v, v, w), extension(w, v, v, u), extension(u, v, v, w), extension(w, v, v, u))) | (~equidistant(extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(u, v, v, w), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)))),
% 17.12/17.29 inference(modus_ponens,[status(thm)],[296, 295])).
% 17.12/17.29 tff(298,plain,
% 17.12/17.29 ($false),
% 17.12/17.29 inference(unit_resolution,[status(thm)],[297, 291, 169, 198, 281, 168, 236, 235, 172])).
% 17.12/17.29 tff(299,plain,(equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (extension(u, v, v, w) = extension(w, v, v, u))), inference(lemma,lemma(discharge,[]))).
% 17.12/17.29 tff(300,plain,
% 17.12/17.29 (equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))),
% 17.12/17.29 inference(unit_resolution,[status(thm)],[299, 169])).
% 17.12/17.29 tff(301,plain,
% 17.12/17.29 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v)))),
% 17.12/17.29 inference(rewrite,[status(thm)],[])).
% 17.12/17.29 tff(302,plain,
% 17.12/17.29 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v)))),
% 17.12/17.30 inference(quant_inst,[status(thm)],[])).
% 17.12/17.30 tff(303,plain,
% 17.12/17.30 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))),
% 17.12/17.30 inference(modus_ponens,[status(thm)],[302, 301])).
% 17.12/17.30 tff(304,plain,
% 17.12/17.30 (between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))),
% 17.12/17.30 inference(unit_resolution,[status(thm)],[303, 46, 216])).
% 17.12/17.30 tff(305,plain,
% 17.12/17.30 (((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | ((extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))) | (extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))))) <=> ((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))) | (extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))))),
% 17.12/17.30 inference(rewrite,[status(thm)],[])).
% 17.12/17.30 tff(306,plain,
% 17.12/17.30 (((extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v)))) <=> ((extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))) | (extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))))),
% 17.12/17.30 inference(rewrite,[status(thm)],[])).
% 17.12/17.30 tff(307,plain,
% 17.12/17.30 (((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | ((extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))))) <=> ((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | ((extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))) | (extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)))))),
% 17.12/17.30 inference(monotonicity,[status(thm)],[306])).
% 17.12/17.30 tff(308,plain,
% 17.12/17.30 (((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | ((extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))))) <=> ((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))) | (extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))))),
% 17.12/17.30 inference(transitivity,[status(thm)],[307, 305])).
% 17.12/17.30 tff(309,plain,
% 17.12/17.30 ((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | ((extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))))),
% 17.12/17.30 inference(quant_inst,[status(thm)],[])).
% 17.12/17.30 tff(310,plain,
% 17.12/17.30 ((~![W: $i, V: $i, W1: $i, U: $i] : ((W = W1) | (U = V) | (~equidistant(V, W, V, W1)) | (~equidistant(U, W, U, W1)) | (~between(U, V, W)))) | (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))) | (extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)))),
% 17.12/17.30 inference(modus_ponens,[status(thm)],[309, 308])).
% 17.12/17.30 tff(311,plain,
% 17.12/17.30 ((extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) | (extension(extension(w, v, v, u), v, v, v) = extension(extension(extension(w, v, v, u), v, v, v), x, x, x)) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(extension(extension(w, v, v, u), v, v, v), x, x, x))) | (~equidistant(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(extension(w, v, v, u), v, v, v), x, x, x)))),
% 17.12/17.30 inference(unit_resolution,[status(thm)],[310, 103, 304])).
% 17.12/17.30 tff(312,plain,
% 17.12/17.30 (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)),
% 17.12/17.30 inference(unit_resolution,[status(thm)],[311, 300, 168, 165])).
% 17.12/17.30 tff(313,plain,
% 17.12/17.30 ((w = extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) <=> (extension(u, v, v, w) = extension(w, v, v, u))),
% 17.12/17.30 inference(monotonicity,[status(thm)],[120, 312])).
% 17.12/17.30 tff(314,plain,
% 17.12/17.30 ((w = extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) <=> (extension(w, v, v, u) = extension(u, v, v, w))),
% 17.12/17.30 inference(transitivity,[status(thm)],[313, 126])).
% 17.12/17.30 tff(315,plain,
% 17.12/17.30 ((extension(w, v, v, u) = extension(u, v, v, w)) <=> (w = extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.31 inference(symmetry,[status(thm)],[314])).
% 17.12/17.31 tff(316,plain,
% 17.12/17.31 ((extension(w, v, v, u) = extension(u, v, v, w)) <=> (u = w)),
% 17.12/17.31 inference(monotonicity,[status(thm)],[66, 121])).
% 17.12/17.31 tff(317,plain,
% 17.12/17.31 ((u = w) <=> (extension(w, v, v, u) = extension(u, v, v, w))),
% 17.12/17.31 inference(symmetry,[status(thm)],[316])).
% 17.12/17.31 tff(318,plain,
% 17.12/17.31 ((w = extension(w, v, v, u)) <=> (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(u, v, v, w))),
% 17.12/17.31 inference(transitivity,[status(thm)],[83, 317, 315, 125])).
% 17.12/17.31 tff(319,plain,
% 17.12/17.31 ((extension(w, v, v, u) = extension(w, extension(w, v, v, u), w, extension(w, v, v, u))) <=> (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u))),
% 17.12/17.31 inference(commutativity,[status(thm)],[])).
% 17.12/17.31 tff(320,plain,
% 17.12/17.31 (^[V: $i, U: $i] : refl((reflection(U, V) = extension(U, V, U, V)) <=> (reflection(U, V) = extension(U, V, U, V)))),
% 17.12/17.31 inference(bind,[status(th)],[])).
% 17.12/17.31 tff(321,plain,
% 17.12/17.31 (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V)) <=> ![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 17.12/17.31 inference(quant_intro,[status(thm)],[320])).
% 17.12/17.31 tff(322,plain,
% 17.12/17.31 (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V)) <=> ![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 17.12/17.31 inference(rewrite,[status(thm)],[])).
% 17.12/17.31 tff(323,axiom,(![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-2.ax','reflection')).
% 17.12/17.31 tff(324,plain,
% 17.12/17.31 (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[323, 322])).
% 17.12/17.31 tff(325,plain,(
% 17.12/17.31 ![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 17.12/17.31 inference(skolemize,[status(sab)],[324])).
% 17.12/17.31 tff(326,plain,
% 17.12/17.31 (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[325, 321])).
% 17.12/17.31 tff(327,plain,
% 17.12/17.31 ((~![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))) | (reflection(w, extension(w, v, v, u)) = extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.31 inference(quant_inst,[status(thm)],[])).
% 17.12/17.31 tff(328,plain,
% 17.12/17.31 (reflection(w, extension(w, v, v, u)) = extension(w, extension(w, v, v, u), w, extension(w, v, v, u))),
% 17.12/17.31 inference(unit_resolution,[status(thm)],[327, 326])).
% 17.12/17.31 tff(329,plain,
% 17.12/17.31 ((extension(w, v, v, u) = reflection(w, extension(w, v, v, u))) <=> (extension(w, v, v, u) = extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.31 inference(monotonicity,[status(thm)],[328])).
% 17.12/17.31 tff(330,plain,
% 17.12/17.31 ((extension(w, v, v, u) = reflection(w, extension(w, v, v, u))) <=> (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u))),
% 17.12/17.31 inference(transitivity,[status(thm)],[329, 319])).
% 17.12/17.31 tff(331,plain,
% 17.12/17.31 ((extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(w, v, v, u)) <=> (extension(w, v, v, u) = reflection(w, extension(w, v, v, u)))),
% 17.12/17.31 inference(symmetry,[status(thm)],[330])).
% 17.12/17.31 tff(332,plain,
% 17.12/17.31 (extension(w, v, v, u) = reflection(w, extension(w, v, v, u))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[312, 331])).
% 17.12/17.31 tff(333,plain,
% 17.12/17.31 (^[V: $i, U: $i] : refl(((~(V = reflection(U, V))) | (U = V)) <=> ((~(V = reflection(U, V))) | (U = V)))),
% 17.12/17.31 inference(bind,[status(th)],[])).
% 17.12/17.31 tff(334,plain,
% 17.12/17.31 (![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V)) <=> ![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))),
% 17.12/17.31 inference(quant_intro,[status(thm)],[333])).
% 17.12/17.31 tff(335,plain,
% 17.12/17.31 (![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V)) <=> ![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))),
% 17.12/17.31 inference(rewrite,[status(thm)],[])).
% 17.12/17.31 tff(336,axiom,(![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','r4')).
% 17.12/17.31 tff(337,plain,
% 17.12/17.31 (![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[336, 335])).
% 17.12/17.31 tff(338,plain,(
% 17.12/17.31 ![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))),
% 17.12/17.31 inference(skolemize,[status(sab)],[337])).
% 17.12/17.31 tff(339,plain,
% 17.12/17.31 (![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[338, 334])).
% 17.12/17.31 tff(340,plain,
% 17.12/17.31 (((~![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))) | ((~(extension(w, v, v, u) = reflection(w, extension(w, v, v, u)))) | (w = extension(w, v, v, u)))) <=> ((~![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))) | (~(extension(w, v, v, u) = reflection(w, extension(w, v, v, u)))) | (w = extension(w, v, v, u)))),
% 17.12/17.31 inference(rewrite,[status(thm)],[])).
% 17.12/17.31 tff(341,plain,
% 17.12/17.31 ((~![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))) | ((~(extension(w, v, v, u) = reflection(w, extension(w, v, v, u)))) | (w = extension(w, v, v, u)))),
% 17.12/17.31 inference(quant_inst,[status(thm)],[])).
% 17.12/17.31 tff(342,plain,
% 17.12/17.31 ((~![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))) | (~(extension(w, v, v, u) = reflection(w, extension(w, v, v, u)))) | (w = extension(w, v, v, u))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[341, 340])).
% 17.12/17.31 tff(343,plain,
% 17.12/17.31 ((~(extension(w, v, v, u) = reflection(w, extension(w, v, v, u)))) | (w = extension(w, v, v, u))),
% 17.12/17.31 inference(unit_resolution,[status(thm)],[342, 339])).
% 17.12/17.31 tff(344,plain,
% 17.12/17.31 (w = extension(w, v, v, u)),
% 17.12/17.31 inference(unit_resolution,[status(thm)],[343, 332])).
% 17.12/17.31 tff(345,plain,
% 17.12/17.31 (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(u, v, v, w)),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[344, 318])).
% 17.12/17.31 tff(346,plain,
% 17.12/17.31 ((extension(w, v, v, u) = extension(u, v, v, w)) <=> (extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(u, v, v, w))),
% 17.12/17.31 inference(transitivity,[status(thm)],[315, 125])).
% 17.12/17.31 tff(347,plain,
% 17.12/17.31 ((~(extension(w, v, v, u) = extension(u, v, v, w))) <=> (~(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(u, v, v, w)))),
% 17.12/17.31 inference(monotonicity,[status(thm)],[346])).
% 17.12/17.31 tff(348,assumption,(w = extension(u, v, v, w)), introduced(assumption)).
% 17.12/17.31 tff(349,plain,
% 17.12/17.31 (extension(u, v, v, w) = w),
% 17.12/17.31 inference(symmetry,[status(thm)],[348])).
% 17.12/17.31 tff(350,plain,
% 17.12/17.31 ((extension(u, v, v, w) = extension(w, v, v, u)) <=> (w = u)),
% 17.12/17.31 inference(monotonicity,[status(thm)],[349, 66])).
% 17.12/17.31 tff(351,plain,
% 17.12/17.31 ((extension(u, v, v, w) = extension(w, v, v, u)) <=> (u = w)),
% 17.12/17.31 inference(transitivity,[status(thm)],[350, 81])).
% 17.12/17.31 tff(352,plain,
% 17.12/17.31 ((u = w) <=> (extension(u, v, v, w) = extension(w, v, v, u))),
% 17.12/17.31 inference(symmetry,[status(thm)],[351])).
% 17.12/17.31 tff(353,plain,
% 17.12/17.31 ((extension(w, v, v, u) = extension(u, v, v, w)) <=> (u = w)),
% 17.12/17.31 inference(monotonicity,[status(thm)],[66, 349])).
% 17.12/17.31 tff(354,plain,
% 17.12/17.31 ((extension(w, v, v, u) = extension(u, v, v, w)) <=> (extension(u, v, v, w) = extension(w, v, v, u))),
% 17.12/17.31 inference(transitivity,[status(thm)],[353, 352])).
% 17.12/17.31 tff(355,assumption,(extension(w, v, v, u) = extension(u, v, v, w)), introduced(assumption)).
% 17.12/17.31 tff(356,plain,
% 17.12/17.31 (extension(u, v, v, w) = extension(w, v, v, u)),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[355, 354])).
% 17.12/17.31 tff(357,plain,
% 17.12/17.31 ($false),
% 17.12/17.31 inference(unit_resolution,[status(thm)],[169, 356])).
% 17.12/17.31 tff(358,plain,((~(extension(w, v, v, u) = extension(u, v, v, w))) | (extension(u, v, v, w) = extension(w, v, v, u)) | (~(w = extension(u, v, v, w)))), inference(lemma,lemma(discharge,[]))).
% 17.12/17.31 tff(359,plain,
% 17.12/17.31 ((~(extension(w, v, v, u) = extension(u, v, v, w))) | (extension(u, v, v, w) = extension(w, v, v, u))),
% 17.12/17.31 inference(unit_resolution,[status(thm)],[358, 120])).
% 17.12/17.31 tff(360,plain,
% 17.12/17.31 (~(extension(w, v, v, u) = extension(u, v, v, w))),
% 17.12/17.31 inference(unit_resolution,[status(thm)],[359, 169])).
% 17.12/17.31 tff(361,plain,
% 17.12/17.31 (~(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)) = extension(u, v, v, w))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[360, 347])).
% 17.12/17.31 tff(362,plain,
% 17.12/17.31 ($false),
% 17.12/17.31 inference(unit_resolution,[status(thm)],[361, 345])).
% 17.12/17.31 tff(363,plain,(extension(u, v, v, w) = extension(w, v, v, u)), inference(lemma,lemma(discharge,[]))).
% 17.12/17.31 tff(364,plain,
% 17.12/17.31 (extension(w, v, v, u) = extension(u, v, v, w)),
% 17.12/17.31 inference(symmetry,[status(thm)],[363])).
% 17.12/17.31 tff(365,plain,
% 17.12/17.31 (extension(w, v, v, u) = w),
% 17.12/17.31 inference(transitivity,[status(thm)],[364, 121])).
% 17.12/17.31 tff(366,plain,
% 17.12/17.31 (between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) <=> between(u, v, w)),
% 17.12/17.31 inference(monotonicity,[status(thm)],[66, 152, 365])).
% 17.12/17.31 tff(367,plain,
% 17.12/17.31 (between(u, v, w) <=> between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))),
% 17.12/17.31 inference(symmetry,[status(thm)],[366])).
% 17.12/17.31 tff(368,plain,
% 17.12/17.31 (between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[39, 367])).
% 17.12/17.31 tff(369,plain,
% 17.12/17.31 ((extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) <=> (u = v)),
% 17.12/17.31 inference(monotonicity,[status(thm)],[66, 152])).
% 17.12/17.31 tff(370,plain,
% 17.12/17.31 ((u = v) <=> (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v))),
% 17.12/17.31 inference(symmetry,[status(thm)],[369])).
% 17.12/17.31 tff(371,plain,
% 17.12/17.31 ((~(u = v)) <=> (~(extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)))),
% 17.12/17.31 inference(monotonicity,[status(thm)],[370])).
% 17.12/17.31 tff(372,plain,
% 17.12/17.31 (~(extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[112, 371])).
% 17.12/17.31 tff(373,plain,
% 17.12/17.31 (^[W: $i, V: $i, U: $i] : refl(((U = V) | (~between(U, V, W)) | (~between(V, U, W))) <=> ((U = V) | (~between(U, V, W)) | (~between(V, U, W))))),
% 17.12/17.31 inference(bind,[status(th)],[])).
% 17.12/17.31 tff(374,plain,
% 17.12/17.31 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))),
% 17.12/17.31 inference(quant_intro,[status(thm)],[373])).
% 17.12/17.31 tff(375,plain,
% 17.12/17.31 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))),
% 17.12/17.31 inference(rewrite,[status(thm)],[])).
% 17.12/17.31 tff(376,plain,
% 17.12/17.31 (^[W: $i, V: $i, U: $i] : rewrite((((~between(U, V, W)) | (~between(V, U, W))) | (U = V)) <=> ((U = V) | (~between(U, V, W)) | (~between(V, U, W))))),
% 17.12/17.31 inference(bind,[status(th)],[])).
% 17.12/17.31 tff(377,plain,
% 17.12/17.31 (![W: $i, V: $i, U: $i] : (((~between(U, V, W)) | (~between(V, U, W))) | (U = V)) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))),
% 17.12/17.31 inference(quant_intro,[status(thm)],[376])).
% 17.12/17.31 tff(378,axiom,(![W: $i, V: $i, U: $i] : (((~between(U, V, W)) | (~between(V, U, W))) | (U = V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b2')).
% 17.12/17.31 tff(379,plain,
% 17.12/17.31 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[378, 377])).
% 17.12/17.31 tff(380,plain,
% 17.12/17.31 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[379, 375])).
% 17.12/17.31 tff(381,plain,(
% 17.12/17.31 ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))),
% 17.12/17.31 inference(skolemize,[status(sab)],[380])).
% 17.12/17.31 tff(382,plain,
% 17.12/17.31 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[381, 374])).
% 17.12/17.31 tff(383,plain,
% 17.12/17.31 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))) | ((extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))),
% 17.12/17.31 inference(rewrite,[status(thm)],[])).
% 17.12/17.31 tff(384,plain,
% 17.12/17.31 (((extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))) <=> ((extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))),
% 17.12/17.31 inference(rewrite,[status(thm)],[])).
% 17.12/17.31 tff(385,plain,
% 17.12/17.31 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))) | ((extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))) | ((extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))))),
% 17.12/17.31 inference(monotonicity,[status(thm)],[384])).
% 17.12/17.31 tff(386,plain,
% 17.12/17.31 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))) | ((extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))),
% 17.12/17.31 inference(transitivity,[status(thm)],[385, 383])).
% 17.12/17.31 tff(387,plain,
% 17.12/17.31 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))) | ((extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))))),
% 17.12/17.31 inference(quant_inst,[status(thm)],[])).
% 17.12/17.31 tff(388,plain,
% 17.12/17.31 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (~between(V, U, W)))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | (~between(extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))),
% 17.12/17.31 inference(modus_ponens,[status(thm)],[387, 386])).
% 17.12/17.31 tff(389,plain,
% 17.12/17.31 (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.31 inference(unit_resolution,[status(thm)],[388, 382, 372, 216])).
% 17.12/17.31 tff(390,plain,
% 17.12/17.31 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))),
% 17.12/17.31 inference(rewrite,[status(thm)],[])).
% 17.12/17.31 tff(391,plain,
% 17.12/17.31 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u))))),
% 17.12/17.31 inference(quant_inst,[status(thm)],[])).
% 17.12/17.31 tff(392,plain,
% 17.12/17.31 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, extension(w, v, v, u), w, extension(w, v, v, u)))),
% 17.12/17.32 inference(modus_ponens,[status(thm)],[391, 390])).
% 17.12/17.32 tff(393,plain,
% 17.12/17.32 (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))),
% 17.12/17.32 inference(unit_resolution,[status(thm)],[392, 46, 389])).
% 17.12/17.32 tff(394,plain,
% 17.12/17.32 (^[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)))),
% 17.12/17.32 inference(bind,[status(th)],[])).
% 17.12/17.32 tff(395,plain,
% 17.12/17.32 (![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))),
% 17.12/17.32 inference(quant_intro,[status(thm)],[394])).
% 17.12/17.32 tff(396,plain,
% 17.12/17.32 (![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))),
% 17.12/17.32 inference(rewrite,[status(thm)],[])).
% 17.12/17.32 tff(397,plain,
% 17.12/17.32 (^[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))))),
% 17.12/17.32 inference(bind,[status(th)],[])).
% 17.12/17.32 tff(398,plain,
% 17.12/17.32 (![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))),
% 17.12/17.32 inference(quant_intro,[status(thm)],[397])).
% 17.12/17.32 tff(399,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/sandbox/benchmark/theBenchmark.p','b6')).
% 17.12/17.32 tff(400,plain,
% 17.12/17.32 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 17.12/17.32 inference(modus_ponens,[status(thm)],[399, 398])).
% 17.12/17.32 tff(401,plain,
% 17.12/17.32 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 17.12/17.32 inference(modus_ponens,[status(thm)],[400, 396])).
% 17.12/17.32 tff(402,plain,(
% 17.12/17.32 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 17.12/17.32 inference(skolemize,[status(sab)],[401])).
% 17.12/17.32 tff(403,plain,
% 17.12/17.32 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))),
% 17.12/17.32 inference(modus_ponens,[status(thm)],[402, 395])).
% 17.12/17.32 tff(404,plain,
% 17.12/17.32 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, 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(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))))),
% 17.12/17.32 inference(rewrite,[status(thm)],[])).
% 17.12/17.32 tff(405,plain,
% 17.12/17.32 (((~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v))) <=> ((~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))))),
% 17.12/17.32 inference(rewrite,[status(thm)],[])).
% 17.12/17.32 tff(406,plain,
% 17.12/17.32 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, 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(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v)))))),
% 17.12/17.32 inference(monotonicity,[status(thm)],[405])).
% 17.12/17.32 tff(407,plain,
% 17.12/17.32 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, 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(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))))),
% 17.12/17.32 inference(transitivity,[status(thm)],[406, 404])).
% 17.12/17.32 tff(408,plain,
% 17.12/17.32 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | ((~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v))) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)))),
% 17.18/17.33 inference(quant_inst,[status(thm)],[])).
% 17.18/17.33 tff(409,plain,
% 17.18/17.33 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(U, W, X) | (~between(V, W, X)) | (V = W))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))) | (extension(w, v, v, u) = extension(extension(w, v, v, u), v, v, v)) | between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u)) | (~between(extension(w, extension(w, v, v, u), w, extension(w, v, v, u)), extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v)))),
% 17.18/17.33 inference(modus_ponens,[status(thm)],[408, 407])).
% 17.18/17.33 tff(410,plain,
% 17.18/17.33 (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(w, v, v, u))),
% 17.18/17.33 inference(unit_resolution,[status(thm)],[409, 403, 372, 393, 304])).
% 17.18/17.33 tff(411,plain,
% 17.18/17.33 ($false),
% 17.18/17.33 inference(unit_resolution,[status(thm)],[410, 368])).
% 17.18/17.33 % SZS output end Proof
% 17.18/17.33 % E exiting
%------------------------------------------------------------------------------