TSTP Solution File: GEO032-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO032-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Fri Sep 16 20:34:24 EDT 2022
% Result : Unsatisfiable 49.13s 30.63s
% Output : Proof 49.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO032-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 04:47:17 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 49.13/30.63 % SZS status Unsatisfiable
% 49.13/30.63 % SZS output start Proof
% 49.13/30.63 tff(equidistant_type, type, (
% 49.13/30.63 equidistant: ( $i * $i * $i * $i ) > $o)).
% 49.13/30.63 tff(extension_type, type, (
% 49.13/30.63 extension: ( $i * $i * $i * $i ) > $i)).
% 49.13/30.63 tff(v1_type, type, (
% 49.13/30.63 v1: $i)).
% 49.13/30.63 tff(u1_type, type, (
% 49.13/30.63 u1: $i)).
% 49.13/30.63 tff(w1_type, type, (
% 49.13/30.63 w1: $i)).
% 49.13/30.63 tff(u_type, type, (
% 49.13/30.63 u: $i)).
% 49.13/30.63 tff(v_type, type, (
% 49.13/30.63 v: $i)).
% 49.13/30.63 tff(w_type, type, (
% 49.13/30.63 w: $i)).
% 49.13/30.63 tff(lower_dimension_point_2_type, type, (
% 49.13/30.63 lower_dimension_point_2: $i)).
% 49.13/30.63 tff(lower_dimension_point_1_type, type, (
% 49.13/30.63 lower_dimension_point_1: $i)).
% 49.13/30.63 tff(between_type, type, (
% 49.13/30.63 between: ( $i * $i * $i ) > $o)).
% 49.13/30.63 tff(1,plain,
% 49.13/30.63 (^[W: $i, V: $i, U: $i] : refl((V = extension(U, V, W, W)) <=> (V = extension(U, V, W, W)))),
% 49.13/30.63 inference(bind,[status(th)],[])).
% 49.13/30.63 tff(2,plain,
% 49.13/30.63 (![W: $i, V: $i, U: $i] : (V = extension(U, V, W, W)) <=> ![W: $i, V: $i, U: $i] : (V = extension(U, V, W, W))),
% 49.13/30.63 inference(quant_intro,[status(thm)],[1])).
% 49.13/30.63 tff(3,plain,
% 49.13/30.63 (![W: $i, V: $i, U: $i] : (V = extension(U, V, W, W)) <=> ![W: $i, V: $i, U: $i] : (V = extension(U, V, W, W))),
% 49.13/30.63 inference(rewrite,[status(thm)],[])).
% 49.13/30.63 tff(4,axiom,(![W: $i, V: $i, U: $i] : (V = extension(U, V, W, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e1')).
% 49.13/30.63 tff(5,plain,
% 49.13/30.63 (![W: $i, V: $i, U: $i] : (V = extension(U, V, W, W))),
% 49.13/30.63 inference(modus_ponens,[status(thm)],[4, 3])).
% 49.13/30.63 tff(6,plain,(
% 49.13/30.63 ![W: $i, V: $i, U: $i] : (V = extension(U, V, W, W))),
% 49.13/30.63 inference(skolemize,[status(sab)],[5])).
% 49.13/30.63 tff(7,plain,
% 49.13/30.63 (![W: $i, V: $i, U: $i] : (V = extension(U, V, W, W))),
% 49.13/30.63 inference(modus_ponens,[status(thm)],[6, 2])).
% 49.13/30.63 tff(8,plain,
% 49.13/30.63 ((~![W: $i, V: $i, U: $i] : (V = extension(U, V, W, W))) | (v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.13/30.63 inference(quant_inst,[status(thm)],[])).
% 49.13/30.63 tff(9,plain,
% 49.13/30.63 (v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)),
% 49.13/30.63 inference(unit_resolution,[status(thm)],[8, 7])).
% 49.13/30.63 tff(10,plain,
% 49.13/30.63 (extension(extension(w1, v1, v1, u1), v1, v1, v1) = v1),
% 49.13/30.63 inference(symmetry,[status(thm)],[9])).
% 49.13/30.63 tff(11,plain,
% 49.13/30.63 ((extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)) <=> (extension(w, v, v, u) = extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2))),
% 49.13/30.63 inference(commutativity,[status(thm)],[])).
% 49.13/30.63 tff(12,plain,
% 49.13/30.63 ((extension(w, v, v, u) = extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2)) <=> (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u))),
% 49.13/30.63 inference(symmetry,[status(thm)],[11])).
% 49.13/30.63 tff(13,plain,
% 49.13/30.63 ((~(extension(w, v, v, u) = extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2))) <=> (~(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)))),
% 49.13/30.63 inference(monotonicity,[status(thm)],[12])).
% 49.13/30.63 tff(14,plain,
% 49.13/30.63 (^[V: $i, U: $i] : refl((~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2))) <=> (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2))))),
% 49.13/30.63 inference(bind,[status(th)],[])).
% 49.13/30.63 tff(15,plain,
% 49.13/30.63 (![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2))) <=> ![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 49.13/30.63 inference(quant_intro,[status(thm)],[14])).
% 49.13/30.63 tff(16,plain,
% 49.13/30.63 (![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2))) <=> ![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 49.13/30.63 inference(rewrite,[status(thm)],[])).
% 49.13/30.63 tff(17,axiom,(![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e3_1')).
% 49.13/30.63 tff(18,plain,
% 49.13/30.63 (![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 49.13/30.63 inference(modus_ponens,[status(thm)],[17, 16])).
% 49.13/30.63 tff(19,plain,(
% 49.13/30.63 ![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 49.13/30.64 inference(skolemize,[status(sab)],[18])).
% 49.13/30.64 tff(20,plain,
% 49.13/30.64 (![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 49.13/30.64 inference(modus_ponens,[status(thm)],[19, 15])).
% 49.13/30.64 tff(21,plain,
% 49.13/30.64 ((~![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))) | (~(extension(w, v, v, u) = extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2)))),
% 49.13/30.64 inference(quant_inst,[status(thm)],[])).
% 49.13/30.64 tff(22,plain,
% 49.13/30.64 (~(extension(w, v, v, u) = extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2))),
% 49.13/30.64 inference(unit_resolution,[status(thm)],[21, 20])).
% 49.13/30.64 tff(23,plain,
% 49.13/30.64 (~(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u))),
% 49.13/30.64 inference(modus_ponens,[status(thm)],[22, 13])).
% 49.13/30.64 tff(24,plain,
% 49.13/30.64 (^[V: $i, U: $i] : refl(between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)) <=> between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 49.13/30.64 inference(bind,[status(th)],[])).
% 49.13/30.64 tff(25,plain,
% 49.13/30.64 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)) <=> ![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 49.13/30.64 inference(quant_intro,[status(thm)],[24])).
% 49.13/30.64 tff(26,plain,
% 49.13/30.64 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2)) <=> ![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 49.13/30.64 inference(rewrite,[status(thm)],[])).
% 49.13/30.64 tff(27,axiom,(![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e3_3')).
% 49.13/30.64 tff(28,plain,
% 49.13/30.64 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 49.13/30.64 inference(modus_ponens,[status(thm)],[27, 26])).
% 49.13/30.64 tff(29,plain,(
% 49.13/30.64 ![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 49.13/30.64 inference(skolemize,[status(sab)],[28])).
% 49.13/30.64 tff(30,plain,
% 49.13/30.64 (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 49.13/30.64 inference(modus_ponens,[status(thm)],[29, 25])).
% 49.13/30.64 tff(31,plain,
% 49.13/30.64 ((~![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))) | between(u1, extension(w, v, v, u), extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2))),
% 49.13/30.64 inference(quant_inst,[status(thm)],[])).
% 49.13/30.64 tff(32,plain,
% 49.13/30.64 (between(u1, extension(w, v, v, u), extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2))),
% 49.13/30.64 inference(unit_resolution,[status(thm)],[31, 30])).
% 49.13/30.64 tff(33,plain,
% 49.13/30.64 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | between(W, V, U)) <=> ((~between(U, V, W)) | between(W, V, U)))),
% 49.13/30.64 inference(bind,[status(th)],[])).
% 49.13/30.64 tff(34,plain,
% 49.13/30.64 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U)) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 49.13/30.64 inference(quant_intro,[status(thm)],[33])).
% 49.13/30.64 tff(35,plain,
% 49.13/30.64 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U)) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 49.13/30.64 inference(rewrite,[status(thm)],[])).
% 49.13/30.64 tff(36,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1')).
% 49.13/30.64 tff(37,plain,
% 49.13/30.64 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 49.13/30.64 inference(modus_ponens,[status(thm)],[36, 35])).
% 49.13/30.64 tff(38,plain,(
% 49.13/30.64 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 49.13/30.64 inference(skolemize,[status(sab)],[37])).
% 49.13/30.64 tff(39,plain,
% 49.13/30.64 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 49.13/30.64 inference(modus_ponens,[status(thm)],[38, 34])).
% 49.13/30.64 tff(40,plain,
% 49.13/30.64 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u1, extension(w, v, v, u), extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2))) | between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u1, extension(w, v, v, u), extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2))) | between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1))),
% 49.13/30.64 inference(rewrite,[status(thm)],[])).
% 49.13/30.64 tff(41,plain,
% 49.13/30.64 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u1, extension(w, v, v, u), extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2))) | between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1))),
% 49.13/30.64 inference(quant_inst,[status(thm)],[])).
% 49.13/30.64 tff(42,plain,
% 49.13/30.64 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u1, extension(w, v, v, u), extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2))) | between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)),
% 49.13/30.64 inference(modus_ponens,[status(thm)],[41, 40])).
% 49.13/30.64 tff(43,plain,
% 49.13/30.64 (between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)),
% 49.13/30.64 inference(unit_resolution,[status(thm)],[42, 39, 32])).
% 49.13/30.64 tff(44,plain,
% 49.13/30.64 (^[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))))),
% 49.13/30.64 inference(bind,[status(th)],[])).
% 49.13/30.64 tff(45,plain,
% 49.13/30.64 (![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)))),
% 49.13/30.64 inference(quant_intro,[status(thm)],[44])).
% 49.13/30.64 tff(46,plain,
% 49.13/30.64 (![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)))),
% 49.13/30.64 inference(rewrite,[status(thm)],[])).
% 49.13/30.64 tff(47,plain,
% 49.13/30.64 (^[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))))),
% 49.13/30.64 inference(bind,[status(th)],[])).
% 49.13/30.64 tff(48,plain,
% 49.13/30.64 (![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)))),
% 49.13/30.64 inference(quant_intro,[status(thm)],[47])).
% 49.13/30.64 tff(49,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')).
% 49.13/30.64 tff(50,plain,
% 49.13/30.64 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 49.13/30.64 inference(modus_ponens,[status(thm)],[49, 48])).
% 49.13/30.64 tff(51,plain,
% 49.13/30.64 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 49.13/30.64 inference(modus_ponens,[status(thm)],[50, 46])).
% 49.13/30.64 tff(52,plain,(
% 49.13/30.64 ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 49.13/30.64 inference(skolemize,[status(sab)],[51])).
% 49.13/30.64 tff(53,plain,
% 49.13/30.64 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 49.13/30.64 inference(modus_ponens,[status(thm)],[52, 45])).
% 49.13/30.64 tff(54,plain,
% 49.13/30.64 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)))),
% 49.13/30.65 inference(rewrite,[status(thm)],[])).
% 49.13/30.65 tff(55,plain,
% 49.13/30.65 (((extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)) | (u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) <=> ((u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)))),
% 49.13/30.65 inference(rewrite,[status(thm)],[])).
% 49.13/30.65 tff(56,plain,
% 49.13/30.65 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)) | (u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u))))),
% 49.13/30.65 inference(monotonicity,[status(thm)],[55])).
% 49.13/30.65 tff(57,plain,
% 49.13/30.65 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)) | (u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)))),
% 49.13/30.65 inference(transitivity,[status(thm)],[56, 54])).
% 49.13/30.65 tff(58,plain,
% 49.13/30.65 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)) | (u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)))),
% 49.13/30.65 inference(quant_inst,[status(thm)],[])).
% 49.13/30.65 tff(59,plain,
% 49.13/30.65 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u))),
% 49.13/30.65 inference(modus_ponens,[status(thm)],[58, 57])).
% 49.13/30.65 tff(60,plain,
% 49.13/30.65 ((u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), u1)) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u))),
% 49.13/30.65 inference(unit_resolution,[status(thm)],[59, 53])).
% 49.13/30.65 tff(61,plain,
% 49.13/30.65 (u1 = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)),
% 49.13/30.65 inference(unit_resolution,[status(thm)],[60, 43, 23])).
% 49.13/30.65 tff(62,plain,
% 49.13/30.65 (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = u1),
% 49.13/30.65 inference(symmetry,[status(thm)],[61])).
% 49.13/30.65 tff(63,plain,
% 49.13/30.65 (^[W: $i, V: $i, Y: $i, X: $i] : refl(between(X, Y, extension(X, Y, W, V)) <=> between(X, Y, extension(X, Y, W, V)))),
% 49.13/30.65 inference(bind,[status(th)],[])).
% 49.13/30.65 tff(64,plain,
% 49.13/30.65 (![W: $i, V: $i, Y: $i, X: $i] : between(X, Y, extension(X, Y, W, V)) <=> ![W: $i, V: $i, Y: $i, X: $i] : between(X, Y, extension(X, Y, W, V))),
% 49.13/30.65 inference(quant_intro,[status(thm)],[63])).
% 49.13/30.65 tff(65,plain,
% 49.13/30.65 (![W: $i, V: $i, Y: $i, X: $i] : between(X, Y, extension(X, Y, W, V)) <=> ![W: $i, V: $i, Y: $i, X: $i] : between(X, Y, extension(X, Y, W, V))),
% 49.13/30.65 inference(rewrite,[status(thm)],[])).
% 49.13/30.65 tff(66,axiom,(![W: $i, V: $i, Y: $i, X: $i] : between(X, Y, extension(X, Y, W, V))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax','segment_construction1')).
% 49.13/30.65 tff(67,plain,
% 49.13/30.65 (![W: $i, V: $i, Y: $i, X: $i] : between(X, Y, extension(X, Y, W, V))),
% 49.13/30.65 inference(modus_ponens,[status(thm)],[66, 65])).
% 49.13/30.65 tff(68,plain,(
% 49.13/30.65 ![W: $i, V: $i, Y: $i, X: $i] : between(X, Y, extension(X, Y, W, V))),
% 49.13/30.65 inference(skolemize,[status(sab)],[67])).
% 49.13/30.65 tff(69,plain,
% 49.13/30.65 (![W: $i, V: $i, Y: $i, X: $i] : between(X, Y, extension(X, Y, W, V))),
% 49.13/30.65 inference(modus_ponens,[status(thm)],[68, 64])).
% 49.13/30.65 tff(70,plain,
% 49.13/30.65 ((~![W: $i, V: $i, Y: $i, X: $i] : between(X, Y, extension(X, Y, W, V))) | between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))),
% 49.13/30.65 inference(quant_inst,[status(thm)],[])).
% 49.13/30.65 tff(71,plain,
% 49.13/30.65 (between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))),
% 49.13/30.65 inference(unit_resolution,[status(thm)],[70, 69])).
% 49.13/30.65 tff(72,plain,
% 49.13/30.65 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)))),
% 49.13/30.66 inference(rewrite,[status(thm)],[])).
% 49.13/30.66 tff(73,plain,
% 49.13/30.66 (((extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)))) <=> ((~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)))),
% 49.13/30.66 inference(rewrite,[status(thm)],[])).
% 49.13/30.66 tff(74,plain,
% 49.13/30.66 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u))))),
% 49.13/30.66 inference(monotonicity,[status(thm)],[73])).
% 49.13/30.66 tff(75,plain,
% 49.13/30.66 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)))),
% 49.13/30.66 inference(transitivity,[status(thm)],[74, 72])).
% 49.13/30.66 tff(76,plain,
% 49.13/30.66 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u)) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))))),
% 49.13/30.66 inference(quant_inst,[status(thm)],[])).
% 49.13/30.66 tff(77,plain,
% 49.13/30.66 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))) | (extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2) = extension(w, v, v, u))),
% 49.13/30.67 inference(modus_ponens,[status(thm)],[76, 75])).
% 49.13/30.67 tff(78,plain,
% 49.13/30.67 (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1))),
% 49.13/30.67 inference(unit_resolution,[status(thm)],[77, 53, 23, 71])).
% 49.13/30.67 tff(79,plain,
% 49.13/30.67 (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)) = extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)),
% 49.13/30.67 inference(symmetry,[status(thm)],[78])).
% 49.13/30.67 tff(80,plain,
% 49.13/30.67 (extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)) = u1),
% 49.13/30.67 inference(transitivity,[status(thm)],[79, 62])).
% 49.13/30.67 tff(81,plain,
% 49.13/30.67 ((~![W: $i, V: $i, U: $i] : (V = extension(U, V, W, W))) | (v = extension(extension(w, v, v, u), v, v, v))),
% 49.13/30.67 inference(quant_inst,[status(thm)],[])).
% 49.13/30.67 tff(82,plain,
% 49.13/30.67 (v = extension(extension(w, v, v, u), v, v, v)),
% 49.13/30.67 inference(unit_resolution,[status(thm)],[81, 7])).
% 49.13/30.67 tff(83,plain,
% 49.13/30.67 (extension(extension(w, v, v, u), v, v, v) = v),
% 49.13/30.67 inference(symmetry,[status(thm)],[82])).
% 49.13/30.67 tff(84,assumption,(w = v), introduced(assumption)).
% 49.13/30.67 tff(85,assumption,(extension(w1, v1, v1, u1) = v1), introduced(assumption)).
% 49.13/30.67 tff(86,plain,
% 49.13/30.67 (v1 = extension(w1, v1, v1, u1)),
% 49.13/30.67 inference(symmetry,[status(thm)],[85])).
% 49.13/30.67 tff(87,plain,
% 49.13/30.67 (extension(extension(w1, v1, v1, u1), v1, v1, v1) = extension(w1, v1, v1, u1)),
% 49.13/30.67 inference(transitivity,[status(thm)],[10, 86])).
% 49.13/30.67 tff(88,plain,
% 49.13/30.67 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), u1, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) <=> equidistant(v1, u1, v1, extension(w1, v1, v1, u1))),
% 49.13/30.67 inference(monotonicity,[status(thm)],[10, 10, 87])).
% 49.13/30.67 tff(89,plain,
% 49.13/30.67 (equidistant(v1, u1, v1, extension(w1, v1, v1, u1)) <=> equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), u1, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.13/30.67 inference(symmetry,[status(thm)],[88])).
% 49.13/30.67 tff(90,plain,
% 49.13/30.67 (^[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))),
% 49.13/30.67 inference(bind,[status(th)],[])).
% 49.13/30.67 tff(91,plain,
% 49.13/30.67 (![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)),
% 49.13/30.67 inference(quant_intro,[status(thm)],[90])).
% 49.13/30.67 tff(92,plain,
% 49.13/30.67 (![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)),
% 49.13/30.67 inference(rewrite,[status(thm)],[])).
% 49.24/30.67 tff(93,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')).
% 49.24/30.67 tff(94,plain,
% 49.24/30.67 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 49.24/30.67 inference(modus_ponens,[status(thm)],[93, 92])).
% 49.24/30.67 tff(95,plain,(
% 49.24/30.67 ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 49.24/30.67 inference(skolemize,[status(sab)],[94])).
% 49.24/30.67 tff(96,plain,
% 49.24/30.67 (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 49.24/30.67 inference(modus_ponens,[status(thm)],[95, 91])).
% 49.24/30.67 tff(97,plain,
% 49.24/30.67 ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(v1, extension(w1, v1, v1, u1), v1, u1)),
% 49.24/30.67 inference(quant_inst,[status(thm)],[])).
% 49.24/30.67 tff(98,plain,
% 49.24/30.67 (equidistant(v1, extension(w1, v1, v1, u1), v1, u1)),
% 49.24/30.67 inference(unit_resolution,[status(thm)],[97, 96])).
% 49.24/30.67 tff(99,plain,
% 49.24/30.67 (^[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)))),
% 49.24/30.67 inference(bind,[status(th)],[])).
% 49.24/30.67 tff(100,plain,
% 49.24/30.67 (![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))),
% 49.24/30.67 inference(quant_intro,[status(thm)],[99])).
% 49.24/30.67 tff(101,plain,
% 49.24/30.67 (![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))),
% 49.24/30.67 inference(rewrite,[status(thm)],[])).
% 49.24/30.67 tff(102,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')).
% 49.24/30.67 tff(103,plain,
% 49.24/30.67 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 49.24/30.67 inference(modus_ponens,[status(thm)],[102, 101])).
% 49.24/30.67 tff(104,plain,(
% 49.24/30.67 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 49.24/30.67 inference(skolemize,[status(sab)],[103])).
% 49.24/30.67 tff(105,plain,
% 49.24/30.67 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 49.24/30.67 inference(modus_ponens,[status(thm)],[104, 100])).
% 49.24/30.67 tff(106,plain,
% 49.24/30.67 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(v1, extension(w1, v1, v1, u1), v1, u1)) | equidistant(v1, u1, v1, extension(w1, v1, v1, u1)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(v1, extension(w1, v1, v1, u1), v1, u1)) | equidistant(v1, u1, v1, extension(w1, v1, v1, u1)))),
% 49.24/30.67 inference(rewrite,[status(thm)],[])).
% 49.24/30.67 tff(107,plain,
% 49.24/30.67 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(v1, extension(w1, v1, v1, u1), v1, u1)) | equidistant(v1, u1, v1, extension(w1, v1, v1, u1)))),
% 49.24/30.67 inference(quant_inst,[status(thm)],[])).
% 49.24/30.67 tff(108,plain,
% 49.24/30.67 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(v1, extension(w1, v1, v1, u1), v1, u1)) | equidistant(v1, u1, v1, extension(w1, v1, v1, u1))),
% 49.24/30.67 inference(modus_ponens,[status(thm)],[107, 106])).
% 49.24/30.67 tff(109,plain,
% 49.24/30.67 (equidistant(v1, u1, v1, extension(w1, v1, v1, u1))),
% 49.24/30.67 inference(unit_resolution,[status(thm)],[108, 105, 98])).
% 49.24/30.67 tff(110,plain,
% 49.24/30.67 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), u1, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.24/30.67 inference(modus_ponens,[status(thm)],[109, 89])).
% 49.24/30.67 tff(111,plain,
% 49.24/30.67 (^[Z: $i, Y: $i, X: $i] : refl(((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ((~equidistant(X, Y, Z, Z)) | (X = Y)))),
% 49.24/30.67 inference(bind,[status(th)],[])).
% 49.24/30.67 tff(112,plain,
% 49.24/30.67 (![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))),
% 49.24/30.67 inference(quant_intro,[status(thm)],[111])).
% 49.24/30.67 tff(113,plain,
% 49.24/30.67 (![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))),
% 49.24/30.67 inference(rewrite,[status(thm)],[])).
% 49.24/30.67 tff(114,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')).
% 49.24/30.67 tff(115,plain,
% 49.24/30.67 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 49.24/30.67 inference(modus_ponens,[status(thm)],[114, 113])).
% 49.24/30.67 tff(116,plain,(
% 49.24/30.67 ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 49.24/30.67 inference(skolemize,[status(sab)],[115])).
% 49.24/30.67 tff(117,plain,
% 49.24/30.67 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 49.24/30.67 inference(modus_ponens,[status(thm)],[116, 112])).
% 49.24/30.67 tff(118,plain,
% 49.24/30.67 (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), u1, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (extension(extension(w1, v1, v1, u1), v1, v1, v1) = u1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), u1, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (extension(extension(w1, v1, v1, u1), v1, v1, v1) = u1))),
% 49.24/30.67 inference(rewrite,[status(thm)],[])).
% 49.24/30.67 tff(119,plain,
% 49.24/30.67 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), u1, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (extension(extension(w1, v1, v1, u1), v1, v1, v1) = u1))),
% 49.24/30.67 inference(quant_inst,[status(thm)],[])).
% 49.24/30.67 tff(120,plain,
% 49.24/30.67 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), u1, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (extension(extension(w1, v1, v1, u1), v1, v1, v1) = u1)),
% 49.24/30.67 inference(modus_ponens,[status(thm)],[119, 118])).
% 49.24/30.67 tff(121,plain,
% 49.24/30.67 ((~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), u1, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (extension(extension(w1, v1, v1, u1), v1, v1, v1) = u1)),
% 49.24/30.67 inference(unit_resolution,[status(thm)],[120, 117])).
% 49.24/30.67 tff(122,plain,
% 49.24/30.67 (extension(extension(w1, v1, v1, u1), v1, v1, v1) = u1),
% 49.24/30.67 inference(unit_resolution,[status(thm)],[121, 110])).
% 49.24/30.67 tff(123,plain,
% 49.24/30.67 (u1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)),
% 49.24/30.67 inference(symmetry,[status(thm)],[122])).
% 49.24/30.67 tff(124,plain,
% 49.24/30.67 (u1 = v1),
% 49.24/30.67 inference(transitivity,[status(thm)],[123, 10])).
% 49.24/30.67 tff(125,plain,
% 49.24/30.67 (between(v1, u1, w1) <=> between(extension(w1, v1, v1, u1), v1, w1)),
% 49.24/30.67 inference(monotonicity,[status(thm)],[86, 124])).
% 49.24/30.67 tff(126,plain,
% 49.24/30.67 (between(extension(w1, v1, v1, u1), v1, w1) <=> between(v1, u1, w1)),
% 49.24/30.67 inference(symmetry,[status(thm)],[125])).
% 49.24/30.67 tff(127,plain,
% 49.24/30.67 ((~![W: $i, V: $i, Y: $i, X: $i] : between(X, Y, extension(X, Y, W, V))) | between(w1, v1, extension(w1, v1, v1, u1))),
% 49.24/30.67 inference(quant_inst,[status(thm)],[])).
% 49.24/30.67 tff(128,plain,
% 49.24/30.67 (between(w1, v1, extension(w1, v1, v1, u1))),
% 49.24/30.67 inference(unit_resolution,[status(thm)],[127, 69])).
% 49.24/30.67 tff(129,plain,
% 49.24/30.67 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(w1, v1, extension(w1, v1, v1, u1))) | between(extension(w1, v1, v1, u1), v1, w1))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(w1, v1, extension(w1, v1, v1, u1))) | between(extension(w1, v1, v1, u1), v1, w1))),
% 49.24/30.67 inference(rewrite,[status(thm)],[])).
% 49.24/30.67 tff(130,plain,
% 49.24/30.67 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(w1, v1, extension(w1, v1, v1, u1))) | between(extension(w1, v1, v1, u1), v1, w1))),
% 49.24/30.67 inference(quant_inst,[status(thm)],[])).
% 49.24/30.67 tff(131,plain,
% 49.24/30.67 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(w1, v1, extension(w1, v1, v1, u1))) | between(extension(w1, v1, v1, u1), v1, w1)),
% 49.24/30.68 inference(modus_ponens,[status(thm)],[130, 129])).
% 49.24/30.68 tff(132,plain,
% 49.24/30.68 (between(extension(w1, v1, v1, u1), v1, w1)),
% 49.24/30.68 inference(unit_resolution,[status(thm)],[131, 39, 128])).
% 49.24/30.68 tff(133,plain,
% 49.24/30.68 (between(v1, u1, w1)),
% 49.24/30.68 inference(modus_ponens,[status(thm)],[132, 126])).
% 49.24/30.68 tff(134,plain,
% 49.24/30.68 (equidistant(u, v, u1, v1) <=> equidistant(u, v, u1, v1)),
% 49.24/30.68 inference(rewrite,[status(thm)],[])).
% 49.24/30.68 tff(135,axiom,(equidistant(u, v, u1, v1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','u_to_v_equals_u1_to_v1')).
% 49.24/30.68 tff(136,plain,
% 49.24/30.68 (equidistant(u, v, u1, v1)),
% 49.24/30.68 inference(modus_ponens,[status(thm)],[135, 134])).
% 49.24/30.68 tff(137,plain,
% 49.24/30.68 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)) <=> ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)))),
% 49.24/30.68 inference(bind,[status(th)],[])).
% 49.24/30.68 tff(138,plain,
% 49.24/30.68 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 49.24/30.68 inference(quant_intro,[status(thm)],[137])).
% 49.24/30.68 tff(139,plain,
% 49.24/30.68 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 49.24/30.68 inference(rewrite,[status(thm)],[])).
% 49.24/30.68 tff(140,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_2')).
% 49.24/30.68 tff(141,plain,
% 49.24/30.68 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 49.24/30.68 inference(modus_ponens,[status(thm)],[140, 139])).
% 49.24/30.68 tff(142,plain,(
% 49.24/30.68 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 49.24/30.68 inference(skolemize,[status(sab)],[141])).
% 49.24/30.68 tff(143,plain,
% 49.24/30.68 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 49.24/30.68 inference(modus_ponens,[status(thm)],[142, 138])).
% 49.24/30.68 tff(144,plain,
% 49.24/30.68 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | ((~equidistant(u, v, u1, v1)) | equidistant(v, u, v1, u1))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | (~equidistant(u, v, u1, v1)) | equidistant(v, u, v1, u1))),
% 49.24/30.68 inference(rewrite,[status(thm)],[])).
% 49.24/30.68 tff(145,plain,
% 49.24/30.68 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | ((~equidistant(u, v, u1, v1)) | equidistant(v, u, v1, u1))),
% 49.24/30.68 inference(quant_inst,[status(thm)],[])).
% 49.24/30.68 tff(146,plain,
% 49.24/30.68 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | (~equidistant(u, v, u1, v1)) | equidistant(v, u, v1, u1)),
% 49.24/30.68 inference(modus_ponens,[status(thm)],[145, 144])).
% 49.24/30.68 tff(147,plain,
% 49.24/30.68 (equidistant(v, u, v1, u1)),
% 49.24/30.68 inference(unit_resolution,[status(thm)],[146, 143, 136])).
% 49.24/30.68 tff(148,plain,
% 49.24/30.68 ((~equidistant(v, w, v1, w1)) <=> (~equidistant(v, w, v1, w1))),
% 49.24/30.68 inference(rewrite,[status(thm)],[])).
% 49.24/30.68 tff(149,axiom,(~equidistant(v, w, v1, w1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v_to_w_equals_v1_to_w1')).
% 49.24/30.68 tff(150,plain,
% 49.24/30.68 (~equidistant(v, w, v1, w1)),
% 49.24/30.68 inference(modus_ponens,[status(thm)],[149, 148])).
% 49.24/30.68 tff(151,plain,
% 49.24/30.68 (equidistant(u, w, u1, w1) <=> equidistant(u, w, u1, w1)),
% 49.24/30.68 inference(rewrite,[status(thm)],[])).
% 49.24/30.68 tff(152,axiom,(equidistant(u, w, u1, w1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','u_to_w_equals_u1_to_w1')).
% 49.24/30.68 tff(153,plain,
% 49.24/30.68 (equidistant(u, w, u1, w1)),
% 49.24/30.68 inference(modus_ponens,[status(thm)],[152, 151])).
% 49.24/30.68 tff(154,plain,
% 49.24/30.68 (^[W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : refl((equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))) <=> (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))))),
% 49.24/30.68 inference(bind,[status(th)],[])).
% 49.24/30.68 tff(155,plain,
% 49.24/30.68 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.24/30.68 inference(quant_intro,[status(thm)],[154])).
% 49.24/30.68 tff(156,plain,
% 49.24/30.68 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.24/30.68 inference(rewrite,[status(thm)],[])).
% 49.24/30.68 tff(157,plain,
% 49.24/30.68 (^[W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) <=> ((~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) <=> (((~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))) | (~between(U1, V1, W1))))), rewrite((((~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))) | (~between(U1, V1, W1))) <=> ((~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) <=> ((~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))))), ((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | equidistant(U, W, U1, W1)) <=> (((~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))) | equidistant(U, W, U1, W1)))), rewrite((((~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1))) | equidistant(U, W, U1, W1)) <=> (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))), ((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | equidistant(U, W, U1, W1)) <=> (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))))),
% 49.24/30.68 inference(bind,[status(th)],[])).
% 49.24/30.68 tff(158,plain,
% 49.24/30.68 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | equidistant(U, W, U1, W1)) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.24/30.68 inference(quant_intro,[status(thm)],[157])).
% 49.24/30.68 tff(159,axiom,(![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | equidistant(U, W, U1, W1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8')).
% 49.24/30.68 tff(160,plain,
% 49.24/30.68 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.24/30.68 inference(modus_ponens,[status(thm)],[159, 158])).
% 49.24/30.68 tff(161,plain,
% 49.24/30.68 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.24/30.68 inference(modus_ponens,[status(thm)],[160, 156])).
% 49.24/30.68 tff(162,plain,(
% 49.26/30.68 ![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.26/30.68 inference(skolemize,[status(sab)],[161])).
% 49.26/30.68 tff(163,plain,
% 49.26/30.68 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.26/30.68 inference(modus_ponens,[status(thm)],[162, 155])).
% 49.26/30.68 tff(164,plain,
% 49.26/30.68 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(v, w, v1, w1) | (~equidistant(u, w, u1, w1)) | (~between(v1, u1, w1)) | (~between(v, u, w)) | (~equidistant(v, u, v1, u1)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | equidistant(v, w, v1, w1) | (~equidistant(u, w, u1, w1)) | (~between(v1, u1, w1)) | (~between(v, u, w)) | (~equidistant(v, u, v1, u1)))),
% 49.26/30.68 inference(rewrite,[status(thm)],[])).
% 49.26/30.68 tff(165,plain,
% 49.26/30.68 ((equidistant(v, w, v1, w1) | (~between(v1, u1, w1)) | (~between(v, u, w)) | (~equidistant(u, w, u1, w1)) | (~equidistant(v, u, v1, u1))) <=> (equidistant(v, w, v1, w1) | (~equidistant(u, w, u1, w1)) | (~between(v1, u1, w1)) | (~between(v, u, w)) | (~equidistant(v, u, v1, u1)))),
% 49.26/30.68 inference(rewrite,[status(thm)],[])).
% 49.26/30.68 tff(166,plain,
% 49.26/30.68 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(v, w, v1, w1) | (~between(v1, u1, w1)) | (~between(v, u, w)) | (~equidistant(u, w, u1, w1)) | (~equidistant(v, u, v1, u1)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(v, w, v1, w1) | (~equidistant(u, w, u1, w1)) | (~between(v1, u1, w1)) | (~between(v, u, w)) | (~equidistant(v, u, v1, u1))))),
% 49.26/30.68 inference(monotonicity,[status(thm)],[165])).
% 49.26/30.68 tff(167,plain,
% 49.26/30.68 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(v, w, v1, w1) | (~between(v1, u1, w1)) | (~between(v, u, w)) | (~equidistant(u, w, u1, w1)) | (~equidistant(v, u, v1, u1)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | equidistant(v, w, v1, w1) | (~equidistant(u, w, u1, w1)) | (~between(v1, u1, w1)) | (~between(v, u, w)) | (~equidistant(v, u, v1, u1)))),
% 49.26/30.68 inference(transitivity,[status(thm)],[166, 164])).
% 49.26/30.68 tff(168,plain,
% 49.26/30.68 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(v, w, v1, w1) | (~between(v1, u1, w1)) | (~between(v, u, w)) | (~equidistant(u, w, u1, w1)) | (~equidistant(v, u, v1, u1)))),
% 49.26/30.68 inference(quant_inst,[status(thm)],[])).
% 49.26/30.68 tff(169,plain,
% 49.26/30.68 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, U1: $i] : (equidistant(U, W, U1, W1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(V, W, V1, W1)) | (~equidistant(U, V, U1, V1)))) | equidistant(v, w, v1, w1) | (~equidistant(u, w, u1, w1)) | (~between(v1, u1, w1)) | (~between(v, u, w)) | (~equidistant(v, u, v1, u1))),
% 49.26/30.68 inference(modus_ponens,[status(thm)],[168, 167])).
% 49.26/30.68 tff(170,plain,
% 49.26/30.68 ((~between(v1, u1, w1)) | (~between(v, u, w))),
% 49.26/30.68 inference(unit_resolution,[status(thm)],[169, 163, 153, 150, 147])).
% 49.26/30.68 tff(171,plain,
% 49.26/30.68 (~between(v, u, w)),
% 49.26/30.68 inference(unit_resolution,[status(thm)],[170, 133])).
% 49.26/30.68 tff(172,plain,
% 49.26/30.69 (equidistant(u, v, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) <=> equidistant(u, v, u1, v1)),
% 49.26/30.69 inference(monotonicity,[status(thm)],[122, 10])).
% 49.26/30.69 tff(173,plain,
% 49.26/30.69 (equidistant(u, v, u1, v1) <=> equidistant(u, v, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.26/30.69 inference(symmetry,[status(thm)],[172])).
% 49.26/30.69 tff(174,plain,
% 49.26/30.69 (equidistant(u, v, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[136, 173])).
% 49.26/30.69 tff(175,plain,
% 49.26/30.69 (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(u, v, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (u = v))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(u, v, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (u = v))),
% 49.26/30.69 inference(rewrite,[status(thm)],[])).
% 49.26/30.69 tff(176,plain,
% 49.26/30.69 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(u, v, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (u = v))),
% 49.26/30.69 inference(quant_inst,[status(thm)],[])).
% 49.26/30.69 tff(177,plain,
% 49.26/30.69 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(u, v, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (u = v)),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[176, 175])).
% 49.26/30.69 tff(178,plain,
% 49.26/30.69 ((~equidistant(u, v, extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (u = v)),
% 49.26/30.69 inference(unit_resolution,[status(thm)],[177, 117])).
% 49.26/30.69 tff(179,plain,
% 49.26/30.69 (u = v),
% 49.26/30.69 inference(unit_resolution,[status(thm)],[178, 174])).
% 49.26/30.69 tff(180,assumption,(u = extension(w, v, v, u)), introduced(assumption)).
% 49.26/30.69 tff(181,assumption,(u = v), introduced(assumption)).
% 49.26/30.69 tff(182,plain,
% 49.26/30.69 (v = u),
% 49.26/30.69 inference(symmetry,[status(thm)],[181])).
% 49.26/30.69 tff(183,plain,
% 49.26/30.69 (v = extension(w, v, v, u)),
% 49.26/30.69 inference(transitivity,[status(thm)],[182, 180])).
% 49.26/30.69 tff(184,plain,
% 49.26/30.69 (between(v, u, w) <=> between(extension(w, v, v, u), extension(w, v, v, u), w)),
% 49.26/30.69 inference(monotonicity,[status(thm)],[183, 180])).
% 49.26/30.69 tff(185,plain,
% 49.26/30.69 (between(extension(w, v, v, u), extension(w, v, v, u), w) <=> between(v, u, w)),
% 49.26/30.69 inference(symmetry,[status(thm)],[184])).
% 49.26/30.69 tff(186,plain,
% 49.26/30.69 (extension(w, v, v, u) = u),
% 49.26/30.69 inference(symmetry,[status(thm)],[180])).
% 49.26/30.69 tff(187,plain,
% 49.26/30.69 (extension(w, v, v, u) = v),
% 49.26/30.69 inference(transitivity,[status(thm)],[186, 181])).
% 49.26/30.69 tff(188,plain,
% 49.26/30.69 (between(extension(w, v, v, u), extension(w, v, v, u), w) <=> between(u, v, w)),
% 49.26/30.69 inference(monotonicity,[status(thm)],[186, 187])).
% 49.26/30.69 tff(189,plain,
% 49.26/30.69 (between(u, v, w) <=> between(extension(w, v, v, u), extension(w, v, v, u), w)),
% 49.26/30.69 inference(symmetry,[status(thm)],[188])).
% 49.26/30.69 tff(190,plain,
% 49.26/30.69 (between(u, v, w) <=> between(u, v, w)),
% 49.26/30.69 inference(rewrite,[status(thm)],[])).
% 49.26/30.69 tff(191,axiom,(between(u, v, w)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v_between_u_and_w')).
% 49.26/30.69 tff(192,plain,
% 49.26/30.69 (between(u, v, w)),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[191, 190])).
% 49.26/30.69 tff(193,plain,
% 49.26/30.69 (between(extension(w, v, v, u), extension(w, v, v, u), w)),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[192, 189])).
% 49.26/30.69 tff(194,plain,
% 49.26/30.69 (between(v, u, w)),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[193, 185])).
% 49.26/30.69 tff(195,assumption,(~between(v, u, w)), introduced(assumption)).
% 49.26/30.69 tff(196,plain,
% 49.26/30.69 ($false),
% 49.26/30.69 inference(unit_resolution,[status(thm)],[195, 194])).
% 49.26/30.69 tff(197,plain,((~(u = v)) | between(v, u, w) | (~(u = extension(w, v, v, u)))), inference(lemma,lemma(discharge,[]))).
% 49.26/30.69 tff(198,plain,
% 49.26/30.69 (~(u = extension(w, v, v, u))),
% 49.26/30.69 inference(unit_resolution,[status(thm)],[197, 179, 171])).
% 49.26/30.69 tff(199,plain,
% 49.26/30.69 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, v, w)) | between(w, v, u))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, v, w)) | between(w, v, u))),
% 49.26/30.69 inference(rewrite,[status(thm)],[])).
% 49.26/30.69 tff(200,plain,
% 49.26/30.69 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, v, w)) | between(w, v, u))),
% 49.26/30.69 inference(quant_inst,[status(thm)],[])).
% 49.26/30.69 tff(201,plain,
% 49.26/30.69 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, v, w)) | between(w, v, u)),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[200, 199])).
% 49.26/30.69 tff(202,plain,
% 49.26/30.69 (between(w, v, u)),
% 49.26/30.69 inference(unit_resolution,[status(thm)],[201, 39, 192])).
% 49.26/30.69 tff(203,plain,
% 49.26/30.69 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((w = v) | (~between(w, v, u)) | (u = extension(w, v, v, u)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (w = v) | (~between(w, v, u)) | (u = extension(w, v, v, u)))),
% 49.26/30.69 inference(rewrite,[status(thm)],[])).
% 49.26/30.69 tff(204,plain,
% 49.26/30.69 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((w = v) | (~between(w, v, u)) | (u = extension(w, v, v, u)))),
% 49.26/30.69 inference(quant_inst,[status(thm)],[])).
% 49.26/30.69 tff(205,plain,
% 49.26/30.69 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (w = v) | (~between(w, v, u)) | (u = extension(w, v, v, u))),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[204, 203])).
% 49.26/30.69 tff(206,plain,
% 49.26/30.69 ((w = v) | (u = extension(w, v, v, u))),
% 49.26/30.69 inference(unit_resolution,[status(thm)],[205, 53, 202])).
% 49.26/30.69 tff(207,plain,
% 49.26/30.69 (w = v),
% 49.26/30.69 inference(unit_resolution,[status(thm)],[206, 198])).
% 49.26/30.69 tff(208,plain,
% 49.26/30.69 (v = w),
% 49.26/30.69 inference(symmetry,[status(thm)],[207])).
% 49.26/30.69 tff(209,plain,
% 49.26/30.69 (u = w),
% 49.26/30.69 inference(transitivity,[status(thm)],[179, 208])).
% 49.26/30.69 tff(210,plain,
% 49.26/30.69 ((w = u) <=> (u = w)),
% 49.26/30.69 inference(commutativity,[status(thm)],[])).
% 49.26/30.69 tff(211,plain,
% 49.26/30.69 ((~(w = u)) <=> (~(u = w))),
% 49.26/30.69 inference(monotonicity,[status(thm)],[210])).
% 49.26/30.69 tff(212,plain,
% 49.26/30.69 (u1 = extension(w1, v1, v1, u1)),
% 49.26/30.69 inference(transitivity,[status(thm)],[123, 10, 86])).
% 49.26/30.69 tff(213,plain,
% 49.26/30.69 (between(u1, v1, u1) <=> between(extension(w1, v1, v1, u1), v1, v1)),
% 49.26/30.69 inference(monotonicity,[status(thm)],[212, 124])).
% 49.26/30.69 tff(214,plain,
% 49.26/30.69 (between(extension(w1, v1, v1, u1), v1, v1) <=> between(u1, v1, u1)),
% 49.26/30.69 inference(symmetry,[status(thm)],[213])).
% 49.26/30.69 tff(215,assumption,(~between(extension(w1, v1, v1, u1), v1, v1)), introduced(assumption)).
% 49.26/30.69 tff(216,plain,
% 49.26/30.69 (^[V: $i, U: $i] : refl(between(U, V, V) <=> between(U, V, V))),
% 49.26/30.69 inference(bind,[status(th)],[])).
% 49.26/30.69 tff(217,plain,
% 49.26/30.69 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 49.26/30.69 inference(quant_intro,[status(thm)],[216])).
% 49.26/30.69 tff(218,plain,
% 49.26/30.69 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 49.26/30.69 inference(rewrite,[status(thm)],[])).
% 49.26/30.69 tff(219,axiom,(![V: $i, U: $i] : between(U, V, V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3')).
% 49.26/30.69 tff(220,plain,
% 49.26/30.69 (![V: $i, U: $i] : between(U, V, V)),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[219, 218])).
% 49.26/30.69 tff(221,plain,(
% 49.26/30.69 ![V: $i, U: $i] : between(U, V, V)),
% 49.26/30.69 inference(skolemize,[status(sab)],[220])).
% 49.26/30.69 tff(222,plain,
% 49.26/30.69 (![V: $i, U: $i] : between(U, V, V)),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[221, 217])).
% 49.26/30.69 tff(223,plain,
% 49.26/30.69 ((~![V: $i, U: $i] : between(U, V, V)) | between(extension(w1, v1, v1, u1), v1, v1)),
% 49.26/30.69 inference(quant_inst,[status(thm)],[])).
% 49.26/30.69 tff(224,plain,
% 49.26/30.69 ($false),
% 49.26/30.69 inference(unit_resolution,[status(thm)],[223, 222, 215])).
% 49.26/30.69 tff(225,plain,(between(extension(w1, v1, v1, u1), v1, v1)), inference(lemma,lemma(discharge,[]))).
% 49.26/30.69 tff(226,plain,
% 49.26/30.69 (between(u1, v1, u1)),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[225, 214])).
% 49.26/30.69 tff(227,assumption,(~equidistant(u1, u1, u, u)), introduced(assumption)).
% 49.26/30.69 tff(228,plain,
% 49.26/30.69 (^[V: $i, U: $i] : refl(equidistant(U, U, V, V) <=> equidistant(U, U, V, V))),
% 49.26/30.69 inference(bind,[status(th)],[])).
% 49.26/30.69 tff(229,plain,
% 49.26/30.69 (![V: $i, U: $i] : equidistant(U, U, V, V) <=> ![V: $i, U: $i] : equidistant(U, U, V, V)),
% 49.26/30.69 inference(quant_intro,[status(thm)],[228])).
% 49.26/30.69 tff(230,plain,
% 49.26/30.69 (![V: $i, U: $i] : equidistant(U, U, V, V) <=> ![V: $i, U: $i] : equidistant(U, U, V, V)),
% 49.26/30.69 inference(rewrite,[status(thm)],[])).
% 49.26/30.69 tff(231,axiom,(![V: $i, U: $i] : equidistant(U, U, V, V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7')).
% 49.26/30.69 tff(232,plain,
% 49.26/30.69 (![V: $i, U: $i] : equidistant(U, U, V, V)),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[231, 230])).
% 49.26/30.69 tff(233,plain,(
% 49.26/30.69 ![V: $i, U: $i] : equidistant(U, U, V, V)),
% 49.26/30.69 inference(skolemize,[status(sab)],[232])).
% 49.26/30.69 tff(234,plain,
% 49.26/30.69 (![V: $i, U: $i] : equidistant(U, U, V, V)),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[233, 229])).
% 49.26/30.69 tff(235,plain,
% 49.26/30.69 ((~![V: $i, U: $i] : equidistant(U, U, V, V)) | equidistant(u1, u1, u, u)),
% 49.26/30.69 inference(quant_inst,[status(thm)],[])).
% 49.26/30.69 tff(236,plain,
% 49.26/30.69 ($false),
% 49.26/30.69 inference(unit_resolution,[status(thm)],[235, 234, 227])).
% 49.26/30.69 tff(237,plain,(equidistant(u1, u1, u, u)), inference(lemma,lemma(discharge,[]))).
% 49.26/30.69 tff(238,plain,
% 49.26/30.69 (^[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)))),
% 49.26/30.69 inference(bind,[status(th)],[])).
% 49.26/30.69 tff(239,plain,
% 49.26/30.69 (![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))),
% 49.26/30.69 inference(quant_intro,[status(thm)],[238])).
% 49.26/30.69 tff(240,plain,
% 49.26/30.69 (![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))),
% 49.26/30.69 inference(rewrite,[status(thm)],[])).
% 49.26/30.69 tff(241,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')).
% 49.26/30.69 tff(242,plain,
% 49.26/30.69 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[241, 240])).
% 49.26/30.69 tff(243,plain,(
% 49.26/30.69 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 49.26/30.69 inference(skolemize,[status(sab)],[242])).
% 49.26/30.69 tff(244,plain,
% 49.26/30.69 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[243, 239])).
% 49.26/30.69 tff(245,plain,
% 49.26/30.69 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(u1, u1, u, u)) | equidistant(u, u, u1, u1))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(u1, u1, u, u)) | equidistant(u, u, u1, u1))),
% 49.26/30.69 inference(rewrite,[status(thm)],[])).
% 49.26/30.69 tff(246,plain,
% 49.26/30.69 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(u1, u1, u, u)) | equidistant(u, u, u1, u1))),
% 49.26/30.69 inference(quant_inst,[status(thm)],[])).
% 49.26/30.69 tff(247,plain,
% 49.26/30.69 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(u1, u1, u, u)) | equidistant(u, u, u1, u1)),
% 49.26/30.69 inference(modus_ponens,[status(thm)],[246, 245])).
% 49.26/30.69 tff(248,plain,
% 49.26/30.69 (equidistant(u, u, u1, u1)),
% 49.26/30.69 inference(unit_resolution,[status(thm)],[247, 244, 237])).
% 49.26/30.69 tff(249,plain,
% 49.26/30.69 (^[W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : refl((equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))) <=> (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))))),
% 49.26/30.69 inference(bind,[status(th)],[])).
% 49.26/30.69 tff(250,plain,
% 49.26/30.69 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.26/30.70 inference(quant_intro,[status(thm)],[249])).
% 49.26/30.70 tff(251,plain,
% 49.26/30.70 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.26/30.70 inference(rewrite,[status(thm)],[])).
% 49.26/30.70 tff(252,plain,
% 49.26/30.70 (^[W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~equidistant(U, X, U1, X1))) <=> ((~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) <=> (((~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))) | (~equidistant(W, X, W1, X1))))), rewrite((((~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))) | (~equidistant(W, X, W1, X1))) <=> ((~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) <=> ((~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))))), ((((((~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) | (~between(U, V, W))) <=> (((~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))) | (~between(U, V, W))))), rewrite((((~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))) | (~between(U, V, W))) <=> ((~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))), ((((((~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) | (~between(U, V, W))) <=> ((~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))))), (((((((~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) <=> (((~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))) | (~between(U1, V1, W1))))), rewrite((((~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))) | (~between(U1, V1, W1))) <=> ((~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))), (((((((~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) <=> ((~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))))), ((((((((~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | equidistant(V, X, V1, X1)) <=> (((~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))) | equidistant(V, X, V1, X1)))), rewrite((((~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1))) | equidistant(V, X, V1, X1)) <=> (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))), ((((((((~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | equidistant(V, X, V1, X1)) <=> (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))))),
% 49.26/30.70 inference(bind,[status(th)],[])).
% 49.26/30.70 tff(253,plain,
% 49.26/30.70 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (((((((~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | equidistant(V, X, V1, X1)) <=> ![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.26/30.70 inference(quant_intro,[status(thm)],[252])).
% 49.26/30.70 tff(254,axiom,(![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (((((((~equidistant(U, V, U1, V1)) | (~equidistant(U, W, U1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) | (~between(U, V, W))) | (~between(U1, V1, W1))) | equidistant(V, X, V1, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d12')).
% 49.26/30.70 tff(255,plain,
% 49.26/30.70 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.26/30.70 inference(modus_ponens,[status(thm)],[254, 253])).
% 49.26/30.70 tff(256,plain,
% 49.26/30.70 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.26/30.70 inference(modus_ponens,[status(thm)],[255, 251])).
% 49.26/30.70 tff(257,plain,(
% 49.26/30.70 ![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.26/30.70 inference(skolemize,[status(sab)],[256])).
% 49.26/30.70 tff(258,plain,
% 49.26/30.70 (![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))),
% 49.26/30.70 inference(modus_ponens,[status(thm)],[257, 250])).
% 49.26/30.70 tff(259,plain,
% 49.26/30.70 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(v, w, v1, w1) | (~equidistant(u, v, u1, v1)) | (~equidistant(u, w, u1, w1)) | (~between(u1, v1, u1)) | (~between(u, v, u)) | (~equidistant(u, u, u1, u1)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | equidistant(v, w, v1, w1) | (~equidistant(u, v, u1, v1)) | (~equidistant(u, w, u1, w1)) | (~between(u1, v1, u1)) | (~between(u, v, u)) | (~equidistant(u, u, u1, u1)))),
% 49.26/30.70 inference(rewrite,[status(thm)],[])).
% 49.26/30.70 tff(260,plain,
% 49.26/30.70 ((equidistant(v, w, v1, w1) | (~between(u1, v1, u1)) | (~between(u, v, u)) | (~equidistant(u, w, u1, w1)) | (~equidistant(u, w, u1, w1)) | (~equidistant(u, u, u1, u1)) | (~equidistant(u, v, u1, v1))) <=> (equidistant(v, w, v1, w1) | (~equidistant(u, v, u1, v1)) | (~equidistant(u, w, u1, w1)) | (~between(u1, v1, u1)) | (~between(u, v, u)) | (~equidistant(u, u, u1, u1)))),
% 49.26/30.70 inference(rewrite,[status(thm)],[])).
% 49.26/30.70 tff(261,plain,
% 49.26/30.70 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(v, w, v1, w1) | (~between(u1, v1, u1)) | (~between(u, v, u)) | (~equidistant(u, w, u1, w1)) | (~equidistant(u, w, u1, w1)) | (~equidistant(u, u, u1, u1)) | (~equidistant(u, v, u1, v1)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(v, w, v1, w1) | (~equidistant(u, v, u1, v1)) | (~equidistant(u, w, u1, w1)) | (~between(u1, v1, u1)) | (~between(u, v, u)) | (~equidistant(u, u, u1, u1))))),
% 49.26/30.70 inference(monotonicity,[status(thm)],[260])).
% 49.26/30.70 tff(262,plain,
% 49.26/30.70 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(v, w, v1, w1) | (~between(u1, v1, u1)) | (~between(u, v, u)) | (~equidistant(u, w, u1, w1)) | (~equidistant(u, w, u1, w1)) | (~equidistant(u, u, u1, u1)) | (~equidistant(u, v, u1, v1)))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | equidistant(v, w, v1, w1) | (~equidistant(u, v, u1, v1)) | (~equidistant(u, w, u1, w1)) | (~between(u1, v1, u1)) | (~between(u, v, u)) | (~equidistant(u, u, u1, u1)))),
% 49.26/30.70 inference(transitivity,[status(thm)],[261, 259])).
% 49.26/30.70 tff(263,plain,
% 49.26/30.70 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(v, w, v1, w1) | (~between(u1, v1, u1)) | (~between(u, v, u)) | (~equidistant(u, w, u1, w1)) | (~equidistant(u, w, u1, w1)) | (~equidistant(u, u, u1, u1)) | (~equidistant(u, v, u1, v1)))),
% 49.26/30.70 inference(quant_inst,[status(thm)],[])).
% 49.26/30.70 tff(264,plain,
% 49.26/30.70 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | equidistant(v, w, v1, w1) | (~equidistant(u, v, u1, v1)) | (~equidistant(u, w, u1, w1)) | (~between(u1, v1, u1)) | (~between(u, v, u)) | (~equidistant(u, u, u1, u1))),
% 49.26/30.70 inference(modus_ponens,[status(thm)],[263, 262])).
% 49.26/30.70 tff(265,plain,
% 49.26/30.70 ((~between(u1, v1, u1)) | (~between(u, v, u)) | (~equidistant(u, u, u1, u1))),
% 49.26/30.70 inference(unit_resolution,[status(thm)],[264, 258, 136, 153, 150])).
% 49.26/30.70 tff(266,plain,
% 49.26/30.70 ((~between(u1, v1, u1)) | (~between(u, v, u))),
% 49.26/30.71 inference(unit_resolution,[status(thm)],[265, 248])).
% 49.26/30.71 tff(267,plain,
% 49.26/30.71 (~between(u, v, u)),
% 49.26/30.71 inference(unit_resolution,[status(thm)],[266, 226])).
% 49.26/30.71 tff(268,plain,
% 49.26/30.71 (^[W: $i, V: $i, U: $i, X: $i] : refl((between(V, W, X) | (~(U = X)) | (~between(U, W, X))) <=> (between(V, W, X) | (~(U = X)) | (~between(U, W, X))))),
% 49.26/30.71 inference(bind,[status(th)],[])).
% 49.26/30.71 tff(269,plain,
% 49.26/30.71 (![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 49.26/30.71 inference(quant_intro,[status(thm)],[268])).
% 49.26/30.71 tff(270,plain,
% 49.26/30.71 (![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 49.26/30.71 inference(rewrite,[status(thm)],[])).
% 49.26/30.71 tff(271,plain,
% 49.26/30.71 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(rewrite(((~between(U, W, X)) | (~(U = X))) <=> ((~(U = X)) | (~between(U, W, X)))), ((((~between(U, W, X)) | (~(U = X))) | between(V, W, X)) <=> (((~(U = X)) | (~between(U, W, X))) | between(V, W, X)))), rewrite((((~(U = X)) | (~between(U, W, X))) | between(V, W, X)) <=> (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))), ((((~between(U, W, X)) | (~(U = X))) | between(V, W, X)) <=> (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))))),
% 49.26/30.71 inference(bind,[status(th)],[])).
% 49.26/30.71 tff(272,plain,
% 49.26/30.71 (![W: $i, V: $i, U: $i, X: $i] : (((~between(U, W, X)) | (~(U = X))) | between(V, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 49.26/30.71 inference(quant_intro,[status(thm)],[271])).
% 49.26/30.71 tff(273,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, W, X)) | (~(U = X))) | between(V, W, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b1')).
% 49.26/30.71 tff(274,plain,
% 49.26/30.71 (![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 49.26/30.71 inference(modus_ponens,[status(thm)],[273, 272])).
% 49.26/30.71 tff(275,plain,
% 49.26/30.71 (![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 49.26/30.71 inference(modus_ponens,[status(thm)],[274, 270])).
% 49.26/30.71 tff(276,plain,(
% 49.26/30.71 ![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 49.26/30.71 inference(skolemize,[status(sab)],[275])).
% 49.26/30.71 tff(277,plain,
% 49.26/30.71 (![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 49.26/30.71 inference(modus_ponens,[status(thm)],[276, 269])).
% 49.26/30.71 tff(278,plain,
% 49.26/30.71 (((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u, v, u) | (~between(w, v, u)) | (~(w = u)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | between(u, v, u) | (~between(w, v, u)) | (~(w = u)))),
% 49.26/30.71 inference(rewrite,[status(thm)],[])).
% 49.26/30.71 tff(279,plain,
% 49.26/30.71 ((between(u, v, u) | (~(w = u)) | (~between(w, v, u))) <=> (between(u, v, u) | (~between(w, v, u)) | (~(w = u)))),
% 49.26/30.71 inference(rewrite,[status(thm)],[])).
% 49.26/30.71 tff(280,plain,
% 49.26/30.71 (((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u, v, u) | (~(w = u)) | (~between(w, v, u)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u, v, u) | (~between(w, v, u)) | (~(w = u))))),
% 49.26/30.71 inference(monotonicity,[status(thm)],[279])).
% 49.26/30.71 tff(281,plain,
% 49.26/30.71 (((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u, v, u) | (~(w = u)) | (~between(w, v, u)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | between(u, v, u) | (~between(w, v, u)) | (~(w = u)))),
% 49.26/30.71 inference(transitivity,[status(thm)],[280, 278])).
% 49.26/30.71 tff(282,plain,
% 49.26/30.71 ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u, v, u) | (~(w = u)) | (~between(w, v, u)))),
% 49.26/30.71 inference(quant_inst,[status(thm)],[])).
% 49.26/30.71 tff(283,plain,
% 49.26/30.71 ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | between(u, v, u) | (~between(w, v, u)) | (~(w = u))),
% 49.28/30.71 inference(modus_ponens,[status(thm)],[282, 281])).
% 49.28/30.71 tff(284,plain,
% 49.28/30.71 (~(w = u)),
% 49.28/30.71 inference(unit_resolution,[status(thm)],[283, 277, 267, 202])).
% 49.28/30.71 tff(285,plain,
% 49.28/30.71 (~(u = w)),
% 49.28/30.71 inference(modus_ponens,[status(thm)],[284, 211])).
% 49.28/30.71 tff(286,plain,
% 49.28/30.71 ($false),
% 49.28/30.71 inference(unit_resolution,[status(thm)],[285, 209])).
% 49.28/30.71 tff(287,plain,(~(extension(w1, v1, v1, u1) = v1)), inference(lemma,lemma(discharge,[]))).
% 49.28/30.71 tff(288,plain,
% 49.28/30.71 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, w1)) | (w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, w1)) | (w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.28/30.71 inference(rewrite,[status(thm)],[])).
% 49.28/30.71 tff(289,plain,
% 49.28/30.71 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, w1)) | (w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.28/30.71 inference(quant_inst,[status(thm)],[])).
% 49.28/30.71 tff(290,plain,
% 49.28/30.71 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, w1)) | (w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.28/30.71 inference(modus_ponens,[status(thm)],[289, 288])).
% 49.28/30.71 tff(291,plain,
% 49.28/30.71 ((extension(w1, v1, v1, u1) = v1) | (w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.28/30.71 inference(unit_resolution,[status(thm)],[290, 53, 132])).
% 49.28/30.71 tff(292,plain,
% 49.28/30.71 (w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1)),
% 49.28/30.71 inference(unit_resolution,[status(thm)],[291, 287])).
% 49.28/30.71 tff(293,plain,
% 49.28/30.71 (extension(extension(w1, v1, v1, u1), v1, v1, w1) = w1),
% 49.28/30.71 inference(symmetry,[status(thm)],[292])).
% 49.28/30.71 tff(294,assumption,(w1 = v1), introduced(assumption)).
% 49.28/30.71 tff(295,plain,
% 49.28/30.71 (extension(extension(w1, v1, v1, u1), v1, v1, w1) = v1),
% 49.28/30.71 inference(transitivity,[status(thm)],[293, 294])).
% 49.28/30.71 tff(296,plain,
% 49.28/30.71 (v = w),
% 49.28/30.71 inference(symmetry,[status(thm)],[84])).
% 49.28/30.71 tff(297,plain,
% 49.28/30.71 (extension(extension(w, v, v, u), v, v, v) = w),
% 49.28/30.71 inference(transitivity,[status(thm)],[83, 296])).
% 49.28/30.71 tff(298,plain,
% 49.28/30.71 (equidistant(extension(extension(w, v, v, u), v, v, v), extension(extension(w, v, v, u), v, v, v), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> equidistant(v, w, v1, w1)),
% 49.28/30.71 inference(monotonicity,[status(thm)],[83, 297, 295, 293])).
% 49.28/30.71 tff(299,plain,
% 49.28/30.71 (equidistant(v, w, v1, w1) <=> equidistant(extension(extension(w, v, v, u), v, v, v), extension(extension(w, v, v, u), v, v, v), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.28/30.71 inference(symmetry,[status(thm)],[298])).
% 49.28/30.71 tff(300,plain,
% 49.28/30.71 ((~equidistant(v, w, v1, w1)) <=> (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(extension(w, v, v, u), v, v, v), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.28/30.71 inference(monotonicity,[status(thm)],[299])).
% 49.28/30.71 tff(301,plain,
% 49.28/30.71 (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(extension(w, v, v, u), v, v, v), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.28/30.71 inference(modus_ponens,[status(thm)],[150, 300])).
% 49.28/30.71 tff(302,plain,
% 49.28/30.71 ((~![V: $i, U: $i] : equidistant(U, U, V, V)) | equidistant(extension(extension(w, v, v, u), v, v, v), extension(extension(w, v, v, u), v, v, v), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.28/30.71 inference(quant_inst,[status(thm)],[])).
% 49.28/30.71 tff(303,plain,
% 49.28/30.71 (equidistant(extension(extension(w, v, v, u), v, v, v), extension(extension(w, v, v, u), v, v, v), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.28/30.72 inference(unit_resolution,[status(thm)],[302, 234])).
% 49.28/30.72 tff(304,plain,
% 49.28/30.72 ($false),
% 49.28/30.72 inference(unit_resolution,[status(thm)],[303, 301])).
% 49.28/30.72 tff(305,plain,((~(w1 = v1)) | (~(w = v))), inference(lemma,lemma(discharge,[]))).
% 49.28/30.72 tff(306,plain,
% 49.28/30.72 (~(w1 = v1)),
% 49.28/30.72 inference(unit_resolution,[status(thm)],[305, 84])).
% 49.28/30.72 tff(307,assumption,(w = extension(u, v, v, w)), introduced(assumption)).
% 49.28/30.72 tff(308,plain,
% 49.28/30.72 (extension(u, v, v, w) = w),
% 49.28/30.72 inference(symmetry,[status(thm)],[307])).
% 49.28/30.72 tff(309,plain,
% 49.28/30.72 (extension(u, v, v, w) = v),
% 49.28/30.72 inference(transitivity,[status(thm)],[308, 84])).
% 49.28/30.72 tff(310,plain,
% 49.28/30.72 (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w)) = extension(w1, v1, u, v)),
% 49.28/30.72 inference(monotonicity,[status(thm)],[293, 10, 309])).
% 49.28/30.72 tff(311,plain,
% 49.28/30.72 (extension(w1, v1, u, v) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w))),
% 49.28/30.72 inference(symmetry,[status(thm)],[310])).
% 49.28/30.72 tff(312,assumption,(~(w1 = v1)), introduced(assumption)).
% 49.28/30.72 tff(313,plain,
% 49.28/30.72 (^[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)))),
% 49.28/30.72 inference(bind,[status(th)],[])).
% 49.28/30.72 tff(314,plain,
% 49.28/30.72 (![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))),
% 49.28/30.72 inference(quant_intro,[status(thm)],[313])).
% 49.28/30.72 tff(315,plain,
% 49.28/30.72 (![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))),
% 49.28/30.72 inference(rewrite,[status(thm)],[])).
% 49.28/30.72 tff(316,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_4')).
% 49.28/30.72 tff(317,plain,
% 49.28/30.72 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 49.28/30.72 inference(modus_ponens,[status(thm)],[316, 315])).
% 49.28/30.72 tff(318,plain,(
% 49.28/30.72 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 49.28/30.72 inference(skolemize,[status(sab)],[317])).
% 49.28/30.72 tff(319,plain,
% 49.28/30.72 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))),
% 49.28/30.72 inference(modus_ponens,[status(thm)],[318, 314])).
% 49.28/30.72 tff(320,plain,
% 49.28/30.72 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(u, v, u1, v1)) | equidistant(v1, u1, u, v))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(u, v, u1, v1)) | equidistant(v1, u1, u, v))),
% 49.28/30.72 inference(rewrite,[status(thm)],[])).
% 49.28/30.72 tff(321,plain,
% 49.28/30.72 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | ((~equidistant(u, v, u1, v1)) | equidistant(v1, u1, u, v))),
% 49.28/30.72 inference(quant_inst,[status(thm)],[])).
% 49.28/30.72 tff(322,plain,
% 49.28/30.72 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, U, V))) | (~equidistant(u, v, u1, v1)) | equidistant(v1, u1, u, v)),
% 49.28/30.72 inference(modus_ponens,[status(thm)],[321, 320])).
% 49.28/30.72 tff(323,plain,
% 49.28/30.72 (equidistant(v1, u1, u, v)),
% 49.28/30.72 inference(unit_resolution,[status(thm)],[322, 319, 136])).
% 49.28/30.72 tff(324,plain,
% 49.28/30.72 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl(((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z))) <=> ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z))))),
% 49.28/30.72 inference(bind,[status(th)],[])).
% 49.28/30.72 tff(325,plain,
% 49.28/30.72 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))),
% 49.28/30.72 inference(quant_intro,[status(thm)],[324])).
% 49.28/30.72 tff(326,plain,
% 49.28/30.72 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))),
% 49.28/30.72 inference(rewrite,[status(thm)],[])).
% 49.28/30.72 tff(327,plain,
% 49.28/30.72 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : rewrite((((~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z))) | (U = V)) <=> ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z))))),
% 49.28/30.72 inference(bind,[status(th)],[])).
% 49.28/30.72 tff(328,plain,
% 49.28/30.72 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z))) | (U = V)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))),
% 49.28/30.72 inference(quant_intro,[status(thm)],[327])).
% 49.28/30.72 tff(329,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z))) | (U = V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_2')).
% 49.28/30.72 tff(330,plain,
% 49.28/30.72 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))),
% 49.28/30.72 inference(modus_ponens,[status(thm)],[329, 328])).
% 49.28/30.72 tff(331,plain,
% 49.28/30.72 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))),
% 49.28/30.72 inference(modus_ponens,[status(thm)],[330, 326])).
% 49.28/30.72 tff(332,plain,(
% 49.28/30.72 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))),
% 49.28/30.72 inference(skolemize,[status(sab)],[331])).
% 49.28/30.72 tff(333,plain,
% 49.28/30.72 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))),
% 49.28/30.72 inference(modus_ponens,[status(thm)],[332, 325])).
% 49.28/30.72 tff(334,plain,
% 49.28/30.72 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | ((w1 = v1) | (~equidistant(v1, u1, u, v)) | (extension(w1, v1, v1, u1) = extension(w1, v1, u, v)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | (w1 = v1) | (~equidistant(v1, u1, u, v)) | (extension(w1, v1, v1, u1) = extension(w1, v1, u, v)))),
% 49.28/30.72 inference(rewrite,[status(thm)],[])).
% 49.28/30.72 tff(335,plain,
% 49.28/30.72 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | ((w1 = v1) | (~equidistant(v1, u1, u, v)) | (extension(w1, v1, v1, u1) = extension(w1, v1, u, v)))),
% 49.28/30.72 inference(quant_inst,[status(thm)],[])).
% 49.28/30.72 tff(336,plain,
% 49.28/30.72 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | (w1 = v1) | (~equidistant(v1, u1, u, v)) | (extension(w1, v1, v1, u1) = extension(w1, v1, u, v))),
% 49.28/30.72 inference(modus_ponens,[status(thm)],[335, 334])).
% 49.28/30.72 tff(337,plain,
% 49.28/30.72 ((w1 = v1) | (extension(w1, v1, v1, u1) = extension(w1, v1, u, v))),
% 49.28/30.72 inference(unit_resolution,[status(thm)],[336, 333, 323])).
% 49.28/30.72 tff(338,plain,
% 49.28/30.72 (extension(w1, v1, v1, u1) = extension(w1, v1, u, v)),
% 49.28/30.72 inference(unit_resolution,[status(thm)],[337, 312])).
% 49.28/30.72 tff(339,plain,
% 49.28/30.72 (((~![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))),
% 49.28/30.72 inference(rewrite,[status(thm)],[])).
% 49.28/30.72 tff(340,plain,
% 49.28/30.72 ((~![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))),
% 49.28/30.72 inference(quant_inst,[status(thm)],[])).
% 49.28/30.72 tff(341,plain,
% 49.28/30.72 ((~![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)),
% 49.30/30.73 inference(modus_ponens,[status(thm)],[340, 339])).
% 49.30/30.73 tff(342,plain,
% 49.30/30.73 (equidistant(v1, u1, v, u)),
% 49.30/30.73 inference(unit_resolution,[status(thm)],[341, 244, 136])).
% 49.30/30.73 tff(343,plain,
% 49.30/30.73 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | ((w1 = v1) | (~equidistant(v1, u1, v, u)) | (extension(w1, v1, v1, u1) = extension(w1, v1, v, u)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | (w1 = v1) | (~equidistant(v1, u1, v, u)) | (extension(w1, v1, v1, u1) = extension(w1, v1, v, u)))),
% 49.30/30.73 inference(rewrite,[status(thm)],[])).
% 49.30/30.73 tff(344,plain,
% 49.30/30.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | ((w1 = v1) | (~equidistant(v1, u1, v, u)) | (extension(w1, v1, v1, u1) = extension(w1, v1, v, u)))),
% 49.30/30.73 inference(quant_inst,[status(thm)],[])).
% 49.30/30.73 tff(345,plain,
% 49.30/30.73 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | (w1 = v1) | (~equidistant(v1, u1, v, u)) | (extension(w1, v1, v1, u1) = extension(w1, v1, v, u))),
% 49.30/30.73 inference(modus_ponens,[status(thm)],[344, 343])).
% 49.30/30.73 tff(346,plain,
% 49.30/30.73 ((w1 = v1) | (extension(w1, v1, v1, u1) = extension(w1, v1, v, u))),
% 49.30/30.73 inference(unit_resolution,[status(thm)],[345, 333, 342])).
% 49.30/30.73 tff(347,plain,
% 49.30/30.73 (extension(w1, v1, v1, u1) = extension(w1, v1, v, u)),
% 49.30/30.73 inference(unit_resolution,[status(thm)],[346, 312])).
% 49.30/30.73 tff(348,plain,
% 49.30/30.73 (extension(w1, v1, v, u) = extension(w1, v1, v1, u1)),
% 49.30/30.73 inference(symmetry,[status(thm)],[347])).
% 49.30/30.73 tff(349,plain,
% 49.30/30.73 (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w, v, v, u), v, v, v), u) = extension(w1, v1, v, u)),
% 49.30/30.73 inference(monotonicity,[status(thm)],[293, 10, 83])).
% 49.30/30.73 tff(350,plain,
% 49.30/30.73 (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w, v, v, u), v, v, v), u) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w))),
% 49.30/30.73 inference(transitivity,[status(thm)],[349, 348, 338, 311])).
% 49.30/30.73 tff(351,plain,
% 49.30/30.73 ((extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w, v, v, u), v, v, v), u) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) <=> (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w)) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.30/30.73 inference(monotonicity,[status(thm)],[350])).
% 49.30/30.73 tff(352,plain,
% 49.30/30.73 ((extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w)) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) <=> (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w, v, v, u), v, v, v), u) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.30/30.73 inference(symmetry,[status(thm)],[351])).
% 49.30/30.73 tff(353,plain,
% 49.30/30.73 ((~(extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w)) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))) <=> (~(extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w, v, v, u), v, v, v), u) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))))),
% 49.30/30.73 inference(monotonicity,[status(thm)],[352])).
% 49.30/30.73 tff(354,plain,
% 49.30/30.73 (between(u1, v1, w1) <=> between(u1, v1, w1)),
% 49.30/30.73 inference(rewrite,[status(thm)],[])).
% 49.30/30.73 tff(355,axiom,(between(u1, v1, w1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v1_between_u1_and_w1')).
% 49.30/30.73 tff(356,plain,
% 49.30/30.73 (between(u1, v1, w1)),
% 49.30/30.73 inference(modus_ponens,[status(thm)],[355, 354])).
% 49.30/30.73 tff(357,plain,
% 49.30/30.73 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u1, v1, w1)) | between(w1, v1, u1))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u1, v1, w1)) | between(w1, v1, u1))),
% 49.30/30.73 inference(rewrite,[status(thm)],[])).
% 49.30/30.73 tff(358,plain,
% 49.30/30.73 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u1, v1, w1)) | between(w1, v1, u1))),
% 49.30/30.73 inference(quant_inst,[status(thm)],[])).
% 49.30/30.73 tff(359,plain,
% 49.30/30.73 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u1, v1, w1)) | between(w1, v1, u1)),
% 49.30/30.73 inference(modus_ponens,[status(thm)],[358, 357])).
% 49.30/30.73 tff(360,plain,
% 49.30/30.73 (between(w1, v1, u1)),
% 49.30/30.73 inference(unit_resolution,[status(thm)],[359, 39, 356])).
% 49.30/30.73 tff(361,plain,
% 49.30/30.73 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((w1 = v1) | (~between(w1, v1, u1)) | (u1 = extension(w1, v1, v1, u1)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (w1 = v1) | (~between(w1, v1, u1)) | (u1 = extension(w1, v1, v1, u1)))),
% 49.30/30.73 inference(rewrite,[status(thm)],[])).
% 49.30/30.73 tff(362,plain,
% 49.30/30.73 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((w1 = v1) | (~between(w1, v1, u1)) | (u1 = extension(w1, v1, v1, u1)))),
% 49.30/30.73 inference(quant_inst,[status(thm)],[])).
% 49.30/30.73 tff(363,plain,
% 49.30/30.73 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (w1 = v1) | (~between(w1, v1, u1)) | (u1 = extension(w1, v1, v1, u1))),
% 49.30/30.73 inference(modus_ponens,[status(thm)],[362, 361])).
% 49.30/30.73 tff(364,plain,
% 49.30/30.73 ((w1 = v1) | (u1 = extension(w1, v1, v1, u1))),
% 49.30/30.73 inference(unit_resolution,[status(thm)],[363, 53, 360])).
% 49.30/30.73 tff(365,plain,
% 49.30/30.73 (u1 = extension(w1, v1, v1, u1)),
% 49.30/30.73 inference(unit_resolution,[status(thm)],[364, 312])).
% 49.30/30.73 tff(366,plain,
% 49.30/30.73 (extension(u1, v1, v1, w1) = extension(extension(w1, v1, v1, u1), v1, v1, w1)),
% 49.30/30.73 inference(monotonicity,[status(thm)],[365])).
% 49.30/30.73 tff(367,plain,
% 49.30/30.73 (extension(extension(w1, v1, v1, u1), v1, v1, w1) = extension(u1, v1, v1, w1)),
% 49.30/30.73 inference(symmetry,[status(thm)],[366])).
% 49.30/30.73 tff(368,plain,
% 49.30/30.73 (w1 = extension(u1, v1, v1, w1)),
% 49.30/30.73 inference(transitivity,[status(thm)],[292, 367])).
% 49.30/30.73 tff(369,assumption,(~(extension(w1, v1, v1, u1) = v1)), introduced(assumption)).
% 49.30/30.73 tff(370,plain,
% 49.30/30.73 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, v1)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, v1)))),
% 49.30/30.73 inference(rewrite,[status(thm)],[])).
% 49.30/30.73 tff(371,plain,
% 49.30/30.73 (((extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, v1)) | (v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1))) <=> ((v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, v1)))),
% 49.30/30.74 inference(rewrite,[status(thm)],[])).
% 49.30/30.74 tff(372,plain,
% 49.30/30.74 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, v1)) | (v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, v1))))),
% 49.30/30.74 inference(monotonicity,[status(thm)],[371])).
% 49.30/30.74 tff(373,plain,
% 49.30/30.74 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, v1)) | (v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, v1)))),
% 49.30/30.74 inference(transitivity,[status(thm)],[372, 370])).
% 49.30/30.74 tff(374,plain,
% 49.30/30.74 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, v1)) | (v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)))),
% 49.30/30.74 inference(quant_inst,[status(thm)],[])).
% 49.30/30.74 tff(375,plain,
% 49.30/30.74 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, v1))),
% 49.30/30.74 inference(modus_ponens,[status(thm)],[374, 373])).
% 49.30/30.74 tff(376,plain,
% 49.30/30.74 ((v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (extension(w1, v1, v1, u1) = v1)),
% 49.30/30.74 inference(unit_resolution,[status(thm)],[375, 53, 225])).
% 49.30/30.74 tff(377,plain,
% 49.30/30.74 (v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)),
% 49.30/30.74 inference(unit_resolution,[status(thm)],[376, 369])).
% 49.30/30.74 tff(378,plain,
% 49.30/30.74 (extension(extension(w1, v1, v1, u1), v1, v1, v1) = v1),
% 49.30/30.74 inference(symmetry,[status(thm)],[377])).
% 49.30/30.74 tff(379,plain,
% 49.30/30.74 (w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1)),
% 49.30/30.74 inference(unit_resolution,[status(thm)],[291, 369])).
% 49.30/30.74 tff(380,plain,
% 49.30/30.74 (extension(extension(w1, v1, v1, u1), v1, v1, w1) = w1),
% 49.30/30.74 inference(symmetry,[status(thm)],[379])).
% 49.30/30.74 tff(381,plain,
% 49.30/30.74 (equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) <=> equidistant(extension(w1, v1, v1, u1), w1, extension(w1, v1, v1, u1), v1)),
% 49.30/30.74 inference(monotonicity,[status(thm)],[380, 378])).
% 49.30/30.74 tff(382,plain,
% 49.30/30.74 (equidistant(extension(w1, v1, v1, u1), w1, extension(w1, v1, v1, u1), v1) <=> equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.74 inference(symmetry,[status(thm)],[381])).
% 49.30/30.74 tff(383,plain,
% 49.30/30.74 ((~equidistant(extension(w1, v1, v1, u1), w1, extension(w1, v1, v1, u1), v1)) <=> (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)))),
% 49.30/30.74 inference(monotonicity,[status(thm)],[382])).
% 49.30/30.74 tff(384,assumption,(w1 = extension(u1, v1, v1, w1)), introduced(assumption)).
% 49.30/30.74 tff(385,plain,
% 49.30/30.74 (equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> equidistant(extension(w1, v1, v1, u1), v1, extension(w1, v1, v1, u1), w1)),
% 49.30/30.74 inference(monotonicity,[status(thm)],[378, 380])).
% 49.30/30.74 tff(386,assumption,(equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))), introduced(assumption)).
% 49.30/30.74 tff(387,plain,
% 49.30/30.74 (equidistant(extension(w1, v1, v1, u1), v1, extension(w1, v1, v1, u1), w1)),
% 49.30/30.74 inference(modus_ponens,[status(thm)],[386, 385])).
% 49.30/30.74 tff(388,plain,
% 49.30/30.74 (extension(w1, v1, v1, u1) = u1),
% 49.30/30.74 inference(symmetry,[status(thm)],[365])).
% 49.30/30.74 tff(389,plain,
% 49.30/30.74 (equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) <=> equidistant(u1, v1, extension(w1, v1, v1, u1), v1)),
% 49.30/30.74 inference(monotonicity,[status(thm)],[388, 378, 378])).
% 49.30/30.74 tff(390,plain,
% 49.30/30.74 (equidistant(u1, v1, extension(w1, v1, v1, u1), v1) <=> equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.74 inference(symmetry,[status(thm)],[389])).
% 49.30/30.74 tff(391,plain,
% 49.30/30.74 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(v1, extension(w1, v1, v1, u1), v1, u1)) | equidistant(u1, v1, extension(w1, v1, v1, u1), v1))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(v1, extension(w1, v1, v1, u1), v1, u1)) | equidistant(u1, v1, extension(w1, v1, v1, u1), v1))),
% 49.30/30.74 inference(rewrite,[status(thm)],[])).
% 49.30/30.74 tff(392,plain,
% 49.30/30.74 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(v1, extension(w1, v1, v1, u1), v1, u1)) | equidistant(u1, v1, extension(w1, v1, v1, u1), v1))),
% 49.30/30.74 inference(quant_inst,[status(thm)],[])).
% 49.30/30.74 tff(393,plain,
% 49.30/30.74 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(v1, extension(w1, v1, v1, u1), v1, u1)) | equidistant(u1, v1, extension(w1, v1, v1, u1), v1)),
% 49.30/30.74 inference(modus_ponens,[status(thm)],[392, 391])).
% 49.30/30.74 tff(394,plain,
% 49.30/30.74 (equidistant(u1, v1, extension(w1, v1, v1, u1), v1)),
% 49.30/30.74 inference(unit_resolution,[status(thm)],[393, 244, 98])).
% 49.30/30.74 tff(395,plain,
% 49.30/30.74 (equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.74 inference(modus_ponens,[status(thm)],[394, 390])).
% 49.30/30.74 tff(396,plain,
% 49.30/30.74 (extension(u1, v1, v1, w1) = w1),
% 49.30/30.74 inference(symmetry,[status(thm)],[384])).
% 49.30/30.74 tff(397,plain,
% 49.30/30.74 (extension(extension(w1, v1, v1, u1), v1, v1, w1) = w1),
% 49.30/30.74 inference(transitivity,[status(thm)],[367, 396])).
% 49.30/30.74 tff(398,plain,
% 49.30/30.74 (equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> equidistant(extension(w1, v1, v1, u1), v1, extension(w1, v1, v1, u1), w1)),
% 49.30/30.74 inference(monotonicity,[status(thm)],[378, 397])).
% 49.30/30.74 tff(399,plain,
% 49.30/30.74 (equidistant(extension(w1, v1, v1, u1), v1, extension(w1, v1, v1, u1), w1) <=> equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.74 inference(symmetry,[status(thm)],[398])).
% 49.30/30.74 tff(400,assumption,(equidistant(extension(w1, v1, v1, u1), v1, extension(w1, v1, v1, u1), w1)), introduced(assumption)).
% 49.30/30.74 tff(401,plain,
% 49.30/30.74 (equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.74 inference(modus_ponens,[status(thm)],[400, 399])).
% 49.30/30.74 tff(402,plain,
% 49.30/30.74 (between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) <=> between(extension(w1, v1, v1, u1), v1, v1)),
% 49.30/30.74 inference(monotonicity,[status(thm)],[378, 378])).
% 49.30/30.74 tff(403,plain,
% 49.30/30.74 (between(extension(w1, v1, v1, u1), v1, v1) <=> between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.74 inference(symmetry,[status(thm)],[402])).
% 49.30/30.74 tff(404,plain,
% 49.30/30.74 (between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.75 inference(modus_ponens,[status(thm)],[225, 403])).
% 49.30/30.75 tff(405,plain,
% 49.30/30.75 (between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> between(extension(w1, v1, v1, u1), v1, w1)),
% 49.30/30.75 inference(monotonicity,[status(thm)],[378, 397])).
% 49.30/30.75 tff(406,plain,
% 49.30/30.75 (between(extension(w1, v1, v1, u1), v1, w1) <=> between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.75 inference(symmetry,[status(thm)],[405])).
% 49.30/30.75 tff(407,plain,
% 49.30/30.75 (between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.75 inference(modus_ponens,[status(thm)],[132, 406])).
% 49.30/30.75 tff(408,plain,
% 49.30/30.75 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) <=> equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), v1)),
% 49.30/30.75 inference(monotonicity,[status(thm)],[378, 378])).
% 49.30/30.75 tff(409,plain,
% 49.30/30.75 (equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), v1) <=> equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.75 inference(symmetry,[status(thm)],[408])).
% 49.30/30.75 tff(410,plain,
% 49.30/30.75 (extension(extension(w1, v1, v1, u1), v1, v1, extension(extension(w1, v1, v1, u1), v1, v1, w1)) = extension(extension(w1, v1, v1, u1), v1, v1, w1)),
% 49.30/30.75 inference(monotonicity,[status(thm)],[397])).
% 49.30/30.75 tff(411,plain,
% 49.30/30.75 (extension(extension(w1, v1, v1, u1), v1, v1, w1) = extension(extension(w1, v1, v1, u1), v1, v1, extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.75 inference(symmetry,[status(thm)],[410])).
% 49.30/30.75 tff(412,plain,
% 49.30/30.75 (equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, extension(extension(w1, v1, v1, u1), v1, v1, w1)), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.75 inference(monotonicity,[status(thm)],[411])).
% 49.30/30.75 tff(413,plain,
% 49.30/30.75 (equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, extension(extension(w1, v1, v1, u1), v1, v1, w1)), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.75 inference(symmetry,[status(thm)],[412])).
% 49.30/30.75 tff(414,plain,
% 49.30/30.75 ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, extension(extension(w1, v1, v1, u1), v1, v1, w1)), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.75 inference(quant_inst,[status(thm)],[])).
% 49.30/30.75 tff(415,plain,
% 49.30/30.75 (equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, extension(extension(w1, v1, v1, u1), v1, v1, w1)), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.75 inference(unit_resolution,[status(thm)],[414, 96])).
% 49.30/30.75 tff(416,plain,
% 49.30/30.75 (equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.75 inference(modus_ponens,[status(thm)],[415, 413])).
% 49.30/30.75 tff(417,plain,
% 49.30/30.75 (^[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)))),
% 49.30/30.75 inference(bind,[status(th)],[])).
% 49.30/30.75 tff(418,plain,
% 49.30/30.75 (![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))),
% 49.30/30.75 inference(quant_intro,[status(thm)],[417])).
% 49.30/30.75 tff(419,plain,
% 49.30/30.75 (![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))),
% 49.30/30.75 inference(rewrite,[status(thm)],[])).
% 49.30/30.75 tff(420,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_3')).
% 49.30/30.75 tff(421,plain,
% 49.30/30.75 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 49.30/30.75 inference(modus_ponens,[status(thm)],[420, 419])).
% 49.30/30.75 tff(422,plain,(
% 49.30/30.75 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 49.30/30.75 inference(skolemize,[status(sab)],[421])).
% 49.30/30.75 tff(423,plain,
% 49.30/30.75 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 49.30/30.75 inference(modus_ponens,[status(thm)],[422, 418])).
% 49.30/30.75 tff(424,plain,
% 49.30/30.75 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), v1))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), v1))),
% 49.30/30.75 inference(rewrite,[status(thm)],[])).
% 49.30/30.75 tff(425,plain,
% 49.30/30.75 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), v1))),
% 49.30/30.75 inference(quant_inst,[status(thm)],[])).
% 49.30/30.75 tff(426,plain,
% 49.30/30.75 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), v1)),
% 49.30/30.75 inference(modus_ponens,[status(thm)],[425, 424])).
% 49.30/30.75 tff(427,plain,
% 49.30/30.75 ((~equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), v1, extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), v1)),
% 49.30/30.75 inference(unit_resolution,[status(thm)],[426, 423])).
% 49.30/30.75 tff(428,plain,
% 49.30/30.75 (equidistant(v1, extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), v1)),
% 49.30/30.75 inference(unit_resolution,[status(thm)],[427, 416])).
% 49.30/30.75 tff(429,plain,
% 49.30/30.75 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.75 inference(modus_ponens,[status(thm)],[428, 409])).
% 49.30/30.75 tff(430,plain,
% 49.30/30.75 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) <=> equidistant(v1, w1, v1, v1)),
% 49.30/30.75 inference(monotonicity,[status(thm)],[378, 397, 378, 378])).
% 49.30/30.75 tff(431,plain,
% 49.30/30.75 (equidistant(v1, w1, v1, v1) <=> equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.75 inference(symmetry,[status(thm)],[430])).
% 49.30/30.75 tff(432,plain,
% 49.30/30.75 ((~equidistant(v1, w1, v1, v1)) <=> (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)))),
% 49.30/30.76 inference(monotonicity,[status(thm)],[431])).
% 49.30/30.76 tff(433,plain,
% 49.30/30.76 (^[W: $i, V: $i, U: $i, X: $i] : refl(((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W))) <=> ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W))))),
% 49.30/30.76 inference(bind,[status(th)],[])).
% 49.30/30.76 tff(434,plain,
% 49.30/30.76 (![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))),
% 49.30/30.76 inference(quant_intro,[status(thm)],[433])).
% 49.30/30.76 tff(435,plain,
% 49.30/30.76 (![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))),
% 49.30/30.76 inference(rewrite,[status(thm)],[])).
% 49.30/30.76 tff(436,plain,
% 49.30/30.76 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~between(U, V, W)) | (~between(U, V, X))) <=> ((~between(U, V, X)) | (~between(U, V, W)))), ((((~between(U, V, W)) | (~between(U, V, X))) | (~equidistant(V, W, V, X))) <=> (((~between(U, V, X)) | (~between(U, V, W))) | (~equidistant(V, W, V, X))))), rewrite((((~between(U, V, X)) | (~between(U, V, W))) | (~equidistant(V, W, V, X))) <=> ((~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))), ((((~between(U, V, W)) | (~between(U, V, X))) | (~equidistant(V, W, V, X))) <=> ((~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W))))), (((((~between(U, V, W)) | (~between(U, V, X))) | (~equidistant(V, W, V, X))) | (U = V)) <=> (((~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W))) | (U = V)))), rewrite((((~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W))) | (U = V)) <=> ((U = V) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))), (((((~between(U, V, W)) | (~between(U, V, X))) | (~equidistant(V, W, V, X))) | (U = V)) <=> ((U = V) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W))))), ((((((~between(U, V, W)) | (~between(U, V, X))) | (~equidistant(V, W, V, X))) | (U = V)) | (W = X)) <=> (((U = V) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W))) | (W = X)))), rewrite((((U = V) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W))) | (W = X)) <=> ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))), ((((((~between(U, V, W)) | (~between(U, V, X))) | (~equidistant(V, W, V, X))) | (U = V)) | (W = X)) <=> ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))))),
% 49.30/30.76 inference(bind,[status(th)],[])).
% 49.30/30.76 tff(437,plain,
% 49.30/30.76 (![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, V, W)) | (~between(U, V, X))) | (~equidistant(V, W, V, X))) | (U = V)) | (W = X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))),
% 49.30/30.76 inference(quant_intro,[status(thm)],[436])).
% 49.30/30.76 tff(438,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, V, W)) | (~between(U, V, X))) | (~equidistant(V, W, V, X))) | (U = V)) | (W = X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9')).
% 49.30/30.76 tff(439,plain,
% 49.30/30.76 (![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))),
% 49.30/30.76 inference(modus_ponens,[status(thm)],[438, 437])).
% 49.30/30.76 tff(440,plain,
% 49.30/30.76 (![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))),
% 49.30/30.76 inference(modus_ponens,[status(thm)],[439, 435])).
% 49.30/30.76 tff(441,plain,(
% 49.30/30.76 ![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))),
% 49.30/30.76 inference(skolemize,[status(sab)],[440])).
% 49.30/30.76 tff(442,plain,
% 49.30/30.76 (![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))),
% 49.30/30.76 inference(modus_ponens,[status(thm)],[441, 434])).
% 49.30/30.76 tff(443,plain,
% 49.30/30.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))) | ((w1 = v1) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, w1)) | (~equidistant(v1, w1, v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, v1)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))) | (w1 = v1) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, w1)) | (~equidistant(v1, w1, v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, v1)))),
% 49.30/30.76 inference(rewrite,[status(thm)],[])).
% 49.30/30.76 tff(444,plain,
% 49.30/30.76 (((extension(w1, v1, v1, u1) = v1) | (w1 = v1) | (~equidistant(v1, w1, v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, w1))) <=> ((w1 = v1) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, w1)) | (~equidistant(v1, w1, v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, v1)))),
% 49.30/30.76 inference(rewrite,[status(thm)],[])).
% 49.30/30.76 tff(445,plain,
% 49.30/30.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))) | ((extension(w1, v1, v1, u1) = v1) | (w1 = v1) | (~equidistant(v1, w1, v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, w1)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))) | ((w1 = v1) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, w1)) | (~equidistant(v1, w1, v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, v1))))),
% 49.30/30.76 inference(monotonicity,[status(thm)],[444])).
% 49.30/30.76 tff(446,plain,
% 49.30/30.76 (((~![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))) | ((extension(w1, v1, v1, u1) = v1) | (w1 = v1) | (~equidistant(v1, w1, v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, w1)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))) | (w1 = v1) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, w1)) | (~equidistant(v1, w1, v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, v1)))),
% 49.30/30.76 inference(transitivity,[status(thm)],[445, 443])).
% 49.30/30.76 tff(447,plain,
% 49.30/30.76 ((~![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))) | ((extension(w1, v1, v1, u1) = v1) | (w1 = v1) | (~equidistant(v1, w1, v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, w1)))),
% 49.30/30.76 inference(quant_inst,[status(thm)],[])).
% 49.30/30.76 tff(448,plain,
% 49.30/30.76 ((~![W: $i, V: $i, U: $i, X: $i] : ((U = V) | (W = X) | (~equidistant(V, W, V, X)) | (~between(U, V, X)) | (~between(U, V, W)))) | (w1 = v1) | (extension(w1, v1, v1, u1) = v1) | (~between(extension(w1, v1, v1, u1), v1, w1)) | (~equidistant(v1, w1, v1, v1)) | (~between(extension(w1, v1, v1, u1), v1, v1))),
% 49.30/30.76 inference(modus_ponens,[status(thm)],[447, 446])).
% 49.30/30.76 tff(449,plain,
% 49.30/30.76 ((w1 = v1) | (extension(w1, v1, v1, u1) = v1) | (~equidistant(v1, w1, v1, v1))),
% 49.30/30.76 inference(unit_resolution,[status(thm)],[448, 442, 225, 132])).
% 49.30/30.76 tff(450,plain,
% 49.30/30.76 (~equidistant(v1, w1, v1, v1)),
% 49.30/30.76 inference(unit_resolution,[status(thm)],[449, 369, 312])).
% 49.30/30.76 tff(451,plain,
% 49.30/30.76 (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.76 inference(modus_ponens,[status(thm)],[450, 432])).
% 49.30/30.76 tff(452,plain,
% 49.30/30.76 (equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) <=> equidistant(extension(w1, v1, v1, u1), w1, extension(w1, v1, v1, u1), v1)),
% 49.30/30.77 inference(monotonicity,[status(thm)],[397, 378])).
% 49.30/30.77 tff(453,plain,
% 49.30/30.77 (equidistant(extension(w1, v1, v1, u1), w1, extension(w1, v1, v1, u1), v1) <=> equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.77 inference(symmetry,[status(thm)],[452])).
% 49.30/30.77 tff(454,assumption,(equidistant(extension(w1, v1, v1, u1), w1, extension(w1, v1, v1, u1), v1)), introduced(assumption)).
% 49.30/30.77 tff(455,plain,
% 49.30/30.77 (equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.77 inference(modus_ponens,[status(thm)],[454, 453])).
% 49.30/30.77 tff(456,plain,
% 49.30/30.77 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))))),
% 49.30/30.77 inference(rewrite,[status(thm)],[])).
% 49.30/30.77 tff(457,plain,
% 49.30/30.77 ((equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)))) <=> (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))))),
% 49.30/30.77 inference(rewrite,[status(thm)],[])).
% 49.30/30.77 tff(458,plain,
% 49.30/30.77 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)))))),
% 49.30/30.78 inference(monotonicity,[status(thm)],[457])).
% 49.30/30.78 tff(459,plain,
% 49.30/30.78 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))))),
% 49.30/30.79 inference(transitivity,[status(thm)],[458, 456])).
% 49.30/30.79 tff(460,plain,
% 49.30/30.79 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))))),
% 49.30/30.79 inference(quant_inst,[status(thm)],[])).
% 49.30/30.79 tff(461,plain,
% 49.30/30.79 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)))),
% 49.30/30.79 inference(modus_ponens,[status(thm)],[460, 459])).
% 49.30/30.79 tff(462,plain,
% 49.30/30.79 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)))),
% 49.30/30.80 inference(unit_resolution,[status(thm)],[461, 258])).
% 49.30/30.80 tff(463,plain,
% 49.30/30.80 ($false),
% 49.30/30.80 inference(unit_resolution,[status(thm)],[462, 455, 451, 429, 407, 404, 401, 395])).
% 49.30/30.80 tff(464,plain,((extension(w1, v1, v1, u1) = v1) | (~equidistant(extension(w1, v1, v1, u1), v1, extension(w1, v1, v1, u1), w1)) | (~(w1 = extension(u1, v1, v1, w1))) | (~equidistant(extension(w1, v1, v1, u1), w1, extension(w1, v1, v1, u1), v1)) | (w1 = v1)), inference(lemma,lemma(discharge,[]))).
% 49.30/30.80 tff(465,plain,
% 49.30/30.80 (~equidistant(extension(w1, v1, v1, u1), w1, extension(w1, v1, v1, u1), v1)),
% 49.30/30.80 inference(unit_resolution,[status(thm)],[464, 387, 369, 384, 312])).
% 49.30/30.80 tff(466,plain,
% 49.30/30.80 (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.80 inference(modus_ponens,[status(thm)],[465, 383])).
% 49.30/30.80 tff(467,assumption,(~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))), introduced(assumption)).
% 49.30/30.80 tff(468,plain,
% 49.30/30.80 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)))),
% 49.30/30.80 inference(rewrite,[status(thm)],[])).
% 49.30/30.80 tff(469,plain,
% 49.30/30.80 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)))),
% 49.30/30.80 inference(quant_inst,[status(thm)],[])).
% 49.30/30.80 tff(470,plain,
% 49.30/30.80 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.80 inference(modus_ponens,[status(thm)],[469, 468])).
% 49.30/30.80 tff(471,plain,
% 49.30/30.80 ($false),
% 49.30/30.80 inference(unit_resolution,[status(thm)],[470, 105, 386, 467])).
% 49.30/30.80 tff(472,plain,(equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))), inference(lemma,lemma(discharge,[]))).
% 49.30/30.80 tff(473,plain,
% 49.30/30.80 (equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.30/30.80 inference(unit_resolution,[status(thm)],[472, 386])).
% 49.30/30.80 tff(474,plain,
% 49.30/30.80 ($false),
% 49.30/30.80 inference(unit_resolution,[status(thm)],[473, 466])).
% 49.30/30.80 tff(475,plain,((~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (extension(w1, v1, v1, u1) = v1) | (~(w1 = extension(u1, v1, v1, w1))) | (w1 = v1)), inference(lemma,lemma(discharge,[]))).
% 49.30/30.80 tff(476,plain,
% 49.30/30.80 ((~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~(w1 = extension(u1, v1, v1, w1))) | (w1 = v1)),
% 49.30/30.80 inference(unit_resolution,[status(thm)],[475, 287])).
% 49.30/30.80 tff(477,plain,
% 49.30/30.80 (~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.80 inference(unit_resolution,[status(thm)],[476, 368, 312])).
% 49.30/30.80 tff(478,assumption,(~equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))), introduced(assumption)).
% 49.30/30.80 tff(479,assumption,(extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w)) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))), introduced(assumption)).
% 49.30/30.80 tff(480,assumption,(v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1)), introduced(assumption)).
% 49.30/30.80 tff(481,plain,
% 49.30/30.80 (extension(extension(w1, v1, v1, u1), v1, v1, v1) = v1),
% 49.30/30.80 inference(symmetry,[status(thm)],[480])).
% 49.30/30.80 tff(482,assumption,(w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1)), introduced(assumption)).
% 49.30/30.80 tff(483,plain,
% 49.30/30.80 (extension(extension(w1, v1, v1, u1), v1, v1, w1) = w1),
% 49.30/30.80 inference(symmetry,[status(thm)],[482])).
% 49.30/30.80 tff(484,plain,
% 49.30/30.80 (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w)) = extension(w1, v1, u, v)),
% 49.30/30.80 inference(monotonicity,[status(thm)],[483, 481, 309])).
% 49.30/30.80 tff(485,plain,
% 49.30/30.80 (extension(w1, v1, u, v) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w))),
% 49.30/30.80 inference(symmetry,[status(thm)],[484])).
% 49.30/30.80 tff(486,assumption,(extension(w1, v1, v1, u1) = extension(w1, v1, u, v)), introduced(assumption)).
% 49.30/30.80 tff(487,plain,
% 49.30/30.80 (extension(w1, v1, v1, u1) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.80 inference(transitivity,[status(thm)],[486, 485, 479])).
% 49.30/30.80 tff(488,plain,
% 49.30/30.80 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.80 inference(monotonicity,[status(thm)],[487])).
% 49.30/30.80 tff(489,plain,
% 49.30/30.80 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.81 inference(symmetry,[status(thm)],[488])).
% 49.30/30.81 tff(490,plain,
% 49.30/30.81 ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.81 inference(quant_inst,[status(thm)],[])).
% 49.30/30.81 tff(491,plain,
% 49.30/30.81 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.81 inference(unit_resolution,[status(thm)],[490, 96])).
% 49.30/30.81 tff(492,plain,
% 49.30/30.81 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.30/30.81 inference(modus_ponens,[status(thm)],[491, 489])).
% 49.30/30.81 tff(493,plain,
% 49.30/30.81 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(V, U, W, X)) <=> ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X)))),
% 49.30/30.81 inference(bind,[status(th)],[])).
% 49.30/30.81 tff(494,plain,
% 49.30/30.81 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))),
% 49.30/30.81 inference(quant_intro,[status(thm)],[493])).
% 49.30/30.81 tff(495,plain,
% 49.30/30.81 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))),
% 49.30/30.81 inference(rewrite,[status(thm)],[])).
% 49.30/30.81 tff(496,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3')).
% 49.30/30.81 tff(497,plain,
% 49.30/30.81 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))),
% 49.30/30.81 inference(modus_ponens,[status(thm)],[496, 495])).
% 49.30/30.81 tff(498,plain,(
% 49.30/30.81 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))),
% 49.30/30.81 inference(skolemize,[status(sab)],[497])).
% 49.30/30.81 tff(499,plain,
% 49.30/30.81 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))),
% 49.30/30.81 inference(modus_ponens,[status(thm)],[498, 494])).
% 49.30/30.81 tff(500,plain,
% 49.30/30.81 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | ((~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.30/30.81 inference(rewrite,[status(thm)],[])).
% 49.30/30.81 tff(501,plain,
% 49.30/30.81 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | ((~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.30/30.81 inference(quant_inst,[status(thm)],[])).
% 49.30/30.81 tff(502,plain,
% 49.30/30.81 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.38/30.82 inference(modus_ponens,[status(thm)],[501, 500])).
% 49.38/30.82 tff(503,plain,
% 49.38/30.82 ((~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.38/30.82 inference(unit_resolution,[status(thm)],[502, 499])).
% 49.38/30.82 tff(504,plain,
% 49.38/30.82 ($false),
% 49.38/30.82 inference(unit_resolution,[status(thm)],[503, 492, 478])).
% 49.38/30.82 tff(505,plain,(equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~(extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w)) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))) | (~(extension(w1, v1, v1, u1) = extension(w1, v1, u, v))) | (~(w = v)) | (~(w = extension(u, v, v, w))) | (~(v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~(w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1)))), inference(lemma,lemma(discharge,[]))).
% 49.38/30.82 tff(506,plain,
% 49.38/30.82 (equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~(extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w)) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))) | (~(extension(w1, v1, v1, u1) = extension(w1, v1, u, v))) | (~(w = v)) | (~(w = extension(u, v, v, w))) | (~(w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.38/30.82 inference(unit_resolution,[status(thm)],[505, 9])).
% 49.38/30.82 tff(507,plain,
% 49.38/30.82 (equidistant(extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~(extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w)) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))) | (~(extension(w1, v1, v1, u1) = extension(w1, v1, u, v))) | (~(w = v)) | (~(w = extension(u, v, v, w)))),
% 49.38/30.82 inference(unit_resolution,[status(thm)],[506, 292])).
% 49.38/30.82 tff(508,plain,
% 49.38/30.82 (~(extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), u, extension(u, v, v, w)) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.38/30.82 inference(unit_resolution,[status(thm)],[507, 477, 84, 307, 338])).
% 49.38/30.82 tff(509,plain,
% 49.38/30.82 (~(extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w, v, v, u), v, v, v), u) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.38/30.82 inference(modus_ponens,[status(thm)],[508, 353])).
% 49.38/30.82 tff(510,plain,
% 49.38/30.82 ((extension(extension(w1, v1, v1, u1), v1, v1, w1) = extension(extension(w1, v1, v1, u1), v1, v1, v1)) <=> (w1 = v1)),
% 49.38/30.82 inference(monotonicity,[status(thm)],[293, 10])).
% 49.38/30.82 tff(511,plain,
% 49.38/30.82 ((w1 = v1) <=> (extension(extension(w1, v1, v1, u1), v1, v1, w1) = extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.38/30.82 inference(symmetry,[status(thm)],[510])).
% 49.38/30.82 tff(512,plain,
% 49.38/30.82 ((~(w1 = v1)) <=> (~(extension(extension(w1, v1, v1, u1), v1, v1, w1) = extension(extension(w1, v1, v1, u1), v1, v1, v1)))),
% 49.38/30.82 inference(monotonicity,[status(thm)],[511])).
% 49.38/30.82 tff(513,plain,
% 49.38/30.82 (~(extension(extension(w1, v1, v1, u1), v1, v1, w1) = extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.38/30.82 inference(modus_ponens,[status(thm)],[312, 512])).
% 49.38/30.82 tff(514,plain,
% 49.38/30.82 (equidistant(extension(extension(w, v, v, u), v, v, v), u, extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> equidistant(w, u, u1, w1)),
% 49.38/30.82 inference(monotonicity,[status(thm)],[297, 388, 293])).
% 49.38/30.82 tff(515,plain,
% 49.38/30.82 (equidistant(w, u, u1, w1) <=> equidistant(extension(extension(w, v, v, u), v, v, v), u, extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.38/30.82 inference(symmetry,[status(thm)],[514])).
% 49.38/30.82 tff(516,plain,
% 49.38/30.82 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | ((~equidistant(u, w, u1, w1)) | equidistant(w, u, u1, w1))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | (~equidistant(u, w, u1, w1)) | equidistant(w, u, u1, w1))),
% 49.38/30.82 inference(rewrite,[status(thm)],[])).
% 49.38/30.82 tff(517,plain,
% 49.38/30.82 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | ((~equidistant(u, w, u1, w1)) | equidistant(w, u, u1, w1))),
% 49.38/30.82 inference(quant_inst,[status(thm)],[])).
% 49.38/30.82 tff(518,plain,
% 49.38/30.82 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | (~equidistant(u, w, u1, w1)) | equidistant(w, u, u1, w1)),
% 49.38/30.82 inference(modus_ponens,[status(thm)],[517, 516])).
% 49.38/30.82 tff(519,plain,
% 49.38/30.82 (equidistant(w, u, u1, w1)),
% 49.38/30.82 inference(unit_resolution,[status(thm)],[518, 499, 153])).
% 49.38/30.82 tff(520,plain,
% 49.38/30.82 (equidistant(extension(extension(w, v, v, u), v, v, v), u, extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.38/30.82 inference(modus_ponens,[status(thm)],[519, 515])).
% 49.38/30.82 tff(521,plain,
% 49.38/30.82 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | ((extension(extension(w1, v1, v1, u1), v1, v1, w1) = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(extension(w, v, v, u), v, v, v), u, extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w, v, v, u), v, v, v), u) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | (extension(extension(w1, v1, v1, u1), v1, v1, w1) = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(extension(w, v, v, u), v, v, v), u, extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w, v, v, u), v, v, v), u) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))))),
% 49.38/30.82 inference(rewrite,[status(thm)],[])).
% 49.38/30.82 tff(522,plain,
% 49.38/30.82 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | ((extension(extension(w1, v1, v1, u1), v1, v1, w1) = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(extension(w, v, v, u), v, v, v), u, extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w, v, v, u), v, v, v), u) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))))),
% 49.38/30.83 inference(quant_inst,[status(thm)],[])).
% 49.38/30.83 tff(523,plain,
% 49.38/30.83 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~equidistant(W, X, Y, Z)) | (extension(U, V, W, X) = extension(U, V, Y, Z)))) | (extension(extension(w1, v1, v1, u1), v1, v1, w1) = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(extension(w, v, v, u), v, v, v), u, extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w, v, v, u), v, v, v), u) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.38/30.83 inference(modus_ponens,[status(thm)],[522, 521])).
% 49.38/30.83 tff(524,plain,
% 49.38/30.83 ((extension(extension(w1, v1, v1, u1), v1, v1, w1) = extension(extension(w1, v1, v1, u1), v1, v1, v1)) | (~equidistant(extension(extension(w, v, v, u), v, v, v), u, extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w, v, v, u), v, v, v), u) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(w1, v1, v1, u1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[523, 333])).
% 49.38/30.83 tff(525,plain,
% 49.38/30.83 ($false),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[524, 520, 513, 509])).
% 49.38/30.83 tff(526,plain,((w1 = v1) | (~(w = extension(u, v, v, w))) | (~(w = v))), inference(lemma,lemma(discharge,[]))).
% 49.38/30.83 tff(527,plain,
% 49.38/30.83 (~(w = extension(u, v, v, w))),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[526, 306, 84])).
% 49.38/30.83 tff(528,plain,
% 49.38/30.83 (extension(w1, v1, v1, u1) = extension(w1, v1, v, u)),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[346, 306])).
% 49.38/30.83 tff(529,plain,
% 49.38/30.83 ((extension(w1, v1, v1, u1) = v1) <=> (v1 = extension(w1, v1, v1, u1))),
% 49.38/30.83 inference(commutativity,[status(thm)],[])).
% 49.38/30.83 tff(530,plain,
% 49.38/30.83 ((~(extension(w1, v1, v1, u1) = v1)) <=> (~(v1 = extension(w1, v1, v1, u1)))),
% 49.38/30.83 inference(monotonicity,[status(thm)],[529])).
% 49.38/30.83 tff(531,plain,
% 49.38/30.83 (~(v1 = extension(w1, v1, v1, u1))),
% 49.38/30.83 inference(modus_ponens,[status(thm)],[287, 530])).
% 49.38/30.83 tff(532,assumption,(extension(w1, v1, v1, u1) = extension(w1, v1, v, u)), introduced(assumption)).
% 49.38/30.83 tff(533,plain,
% 49.38/30.83 (extension(w1, v1, v, u) = extension(w1, v1, v1, u1)),
% 49.38/30.83 inference(symmetry,[status(thm)],[532])).
% 49.38/30.83 tff(534,plain,
% 49.38/30.83 (extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), v, v) = extension(w1, v1, v, u)),
% 49.38/30.83 inference(monotonicity,[status(thm)],[483, 481, 182])).
% 49.38/30.83 tff(535,plain,
% 49.38/30.83 ((~![W: $i, V: $i, U: $i] : (V = extension(U, V, W, W))) | (extension(extension(w1, v1, v1, u1), v1, v1, v1) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), v, v))),
% 49.38/30.83 inference(quant_inst,[status(thm)],[])).
% 49.38/30.83 tff(536,plain,
% 49.38/30.83 (extension(extension(w1, v1, v1, u1), v1, v1, v1) = extension(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, v1), v, v)),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[535, 7])).
% 49.38/30.83 tff(537,plain,
% 49.38/30.83 (v1 = extension(w1, v1, v1, u1)),
% 49.38/30.83 inference(transitivity,[status(thm)],[480, 536, 534, 533])).
% 49.38/30.83 tff(538,assumption,(~(v1 = extension(w1, v1, v1, u1))), introduced(assumption)).
% 49.38/30.83 tff(539,plain,
% 49.38/30.83 ($false),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[538, 537])).
% 49.38/30.83 tff(540,plain,((~(u = v)) | (v1 = extension(w1, v1, v1, u1)) | (~(v1 = extension(extension(w1, v1, v1, u1), v1, v1, v1))) | (~(extension(w1, v1, v1, u1) = extension(w1, v1, v, u))) | (~(w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1)))), inference(lemma,lemma(discharge,[]))).
% 49.38/30.83 tff(541,plain,
% 49.38/30.83 ((~(u = v)) | (v1 = extension(w1, v1, v1, u1)) | (~(extension(w1, v1, v1, u1) = extension(w1, v1, v, u))) | (~(w1 = extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[540, 9])).
% 49.38/30.83 tff(542,plain,
% 49.38/30.83 ((~(u = v)) | (~(extension(w1, v1, v1, u1) = extension(w1, v1, v, u)))),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[541, 531, 292])).
% 49.38/30.83 tff(543,plain,
% 49.38/30.83 (~(u = v)),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[542, 528])).
% 49.38/30.83 tff(544,plain,
% 49.38/30.83 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))),
% 49.38/30.83 inference(rewrite,[status(thm)],[])).
% 49.38/30.83 tff(545,plain,
% 49.38/30.83 (((u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w))) <=> ((~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))),
% 49.38/30.83 inference(rewrite,[status(thm)],[])).
% 49.38/30.83 tff(546,plain,
% 49.38/30.83 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w))))),
% 49.38/30.83 inference(monotonicity,[status(thm)],[545])).
% 49.38/30.83 tff(547,plain,
% 49.38/30.83 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))),
% 49.38/30.83 inference(transitivity,[status(thm)],[546, 544])).
% 49.38/30.83 tff(548,plain,
% 49.38/30.83 ((~![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)))),
% 49.38/30.83 inference(quant_inst,[status(thm)],[])).
% 49.38/30.83 tff(549,plain,
% 49.38/30.83 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w))),
% 49.38/30.83 inference(modus_ponens,[status(thm)],[548, 547])).
% 49.38/30.83 tff(550,plain,
% 49.38/30.83 ((u = v) | (w = extension(u, v, v, w))),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[549, 53, 192])).
% 49.38/30.83 tff(551,plain,
% 49.38/30.83 ($false),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[550, 543, 527])).
% 49.38/30.83 tff(552,plain,(~(w = v)), inference(lemma,lemma(discharge,[]))).
% 49.38/30.83 tff(553,plain,
% 49.38/30.83 (u = extension(w, v, v, u)),
% 49.38/30.83 inference(unit_resolution,[status(thm)],[206, 552])).
% 49.38/30.83 tff(554,plain,
% 49.38/30.83 (extension(w, v, v, u) = u),
% 49.38/30.83 inference(symmetry,[status(thm)],[553])).
% 49.38/30.83 tff(555,plain,
% 49.38/30.83 (equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1)) <=> equidistant(u, v, u1, v1)),
% 49.38/30.83 inference(monotonicity,[status(thm)],[554, 83, 80, 10])).
% 49.38/30.83 tff(556,plain,
% 49.38/30.83 (equidistant(u, v, u1, v1) <=> equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.38/30.83 inference(symmetry,[status(thm)],[555])).
% 49.38/30.84 tff(557,plain,
% 49.38/30.84 (equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1))),
% 49.38/30.84 inference(modus_ponens,[status(thm)],[136, 556])).
% 49.38/30.84 tff(558,plain,
% 49.38/30.84 (between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> between(u1, v1, w1)),
% 49.38/30.84 inference(monotonicity,[status(thm)],[80, 10, 293])).
% 49.38/30.84 tff(559,plain,
% 49.38/30.84 (between(u1, v1, w1) <=> between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.38/30.84 inference(symmetry,[status(thm)],[558])).
% 49.38/30.84 tff(560,plain,
% 49.38/30.84 (between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.38/30.84 inference(modus_ponens,[status(thm)],[356, 559])).
% 49.38/30.84 tff(561,plain,
% 49.38/30.84 (~(extension(w1, v1, v1, u1) = extension(w1, v1, v, u))),
% 49.38/30.84 inference(unit_resolution,[status(thm)],[542, 181])).
% 49.38/30.84 tff(562,plain,
% 49.38/30.84 (w1 = v1),
% 49.38/30.84 inference(unit_resolution,[status(thm)],[346, 561])).
% 49.38/30.84 tff(563,plain,
% 49.38/30.84 (extension(extension(w1, v1, v1, u1), v1, v1, w1) = v1),
% 49.38/30.84 inference(transitivity,[status(thm)],[293, 562])).
% 49.38/30.84 tff(564,plain,
% 49.38/30.84 (between(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), u1) <=> between(w1, v1, u1)),
% 49.38/30.84 inference(monotonicity,[status(thm)],[293, 563])).
% 49.38/30.84 tff(565,plain,
% 49.38/30.84 (between(w1, v1, u1) <=> between(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), u1)),
% 49.38/30.84 inference(symmetry,[status(thm)],[564])).
% 49.38/30.84 tff(566,plain,
% 49.38/30.84 (between(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), u1)),
% 49.38/30.84 inference(modus_ponens,[status(thm)],[360, 565])).
% 49.38/30.84 tff(567,plain,
% 49.38/30.84 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, w1), u1, extension(w, v, v, u), extension(w, v, v, u)) <=> equidistant(v1, u1, v, u)),
% 49.38/30.84 inference(monotonicity,[status(thm)],[563, 187, 186])).
% 49.38/30.84 tff(568,plain,
% 49.38/30.84 (equidistant(v1, u1, v, u) <=> equidistant(extension(extension(w1, v1, v1, u1), v1, v1, w1), u1, extension(w, v, v, u), extension(w, v, v, u))),
% 49.38/30.84 inference(symmetry,[status(thm)],[567])).
% 49.38/30.84 tff(569,plain,
% 49.38/30.84 (equidistant(extension(extension(w1, v1, v1, u1), v1, v1, w1), u1, extension(w, v, v, u), extension(w, v, v, u))),
% 49.38/30.84 inference(modus_ponens,[status(thm)],[342, 568])).
% 49.38/30.84 tff(570,plain,
% 49.38/30.84 (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, w1), u1, extension(w, v, v, u), extension(w, v, v, u))) | (extension(extension(w1, v1, v1, u1), v1, v1, w1) = u1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, w1), u1, extension(w, v, v, u), extension(w, v, v, u))) | (extension(extension(w1, v1, v1, u1), v1, v1, w1) = u1))),
% 49.38/30.84 inference(rewrite,[status(thm)],[])).
% 49.38/30.84 tff(571,plain,
% 49.38/30.84 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, w1), u1, extension(w, v, v, u), extension(w, v, v, u))) | (extension(extension(w1, v1, v1, u1), v1, v1, w1) = u1))),
% 49.38/30.84 inference(quant_inst,[status(thm)],[])).
% 49.38/30.84 tff(572,plain,
% 49.38/30.84 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, w1), u1, extension(w, v, v, u), extension(w, v, v, u))) | (extension(extension(w1, v1, v1, u1), v1, v1, w1) = u1)),
% 49.38/30.84 inference(modus_ponens,[status(thm)],[571, 570])).
% 49.38/30.84 tff(573,plain,
% 49.38/30.84 ((~equidistant(extension(extension(w1, v1, v1, u1), v1, v1, w1), u1, extension(w, v, v, u), extension(w, v, v, u))) | (extension(extension(w1, v1, v1, u1), v1, v1, w1) = u1)),
% 49.38/30.84 inference(unit_resolution,[status(thm)],[572, 117])).
% 49.38/30.84 tff(574,plain,
% 49.38/30.84 (extension(extension(w1, v1, v1, u1), v1, v1, w1) = u1),
% 49.38/30.84 inference(unit_resolution,[status(thm)],[573, 569])).
% 49.38/30.84 tff(575,plain,
% 49.38/30.84 (between(u1, extension(extension(w1, v1, v1, u1), v1, v1, w1), u1) <=> between(u1, w1, u1)),
% 49.38/30.84 inference(monotonicity,[status(thm)],[293])).
% 49.38/30.84 tff(576,plain,
% 49.38/30.84 (between(u1, w1, u1) <=> between(u1, extension(extension(w1, v1, v1, u1), v1, v1, w1), u1)),
% 49.38/30.84 inference(symmetry,[status(thm)],[575])).
% 49.38/30.84 tff(577,plain,
% 49.38/30.84 (v1 = w1),
% 49.38/30.84 inference(symmetry,[status(thm)],[562])).
% 49.38/30.84 tff(578,plain,
% 49.38/30.84 (between(u1, v1, u1) <=> between(u1, w1, u1)),
% 49.38/30.84 inference(monotonicity,[status(thm)],[577])).
% 49.38/30.84 tff(579,plain,
% 49.38/30.84 (between(u1, v1, u1) <=> between(u1, extension(extension(w1, v1, v1, u1), v1, v1, w1), u1)),
% 49.38/30.84 inference(transitivity,[status(thm)],[578, 576])).
% 49.38/30.84 tff(580,plain,
% 49.38/30.84 ((~between(u1, v1, u1)) <=> (~between(u1, extension(extension(w1, v1, v1, u1), v1, v1, w1), u1))),
% 49.38/30.84 inference(monotonicity,[status(thm)],[579])).
% 49.38/30.84 tff(581,plain,
% 49.38/30.84 (between(extension(w, v, v, u), v, v) <=> between(u, v, u)),
% 49.38/30.84 inference(monotonicity,[status(thm)],[186, 182])).
% 49.38/30.84 tff(582,assumption,(~between(extension(w, v, v, u), v, v)), introduced(assumption)).
% 49.38/30.84 tff(583,plain,
% 49.38/30.84 ((~![V: $i, U: $i] : between(U, V, V)) | between(extension(w, v, v, u), v, v)),
% 49.38/30.84 inference(quant_inst,[status(thm)],[])).
% 49.38/30.84 tff(584,plain,
% 49.38/30.84 ($false),
% 49.38/30.84 inference(unit_resolution,[status(thm)],[583, 222, 582])).
% 49.38/30.84 tff(585,plain,(between(extension(w, v, v, u), v, v)), inference(lemma,lemma(discharge,[]))).
% 49.38/30.84 tff(586,plain,
% 49.38/30.84 (between(u, v, u)),
% 49.38/30.84 inference(modus_ponens,[status(thm)],[585, 581])).
% 49.38/30.84 tff(587,plain,
% 49.38/30.84 (~between(u1, v1, u1)),
% 49.38/30.84 inference(unit_resolution,[status(thm)],[266, 586])).
% 49.38/30.84 tff(588,plain,
% 49.38/30.84 (~between(u1, extension(extension(w1, v1, v1, u1), v1, v1, w1), u1)),
% 49.38/30.84 inference(modus_ponens,[status(thm)],[587, 580])).
% 49.38/30.84 tff(589,plain,
% 49.38/30.84 (((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u1, extension(extension(w1, v1, v1, u1), v1, v1, w1), u1) | (~(extension(extension(w1, v1, v1, u1), v1, v1, w1) = u1)) | (~between(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), u1)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | between(u1, extension(extension(w1, v1, v1, u1), v1, v1, w1), u1) | (~(extension(extension(w1, v1, v1, u1), v1, v1, w1) = u1)) | (~between(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), u1)))),
% 49.38/30.84 inference(rewrite,[status(thm)],[])).
% 49.38/30.84 tff(590,plain,
% 49.38/30.84 ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u1, extension(extension(w1, v1, v1, u1), v1, v1, w1), u1) | (~(extension(extension(w1, v1, v1, u1), v1, v1, w1) = u1)) | (~between(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), u1)))),
% 49.38/30.84 inference(quant_inst,[status(thm)],[])).
% 49.38/30.84 tff(591,plain,
% 49.38/30.84 ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | between(u1, extension(extension(w1, v1, v1, u1), v1, v1, w1), u1) | (~(extension(extension(w1, v1, v1, u1), v1, v1, w1) = u1)) | (~between(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), u1))),
% 49.38/30.85 inference(modus_ponens,[status(thm)],[590, 589])).
% 49.38/30.85 tff(592,plain,
% 49.38/30.85 ((~(extension(extension(w1, v1, v1, u1), v1, v1, w1) = u1)) | (~between(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), u1))),
% 49.38/30.85 inference(unit_resolution,[status(thm)],[591, 277, 588])).
% 49.38/30.85 tff(593,plain,
% 49.38/30.85 (~between(extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1), u1)),
% 49.38/30.85 inference(unit_resolution,[status(thm)],[592, 574])).
% 49.38/30.85 tff(594,plain,
% 49.38/30.85 ($false),
% 49.38/30.85 inference(unit_resolution,[status(thm)],[593, 566])).
% 49.38/30.85 tff(595,plain,((~(u = v)) | (~(u = extension(w, v, v, u)))), inference(lemma,lemma(discharge,[]))).
% 49.38/30.85 tff(596,plain,
% 49.38/30.85 (~(u = v)),
% 49.38/30.85 inference(unit_resolution,[status(thm)],[595, 553])).
% 49.38/30.85 tff(597,plain,
% 49.38/30.85 (w = extension(u, v, v, w)),
% 49.38/30.85 inference(unit_resolution,[status(thm)],[550, 596])).
% 49.38/30.85 tff(598,plain,
% 49.38/30.85 (extension(u, v, v, w) = w),
% 49.38/30.85 inference(symmetry,[status(thm)],[597])).
% 49.38/30.85 tff(599,plain,
% 49.38/30.85 (equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> equidistant(u, w, u1, w1)),
% 49.38/30.85 inference(monotonicity,[status(thm)],[554, 598, 80, 293])).
% 49.38/30.85 tff(600,plain,
% 49.38/30.85 (equidistant(u, w, u1, w1) <=> equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.38/30.85 inference(symmetry,[status(thm)],[599])).
% 49.38/30.85 tff(601,plain,
% 49.38/30.85 (equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.38/30.85 inference(modus_ponens,[status(thm)],[153, 600])).
% 49.38/30.85 tff(602,assumption,(~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))), introduced(assumption)).
% 49.38/30.85 tff(603,plain,
% 49.38/30.85 ((~![V: $i, U: $i] : equidistant(U, U, V, V)) | equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.38/30.85 inference(quant_inst,[status(thm)],[])).
% 49.38/30.85 tff(604,plain,
% 49.38/30.85 ($false),
% 49.38/30.85 inference(unit_resolution,[status(thm)],[603, 234, 602])).
% 49.38/30.85 tff(605,plain,(equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))), inference(lemma,lemma(discharge,[]))).
% 49.38/30.85 tff(606,plain,
% 49.38/30.85 (equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) <=> equidistant(v, w, v1, w1)),
% 49.38/30.85 inference(monotonicity,[status(thm)],[83, 598, 10, 293])).
% 49.38/30.85 tff(607,plain,
% 49.38/30.85 (equidistant(v, w, v1, w1) <=> equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.38/30.85 inference(symmetry,[status(thm)],[606])).
% 49.38/30.85 tff(608,plain,
% 49.38/30.85 ((~equidistant(v, w, v1, w1)) <=> (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)))),
% 49.38/30.85 inference(monotonicity,[status(thm)],[607])).
% 49.38/30.85 tff(609,plain,
% 49.38/30.85 (~equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))),
% 49.38/30.85 inference(modus_ponens,[status(thm)],[150, 608])).
% 49.38/30.85 tff(610,plain,
% 49.38/30.85 (between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w)) <=> between(extension(w, v, v, u), v, w)),
% 49.38/30.85 inference(monotonicity,[status(thm)],[83, 598])).
% 49.38/30.85 tff(611,plain,
% 49.38/30.85 (between(extension(w, v, v, u), v, w) <=> between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))),
% 49.38/30.85 inference(symmetry,[status(thm)],[610])).
% 49.38/30.85 tff(612,plain,
% 49.38/30.85 ((~![W: $i, V: $i, Y: $i, X: $i] : between(X, Y, extension(X, Y, W, V))) | between(w, v, extension(w, v, v, u))),
% 49.38/30.85 inference(quant_inst,[status(thm)],[])).
% 49.38/30.85 tff(613,plain,
% 49.38/30.85 (between(w, v, extension(w, v, v, u))),
% 49.38/30.85 inference(unit_resolution,[status(thm)],[612, 69])).
% 49.38/30.85 tff(614,plain,
% 49.38/30.85 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(w, v, extension(w, v, v, u))) | between(extension(w, v, v, u), v, w))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(w, v, extension(w, v, v, u))) | between(extension(w, v, v, u), v, w))),
% 49.38/30.85 inference(rewrite,[status(thm)],[])).
% 49.38/30.85 tff(615,plain,
% 49.38/30.85 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(w, v, extension(w, v, v, u))) | between(extension(w, v, v, u), v, w))),
% 49.38/30.85 inference(quant_inst,[status(thm)],[])).
% 49.38/30.85 tff(616,plain,
% 49.38/30.85 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(w, v, extension(w, v, v, u))) | between(extension(w, v, v, u), v, w)),
% 49.38/30.85 inference(modus_ponens,[status(thm)],[615, 614])).
% 49.38/30.85 tff(617,plain,
% 49.38/30.85 (between(extension(w, v, v, u), v, w)),
% 49.38/30.85 inference(unit_resolution,[status(thm)],[616, 39, 613])).
% 49.38/30.85 tff(618,plain,
% 49.38/30.85 (between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))),
% 49.38/30.85 inference(modus_ponens,[status(thm)],[617, 611])).
% 49.38/30.85 tff(619,plain,
% 49.38/30.85 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | ((~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1))))),
% 49.38/30.86 inference(rewrite,[status(thm)],[])).
% 49.38/30.86 tff(620,plain,
% 49.38/30.86 ((equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1)))) <=> ((~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1))))),
% 49.38/30.87 inference(rewrite,[status(thm)],[])).
% 49.38/30.87 tff(621,plain,
% 49.38/30.87 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | ((~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1)))))),
% 49.38/30.88 inference(monotonicity,[status(thm)],[620])).
% 49.38/30.88 tff(622,plain,
% 49.38/30.88 (((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1))))) <=> ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1))))),
% 49.38/30.88 inference(transitivity,[status(thm)],[621, 619])).
% 49.38/30.88 tff(623,plain,
% 49.38/30.88 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1))))),
% 49.46/30.89 inference(quant_inst,[status(thm)],[])).
% 49.46/30.89 tff(624,plain,
% 49.46/30.89 ((~![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (equidistant(V, X, V1, X1) | (~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, W, U1, W1)) | (~equidistant(U, V, U1, V1)))) | (~between(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w))) | equidistant(extension(extension(w, v, v, u), v, v, v), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1)) | (~between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(u, v, v, w), extension(u, v, v, w), extension(extension(w1, v1, v1, u1), v1, v1, w1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1)))),
% 49.46/30.89 inference(modus_ponens,[status(thm)],[623, 622])).
% 49.46/30.89 tff(625,plain,
% 49.46/30.89 ((~between(extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(u, v, v, w), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, w1))) | (~equidistant(extension(w, v, v, u), extension(extension(w, v, v, u), v, v, v), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), extension(extension(u1, extension(w, v, v, u), lower_dimension_point_1, lower_dimension_point_2), extension(w, v, v, u), extension(w, v, v, u), u1)), extension(extension(w1, v1, v1, u1), v1, v1, v1)))),
% 49.46/30.90 inference(unit_resolution,[status(thm)],[624, 258, 618, 609, 605])).
% 49.46/30.90 tff(626,plain,
% 49.46/30.90 ($false),
% 49.46/30.90 inference(unit_resolution,[status(thm)],[625, 601, 560, 557])).
% 49.46/30.90 % SZS output end Proof
%------------------------------------------------------------------------------