%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO037-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:05:24 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO037-3 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 14:07:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(equidistant_type, type, (
% 0.19/0.38 equidistant: ( $i * $i * $i * $i ) > $o)).
% 0.19/0.38 tff(extension_type, type, (
% 0.19/0.38 extension: ( $i * $i * $i * $i ) > $i)).
% 0.19/0.38 tff(lower_dimension_point_2_type, type, (
% 0.19/0.38 lower_dimension_point_2: $i)).
% 0.19/0.38 tff(lower_dimension_point_1_type, type, (
% 0.19/0.38 lower_dimension_point_1: $i)).
% 0.19/0.38 tff(v_type, type, (
% 0.19/0.38 v: $i)).
% 0.19/0.38 tff(u_type, type, (
% 0.19/0.38 u: $i)).
% 0.19/0.38 tff(x_type, type, (
% 0.19/0.38 x: $i)).
% 0.19/0.38 tff(w_type, type, (
% 0.19/0.38 w: $i)).
% 0.19/0.38 tff(between_type, type, (
% 0.19/0.38 between: ( $i * $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[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))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![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)),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![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)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,axiom,(![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','segment_construction2')).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.38 tff(6,plain,(
% 0.19/0.38 ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.19/0.38 inference(skolemize,[status(sab)],[5])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.38 tff(10,assumption,(~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)), introduced(assumption)).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[11, 7])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (^[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)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (![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))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![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))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(16,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_3')).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.38 tff(18,plain,(
% 0.19/0.38 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 0.19/0.39 inference(skolemize,[status(sab)],[17])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)) | equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)) | equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)) | equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)) | equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[22, 19, 12])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X))) <=> (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : rewrite((((~equidistant(U, V, W, X)) | (~equidistant(W, X, Y, Z))) | equidistant(U, V, Y, Z)) <=> (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((~equidistant(U, V, W, X)) | (~equidistant(W, X, Y, Z))) | equidistant(U, V, Y, Z)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.39 tff(29,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((~equidistant(U, V, W, X)) | (~equidistant(W, X, Y, Z))) | equidistant(U, V, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5')).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.39 tff(32,plain,(
% 0.19/0.39 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[31])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | ((~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ((equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v) | (~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2))) <=> ((~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v) | (~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | ((~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v) | (~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[36, 34])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v) | (~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, lower_dimension_point_2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 33, 23, 10, 9])).
% 0.19/0.39 tff(41,plain,(equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(X, W, U, V)) <=> ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(45,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_4')).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.39 tff(47,plain,(
% 0.19/0.39 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 0.19/0.39 inference(skolemize,[status(sab)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)) | equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[51, 48, 41])).
% 0.19/0.39 tff(53,assumption,(~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2))), introduced(assumption)).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (^[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)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(transitivity,[status(thm)],[58, 57])).
% 0.19/0.40 tff(60,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~(Y = extension(U, V, W, X))) | between(U, V, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b0')).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 56])).
% 0.19/0.40 tff(63,plain,(
% 0.19/0.40 ![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 0.19/0.40 inference(skolemize,[status(sab)],[62])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 55])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 ((~![W: $i, V: $i, U: $i, X: $i] : between(U, V, extension(U, V, W, X))) | between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[65, 64, 53])).
% 0.19/0.40 tff(67,plain,(between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)))) <=> ((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)))) <=> ((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)))) <=> ((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 ((((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)))) <=> (((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[70])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)))) <=> ((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[71, 69])).
% 0.19/0.40 tff(73,axiom,(((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_lengthen')).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[74, 68])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[76, 68])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2))) | (~between(u, v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[77, 68])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 ((v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) | (~equidistant(v, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), x, extension(w, x, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 67])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (v = extension(u, v, lower_dimension_point_1, lower_dimension_point_2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[79, 52])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (extension(u, v, lower_dimension_point_1, lower_dimension_point_2) = v),
% 0.19/0.40 inference(symmetry,[status(thm)],[80])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2)) <=> equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), v) <=> equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2))),
% 0.19/0.40 inference(symmetry,[status(thm)],[82])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[23, 83])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 ((~(lower_dimension_point_1 = lower_dimension_point_2)) <=> (~(lower_dimension_point_1 = lower_dimension_point_2))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(86,axiom,(~(lower_dimension_point_1 = lower_dimension_point_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','e2_1')).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (~(lower_dimension_point_1 = lower_dimension_point_2)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (^[Z: $i, Y: $i, X: $i] : refl(((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ((~equidistant(X, Y, Z, Z)) | (X = Y)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(91,axiom,(![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','identity_for_equidistance')).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.41 tff(93,plain,(
% 0.19/0.41 ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.19/0.41 inference(skolemize,[status(sab)],[92])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2))) | (lower_dimension_point_1 = lower_dimension_point_2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2))) | (lower_dimension_point_1 = lower_dimension_point_2))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2))) | (lower_dimension_point_1 = lower_dimension_point_2))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2))) | (lower_dimension_point_1 = lower_dimension_point_2)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (~equidistant(lower_dimension_point_1, lower_dimension_point_2, extension(u, v, lower_dimension_point_1, lower_dimension_point_2), extension(u, v, lower_dimension_point_1, lower_dimension_point_2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[97, 94, 87])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[98, 84])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------