%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO030-3 : TPTP v9.0.0. Released v1.0.0.
% 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 0.18s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO030-3 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.12 % 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
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 300
% 0.18/0.33 % DateTime : Thu Jun 19 14:10:18 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.40 % SZS status Unsatisfiable
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(equidistant_type, type, (
% 0.18/0.40 equidistant: ( $i * $i * $i * $i ) > $o)).
% 0.18/0.40 tff(extension_type, type, (
% 0.18/0.40 extension: ( $i * $i * $i * $i ) > $i)).
% 0.18/0.40 tff(w_type, type, (
% 0.18/0.40 w: $i)).
% 0.18/0.40 tff(v_type, type, (
% 0.18/0.40 v: $i)).
% 0.18/0.40 tff(u_type, type, (
% 0.18/0.40 u: $i)).
% 0.18/0.40 tff(w1_type, type, (
% 0.18/0.40 w1: $i)).
% 0.18/0.40 tff(between_type, type, (
% 0.18/0.40 between: ( $i * $i * $i ) > $o)).
% 0.18/0.40 tff(1,assumption,(~equidistant(u, v, u, v)), introduced(assumption)).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (^[V: $i, U: $i] : refl(equidistant(U, V, U, V) <=> equidistant(U, V, U, V))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (![V: $i, U: $i] : equidistant(U, V, U, V) <=> ![V: $i, U: $i] : equidistant(U, V, U, V)),
% 0.18/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (![V: $i, U: $i] : equidistant(U, V, U, V) <=> ![V: $i, U: $i] : equidistant(U, V, U, V)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(5,axiom,(![V: $i, U: $i] : equidistant(U, V, U, V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1')).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 (![V: $i, U: $i] : equidistant(U, V, U, V)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.40 tff(7,plain,(
% 0.18/0.40 ![V: $i, U: $i] : equidistant(U, V, U, V)),
% 0.18/0.40 inference(skolemize,[status(sab)],[6])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (![V: $i, U: $i] : equidistant(U, V, U, V)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.40 tff(9,plain,
% 0.18/0.40 ((~![V: $i, U: $i] : equidistant(U, V, U, V)) | equidistant(u, v, u, v)),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.40 tff(11,plain,(equidistant(u, v, u, v)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(12,assumption,(~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1)), introduced(assumption)).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 ((~(u = v)) <=> (~(u = v))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(14,axiom,(~(u = v)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','u_not_v')).
% 0.18/0.40 tff(15,plain,
% 0.18/0.40 (~(u = v)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 (between(u, v, w) <=> between(u, v, w)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(17,axiom,(between(u, v, w)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v_between_u_and_w')).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 (between(u, v, w)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(20,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.40 tff(21,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(22,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.40 tff(24,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')).
% 0.18/0.40 tff(25,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.18/0.40 tff(27,plain,(
% 0.18/0.40 ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[26])).
% 0.18/0.40 tff(28,plain,
% 0.18/0.40 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.18/0.40 tff(29,plain,
% 0.18/0.40 (((~![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)))) | (u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(30,plain,
% 0.18/0.40 ((~![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)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 ((~![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))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 (w = extension(u, v, v, w)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[31, 28, 18, 15])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (extension(u, v, v, w) = w),
% 0.18/0.40 inference(symmetry,[status(thm)],[32])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 (between(u, v, extension(u, v, v, w)) <=> between(u, v, w)),
% 0.18/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 (between(u, v, w) <=> between(u, v, extension(u, v, v, w))),
% 0.18/0.40 inference(symmetry,[status(thm)],[34])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (between(u, v, extension(u, v, v, w))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[18, 35])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (equidistant(u, extension(u, v, v, w), u, w1) <=> equidistant(u, w, u, w1)),
% 0.18/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (equidistant(u, w, u, w1) <=> equidistant(u, extension(u, v, v, w), u, w1)),
% 0.18/0.40 inference(symmetry,[status(thm)],[37])).
% 0.18/0.40 tff(39,plain,
% 0.18/0.40 (equidistant(u, w, u, w1) <=> equidistant(u, w, u, w1)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(40,axiom,(equidistant(u, w, u, w1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','u_to_w_equals_u_to_w1')).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 (equidistant(u, w, u, w1)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 (equidistant(u, extension(u, v, v, w), u, w1)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (extension(u, v, v, extension(u, v, v, w)) = extension(u, v, v, w)),
% 0.18/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (extension(u, v, v, w) = extension(u, v, v, extension(u, v, v, w))),
% 0.18/0.40 inference(symmetry,[status(thm)],[43])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w)) <=> equidistant(v, extension(u, v, v, extension(u, v, v, w)), v, extension(u, v, v, w))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[44])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 (equidistant(v, extension(u, v, v, extension(u, v, v, w)), v, extension(u, v, v, w)) <=> equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))),
% 0.18/0.40 inference(symmetry,[status(thm)],[45])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 (^[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))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 (![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)),
% 0.18/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (![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)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(50,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')).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.40 tff(52,plain,(
% 0.18/0.40 ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.18/0.40 inference(skolemize,[status(sab)],[51])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(v, extension(u, v, v, extension(u, v, v, w)), v, extension(u, v, v, w))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 (equidistant(v, extension(u, v, v, extension(u, v, v, w)), v, extension(u, v, v, w))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 (equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[55, 46])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 (equidistant(v, extension(u, v, v, w), v, w1) <=> equidistant(v, w, v, w1)),
% 0.18/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (equidistant(v, w, v, w1) <=> equidistant(v, extension(u, v, v, w), v, w1)),
% 0.18/0.40 inference(symmetry,[status(thm)],[57])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 (equidistant(v, w, v, w1) <=> equidistant(v, w, v, w1)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(60,axiom,(equidistant(v, w, v, w1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v_to_w_equals_v_to_w1')).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (equidistant(v, w, v, w1)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (equidistant(v, extension(u, v, v, w), v, w1)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(67,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.18/0.41 tff(68,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')).
% 0.18/0.41 tff(69,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.18/0.41 tff(70,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.18/0.41 tff(71,plain,(
% 0.18/0.41 ![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)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[70])).
% 0.18/0.41 tff(72,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.18/0.41 tff(73,plain,
% 0.18/0.41 (((~![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)))) | ((u = v) | (~equidistant(v, extension(u, v, v, w), v, w1)) | (~equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))) | (~equidistant(u, extension(u, v, v, w), u, w1)) | (~between(u, v, extension(u, v, v, w))) | equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1) | (~equidistant(u, v, u, v)))) <=> ((~![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)))) | (u = v) | (~equidistant(v, extension(u, v, v, w), v, w1)) | (~equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))) | (~equidistant(u, extension(u, v, v, w), u, w1)) | (~between(u, v, extension(u, v, v, w))) | equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1) | (~equidistant(u, v, u, v)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(74,plain,
% 0.18/0.41 ((equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1) | (u = v) | (~between(u, v, extension(u, v, v, w))) | (~between(u, v, extension(u, v, v, w))) | (~equidistant(v, extension(u, v, v, w), v, w1)) | (~equidistant(u, extension(u, v, v, w), u, w1)) | (~equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))) | (~equidistant(u, v, u, v))) <=> ((u = v) | (~equidistant(v, extension(u, v, v, w), v, w1)) | (~equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))) | (~equidistant(u, extension(u, v, v, w), u, w1)) | (~between(u, v, extension(u, v, v, w))) | equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1) | (~equidistant(u, v, u, v)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(75,plain,
% 0.18/0.41 (((~![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(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1) | (u = v) | (~between(u, v, extension(u, v, v, w))) | (~between(u, v, extension(u, v, v, w))) | (~equidistant(v, extension(u, v, v, w), v, w1)) | (~equidistant(u, extension(u, v, v, w), u, w1)) | (~equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))) | (~equidistant(u, v, u, v)))) <=> ((~![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)))) | ((u = v) | (~equidistant(v, extension(u, v, v, w), v, w1)) | (~equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))) | (~equidistant(u, extension(u, v, v, w), u, w1)) | (~between(u, v, extension(u, v, v, w))) | equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1) | (~equidistant(u, v, u, v))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[74])).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 (((~![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(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1) | (u = v) | (~between(u, v, extension(u, v, v, w))) | (~between(u, v, extension(u, v, v, w))) | (~equidistant(v, extension(u, v, v, w), v, w1)) | (~equidistant(u, extension(u, v, v, w), u, w1)) | (~equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))) | (~equidistant(u, v, u, v)))) <=> ((~![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)))) | (u = v) | (~equidistant(v, extension(u, v, v, w), v, w1)) | (~equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))) | (~equidistant(u, extension(u, v, v, w), u, w1)) | (~between(u, v, extension(u, v, v, w))) | equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1) | (~equidistant(u, v, u, v)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[75, 73])).
% 0.18/0.41 tff(77,plain,
% 0.18/0.41 ((~![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(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1) | (u = v) | (~between(u, v, extension(u, v, v, w))) | (~between(u, v, extension(u, v, v, w))) | (~equidistant(v, extension(u, v, v, w), v, w1)) | (~equidistant(u, extension(u, v, v, w), u, w1)) | (~equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))) | (~equidistant(u, v, u, v)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (u = v) | (~equidistant(v, extension(u, v, v, w), v, w1)) | (~equidistant(v, extension(u, v, v, w), v, extension(u, v, v, w))) | (~equidistant(u, extension(u, v, v, w), u, w1)) | (~between(u, v, extension(u, v, v, w))) | equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1) | (~equidistant(u, v, u, v))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[78, 72, 15, 62, 56, 42, 36, 12, 11])).
% 0.19/0.42 tff(80,plain,(equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (^[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)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![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))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (![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))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(84,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')).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.42 tff(86,plain,(
% 0.19/0.42 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 0.19/0.42 inference(skolemize,[status(sab)],[85])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1)) | equidistant(w1, extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1)) | equidistant(w1, extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1)) | equidistant(w1, extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w), w1)) | equidistant(w1, extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (equidistant(w1, extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[90, 87, 80])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 ((w1 = w) <=> (w = w1)),
% 0.19/0.43 inference(commutativity,[status(thm)],[])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 ((w1 = extension(u, v, v, w)) <=> (w1 = w)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 ((w1 = extension(u, v, v, w)) <=> (w = w1)),
% 0.19/0.43 inference(transitivity,[status(thm)],[93, 92])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 ((w = w1) <=> (w1 = extension(u, v, v, w))),
% 0.19/0.43 inference(symmetry,[status(thm)],[94])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 ((~(w = w1)) <=> (~(w1 = extension(u, v, v, w)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 ((~(w = w1)) <=> (~(w = w1))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(98,axiom,(~(w = w1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_w_is_w1')).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (~(w = w1)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (~(w1 = extension(u, v, v, w))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (^[Z: $i, Y: $i, X: $i] : refl(((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ((~equidistant(X, Y, Z, Z)) | (X = Y)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(104,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')).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.43 tff(106,plain,(
% 0.19/0.43 ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.19/0.43 inference(skolemize,[status(sab)],[105])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(w1, extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w))) | (w1 = extension(u, v, v, w)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(w1, extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w))) | (w1 = extension(u, v, v, w)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(w1, extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w))) | (w1 = extension(u, v, v, w)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(w1, extension(u, v, v, w), extension(u, v, v, w), extension(u, v, v, w))) | (w1 = extension(u, v, v, w))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[110, 107, 100, 91])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------