%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO025-3 : 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 05:05:22 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO025-3 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % 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 14:10:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(equidistant_type, type, (
% 0.20/0.49 equidistant: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.49 tff(w1_type, type, (
% 0.20/0.49 w1: $i)).
% 0.20/0.49 tff(v1_type, type, (
% 0.20/0.49 v1: $i)).
% 0.20/0.49 tff(w_type, type, (
% 0.20/0.49 w: $i)).
% 0.20/0.49 tff(v_type, type, (
% 0.20/0.49 v: $i)).
% 0.20/0.49 tff(u1_type, type, (
% 0.20/0.49 u1: $i)).
% 0.20/0.49 tff(u_type, type, (
% 0.20/0.49 u: $i)).
% 0.20/0.49 tff(between_type, type, (
% 0.20/0.49 between: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(1,assumption,(~equidistant(u1, u1, u, u)), introduced(assumption)).
% 0.20/0.49 tff(2,plain,
% 0.20/0.49 (^[V: $i, U: $i] : refl(equidistant(U, U, V, V) <=> equidistant(U, U, V, V))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 (![V: $i, U: $i] : equidistant(U, U, V, V) <=> ![V: $i, U: $i] : equidistant(U, U, V, V)),
% 0.20/0.49 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.49 tff(4,plain,
% 0.20/0.49 (![V: $i, U: $i] : equidistant(U, U, V, V) <=> ![V: $i, U: $i] : equidistant(U, U, V, V)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(5,axiom,(![V: $i, U: $i] : equidistant(U, U, V, V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7')).
% 0.20/0.49 tff(6,plain,
% 0.20/0.49 (![V: $i, U: $i] : equidistant(U, U, V, V)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.49 tff(7,plain,(
% 0.20/0.49 ![V: $i, U: $i] : equidistant(U, U, V, V)),
% 0.20/0.49 inference(skolemize,[status(sab)],[6])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (![V: $i, U: $i] : equidistant(U, U, V, V)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.49 tff(9,plain,
% 0.20/0.49 ((~![V: $i, U: $i] : equidistant(U, U, V, V)) | equidistant(u1, u1, u, u)),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.49 tff(11,plain,(equidistant(u1, u1, u, u)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 ((~equidistant(u, w, u1, w1)) <=> (~equidistant(u, w, u1, w1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(13,axiom,(~equidistant(u, w, u1, w1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_equal_sums')).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (~equidistant(u, w, u1, w1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 (^[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)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(18,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')).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.49 tff(20,plain,(
% 0.20/0.49 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 0.20/0.49 inference(skolemize,[status(sab)],[19])).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(w1, u1, w, u)) | equidistant(u, w, u1, w1))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(w1, u1, w, u)) | equidistant(u, w, u1, w1))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(w1, u1, w, u)) | equidistant(u, w, u1, w1))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(24,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(w1, u1, w, u)) | equidistant(u, w, u1, w1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (~equidistant(w1, u1, w, u)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[24, 21, 14])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 (equidistant(v, w, v1, w1) <=> equidistant(v, w, v1, w1)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(27,axiom,(equidistant(v, w, v1, w1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v_to_w_equals_v1_to_w1')).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (equidistant(v, w, v1, w1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(30,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.49 tff(31,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(32,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2')).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.49 tff(34,plain,(
% 0.20/0.49 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 0.20/0.49 inference(skolemize,[status(sab)],[33])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(v, w, v1, w1)) | equidistant(v1, w1, v, w))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(v, w, v1, w1)) | equidistant(v1, w1, v, w))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(v, w, v1, w1)) | equidistant(v1, w1, v, w))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(38,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(v, w, v1, w1)) | equidistant(v1, w1, v, w)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.49 tff(39,plain,
% 0.20/0.49 (equidistant(v1, w1, v, w)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[38, 35, 28])).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (equidistant(u, v, u1, v1) <=> equidistant(u, v, u1, v1)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(41,axiom,(equidistant(u, v, u1, v1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','u_to_v_equals_u1_to_v1')).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (equidistant(u, v, u1, v1)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(u, v, u1, v1)) | equidistant(u1, v1, u, v))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(u, v, u1, v1)) | equidistant(u1, v1, u, v))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(u, v, u1, v1)) | equidistant(u1, v1, u, v))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(u, v, u1, v1)) | equidistant(u1, v1, u, v)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 (equidistant(u1, v1, u, v)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[45, 35, 42])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(u, v, u1, v1)) | equidistant(v1, u1, v, u))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(u, v, u1, v1)) | equidistant(v1, u1, v, u))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(48,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(u, v, u1, v1)) | equidistant(v1, u1, v, u))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(49,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(u, v, u1, v1)) | equidistant(v1, u1, v, u)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.50 tff(50,plain,
% 0.20/0.50 (equidistant(v1, u1, v, u)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[49, 21, 42])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 (between(u1, v1, w1) <=> between(u1, v1, w1)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(52,axiom,(between(u1, v1, w1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v1_between_u1_and_w1')).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 (between(u1, v1, w1)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.50 tff(54,plain,
% 0.20/0.50 (between(u, v, w) <=> between(u, v, w)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(55,axiom,(between(u, v, w)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v_between_u_and_w')).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 (between(u, v, w)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.50 tff(57,plain,
% 0.20/0.50 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.50 tff(59,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 (^[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)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(61,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.50 tff(62,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')).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.50 tff(65,plain,(
% 0.20/0.50 ![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)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[64])).
% 0.20/0.50 tff(66,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (((~![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(w1, u1, w, u) | (~between(u, v, w)) | (~equidistant(v1, u1, v, u)) | (~between(u1, v1, w1)) | (u1 = v1) | (~equidistant(v1, w1, v, w)) | (~equidistant(u1, v1, u, v)) | (~equidistant(u1, u1, u, 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)))) | equidistant(w1, u1, w, u) | (~between(u, v, w)) | (~equidistant(v1, u1, v, u)) | (~between(u1, v1, w1)) | (u1 = v1) | (~equidistant(v1, w1, v, w)) | (~equidistant(u1, v1, u, v)) | (~equidistant(u1, u1, u, u)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 ((equidistant(w1, u1, w, u) | (u1 = v1) | (~between(u, v, w)) | (~between(u1, v1, w1)) | (~equidistant(v1, u1, v, u)) | (~equidistant(u1, u1, u, u)) | (~equidistant(v1, w1, v, w)) | (~equidistant(u1, v1, u, v))) <=> (equidistant(w1, u1, w, u) | (~between(u, v, w)) | (~equidistant(v1, u1, v, u)) | (~between(u1, v1, w1)) | (u1 = v1) | (~equidistant(v1, w1, v, w)) | (~equidistant(u1, v1, u, v)) | (~equidistant(u1, u1, u, u)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 (((~![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(w1, u1, w, u) | (u1 = v1) | (~between(u, v, w)) | (~between(u1, v1, w1)) | (~equidistant(v1, u1, v, u)) | (~equidistant(u1, u1, u, u)) | (~equidistant(v1, w1, v, w)) | (~equidistant(u1, v1, 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)))) | (equidistant(w1, u1, w, u) | (~between(u, v, w)) | (~equidistant(v1, u1, v, u)) | (~between(u1, v1, w1)) | (u1 = v1) | (~equidistant(v1, w1, v, w)) | (~equidistant(u1, v1, u, v)) | (~equidistant(u1, u1, u, u))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.50 tff(70,plain,
% 0.20/0.50 (((~![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(w1, u1, w, u) | (u1 = v1) | (~between(u, v, w)) | (~between(u1, v1, w1)) | (~equidistant(v1, u1, v, u)) | (~equidistant(u1, u1, u, u)) | (~equidistant(v1, w1, v, w)) | (~equidistant(u1, v1, 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)))) | equidistant(w1, u1, w, u) | (~between(u, v, w)) | (~equidistant(v1, u1, v, u)) | (~between(u1, v1, w1)) | (u1 = v1) | (~equidistant(v1, w1, v, w)) | (~equidistant(u1, v1, u, v)) | (~equidistant(u1, u1, u, u)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 ((~![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(w1, u1, w, u) | (u1 = v1) | (~between(u, v, w)) | (~between(u1, v1, w1)) | (~equidistant(v1, u1, v, u)) | (~equidistant(u1, u1, u, u)) | (~equidistant(v1, w1, v, w)) | (~equidistant(u1, v1, u, v)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(72,plain,
% 0.20/0.50 ((~![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(w1, u1, w, u) | (~between(u, v, w)) | (~equidistant(v1, u1, v, u)) | (~between(u1, v1, w1)) | (u1 = v1) | (~equidistant(v1, w1, v, w)) | (~equidistant(u1, v1, u, v)) | (~equidistant(u1, u1, u, u))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.50 tff(73,plain,
% 0.20/0.50 ((u1 = v1) | (~equidistant(u1, u1, u, u))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[72, 66, 56, 53, 50, 46, 39, 25])).
% 0.20/0.50 tff(74,plain,
% 0.20/0.50 (u1 = v1),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[73, 11])).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 (v1 = u1),
% 0.20/0.50 inference(symmetry,[status(thm)],[74])).
% 0.20/0.51 tff(76,plain,
% 0.20/0.51 (equidistant(u, v, v1, v1) <=> equidistant(u, v, u1, v1)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.51 tff(77,plain,
% 0.20/0.51 (equidistant(u, v, u1, v1) <=> equidistant(u, v, v1, v1)),
% 0.20/0.51 inference(symmetry,[status(thm)],[76])).
% 0.20/0.51 tff(78,plain,
% 0.20/0.51 (equidistant(u, v, v1, v1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[42, 77])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 (^[Z: $i, Y: $i, X: $i] : refl(((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ((~equidistant(X, Y, Z, Z)) | (X = Y)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(80,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.51 tff(81,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(82,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')).
% 0.20/0.51 tff(83,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.51 tff(84,plain,(
% 0.20/0.51 ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.20/0.51 inference(skolemize,[status(sab)],[83])).
% 0.20/0.51 tff(85,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.51 tff(86,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(u, v, v1, v1)) | (u = v))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(u, v, v1, v1)) | (u = v))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(87,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(u, v, v1, v1)) | (u = v))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(88,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(u, v, v1, v1)) | (u = v)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.51 tff(89,plain,
% 0.20/0.51 ((~equidistant(u, v, v1, v1)) | (u = v)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[88, 85])).
% 0.20/0.51 tff(90,plain,
% 0.20/0.51 (u = v),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[89, 78])).
% 0.20/0.51 tff(91,plain,
% 0.20/0.51 (v = u),
% 0.20/0.51 inference(symmetry,[status(thm)],[90])).
% 0.20/0.51 tff(92,plain,
% 0.20/0.51 (equidistant(v, w, v1, w1) <=> equidistant(u, w, u1, w1)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[91, 75])).
% 0.20/0.51 tff(93,plain,
% 0.20/0.51 (equidistant(u, w, u1, w1) <=> equidistant(v, w, v1, w1)),
% 0.20/0.51 inference(symmetry,[status(thm)],[92])).
% 0.20/0.51 tff(94,plain,
% 0.20/0.51 ((~equidistant(u, w, u1, w1)) <=> (~equidistant(v, w, v1, w1))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.51 tff(95,plain,
% 0.20/0.51 (~equidistant(v, w, v1, w1)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[14, 94])).
% 0.20/0.51 tff(96,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[28, 95])).
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------