%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GEO034-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n027.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 20:34:25 EDT 2022

% Result   : Unsatisfiable 0.96s 0.85s
% Output   : Proof 0.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GEO034-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Aug 31 05:04:17 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.96/0.85  % SZS status Unsatisfiable
% 0.96/0.85  % SZS output start Proof
% 0.96/0.85  tff(equidistant_type, type, (
% 0.96/0.85     equidistant: ( $i * $i * $i * $i ) > $o)).
% 0.96/0.85  tff(extension_type, type, (
% 0.96/0.85     extension: ( $i * $i * $i * $i ) > $i)).
% 0.96/0.85  tff(v_type, type, (
% 0.96/0.85     v: $i)).
% 0.96/0.85  tff(reflection_type, type, (
% 0.96/0.85     reflection: ( $i * $i ) > $i)).
% 0.96/0.85  tff(lower_dimension_point_1_type, type, (
% 0.96/0.85     lower_dimension_point_1: $i)).
% 0.96/0.85  tff(x_type, type, (
% 0.96/0.85     x: $i)).
% 0.96/0.85  tff(between_type, type, (
% 0.96/0.85     between: ( $i * $i * $i ) > $o)).
% 0.96/0.85  tff(w_type, type, (
% 0.96/0.85     w: $i)).
% 0.96/0.85  tff(lower_dimension_point_2_type, type, (
% 0.96/0.85     lower_dimension_point_2: $i)).
% 0.96/0.85  tff(u_type, type, (
% 0.96/0.85     u: $i)).
% 0.96/0.85  tff(1,plain,
% 0.96/0.85      (^[V: $i, U: $i] : refl((U = reflection(reflection(U, V), V)) <=> (U = reflection(reflection(U, V), V)))),
% 0.96/0.85      inference(bind,[status(th)],[])).
% 0.96/0.85  tff(2,plain,
% 0.96/0.85      (![V: $i, U: $i] : (U = reflection(reflection(U, V), V)) <=> ![V: $i, U: $i] : (U = reflection(reflection(U, V), V))),
% 0.96/0.85      inference(quant_intro,[status(thm)],[1])).
% 0.96/0.85  tff(3,plain,
% 0.96/0.85      (![V: $i, U: $i] : (U = reflection(reflection(U, V), V)) <=> ![V: $i, U: $i] : (U = reflection(reflection(U, V), V))),
% 0.96/0.85      inference(rewrite,[status(thm)],[])).
% 0.96/0.85  tff(4,axiom,(![V: $i, U: $i] : (U = reflection(reflection(U, V), V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','r6')).
% 0.96/0.85  tff(5,plain,
% 0.96/0.85      (![V: $i, U: $i] : (U = reflection(reflection(U, V), V))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.96/0.85  tff(6,plain,(
% 0.96/0.85      ![V: $i, U: $i] : (U = reflection(reflection(U, V), V))),
% 0.96/0.85      inference(skolemize,[status(sab)],[5])).
% 0.96/0.85  tff(7,plain,
% 0.96/0.85      (![V: $i, U: $i] : (U = reflection(reflection(U, V), V))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[6, 2])).
% 0.96/0.85  tff(8,plain,
% 0.96/0.85      ((~![V: $i, U: $i] : (U = reflection(reflection(U, V), V))) | (x = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.85      inference(quant_inst,[status(thm)],[])).
% 0.96/0.85  tff(9,plain,
% 0.96/0.85      (x = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)),
% 0.96/0.85      inference(unit_resolution,[status(thm)],[8, 7])).
% 0.96/0.85  tff(10,plain,
% 0.96/0.85      (reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = x),
% 0.96/0.85      inference(symmetry,[status(thm)],[9])).
% 0.96/0.85  tff(11,plain,
% 0.96/0.85      (^[V: $i, U: $i] : refl((reflection(U, V) = extension(U, V, U, V)) <=> (reflection(U, V) = extension(U, V, U, V)))),
% 0.96/0.85      inference(bind,[status(th)],[])).
% 0.96/0.85  tff(12,plain,
% 0.96/0.85      (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V)) <=> ![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 0.96/0.85      inference(quant_intro,[status(thm)],[11])).
% 0.96/0.85  tff(13,plain,
% 0.96/0.85      (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V)) <=> ![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 0.96/0.85      inference(rewrite,[status(thm)],[])).
% 0.96/0.85  tff(14,axiom,(![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-2.ax','reflection')).
% 0.96/0.85  tff(15,plain,
% 0.96/0.85      (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[14, 13])).
% 0.96/0.85  tff(16,plain,(
% 0.96/0.85      ![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 0.96/0.85      inference(skolemize,[status(sab)],[15])).
% 0.96/0.85  tff(17,plain,
% 0.96/0.85      (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[16, 12])).
% 0.96/0.85  tff(18,plain,
% 0.96/0.85      ((~![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))) | (reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(quant_inst,[status(thm)],[])).
% 0.96/0.85  tff(19,plain,
% 0.96/0.85      (reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.85      inference(unit_resolution,[status(thm)],[18, 17])).
% 0.96/0.85  tff(20,plain,
% 0.96/0.85      (extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.85      inference(symmetry,[status(thm)],[19])).
% 0.96/0.85  tff(21,plain,
% 0.96/0.85      (between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))) <=> between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(monotonicity,[status(thm)],[20])).
% 0.96/0.85  tff(22,plain,
% 0.96/0.85      (between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))) <=> between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(symmetry,[status(thm)],[21])).
% 0.96/0.85  tff(23,plain,
% 0.96/0.85      (^[V: $i, U: $i] : refl(between(U, V, reflection(U, V)) <=> between(U, V, reflection(U, V)))),
% 0.96/0.85      inference(bind,[status(th)],[])).
% 0.96/0.85  tff(24,plain,
% 0.96/0.85      (![V: $i, U: $i] : between(U, V, reflection(U, V)) <=> ![V: $i, U: $i] : between(U, V, reflection(U, V))),
% 0.96/0.85      inference(quant_intro,[status(thm)],[23])).
% 0.96/0.85  tff(25,plain,
% 0.96/0.85      (![V: $i, U: $i] : between(U, V, reflection(U, V)) <=> ![V: $i, U: $i] : between(U, V, reflection(U, V))),
% 0.96/0.85      inference(rewrite,[status(thm)],[])).
% 0.96/0.85  tff(26,axiom,(![V: $i, U: $i] : between(U, V, reflection(U, V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','r2_1')).
% 0.96/0.85  tff(27,plain,
% 0.96/0.85      (![V: $i, U: $i] : between(U, V, reflection(U, V))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[26, 25])).
% 0.96/0.85  tff(28,plain,(
% 0.96/0.85      ![V: $i, U: $i] : between(U, V, reflection(U, V))),
% 0.96/0.85      inference(skolemize,[status(sab)],[27])).
% 0.96/0.85  tff(29,plain,
% 0.96/0.85      (![V: $i, U: $i] : between(U, V, reflection(U, V))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[28, 24])).
% 0.96/0.85  tff(30,plain,
% 0.96/0.85      ((~![V: $i, U: $i] : between(U, V, reflection(U, V))) | between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(quant_inst,[status(thm)],[])).
% 0.96/0.85  tff(31,plain,
% 0.96/0.85      (between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(unit_resolution,[status(thm)],[30, 29])).
% 0.96/0.85  tff(32,plain,
% 0.96/0.85      (between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[31, 22])).
% 0.96/0.85  tff(33,plain,
% 0.96/0.85      (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | between(W, V, U)) <=> ((~between(U, V, W)) | between(W, V, U)))),
% 0.96/0.85      inference(bind,[status(th)],[])).
% 0.96/0.85  tff(34,plain,
% 0.96/0.85      (![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))),
% 0.96/0.85      inference(quant_intro,[status(thm)],[33])).
% 0.96/0.85  tff(35,plain,
% 0.96/0.85      (![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))),
% 0.96/0.85      inference(rewrite,[status(thm)],[])).
% 0.96/0.85  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')).
% 0.96/0.85  tff(37,plain,
% 0.96/0.85      (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[36, 35])).
% 0.96/0.85  tff(38,plain,(
% 0.96/0.85      ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.96/0.85      inference(skolemize,[status(sab)],[37])).
% 0.96/0.85  tff(39,plain,
% 0.96/0.85      (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[38, 34])).
% 0.96/0.85  tff(40,plain,
% 0.96/0.85      (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) | between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) | between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))),
% 0.96/0.85      inference(rewrite,[status(thm)],[])).
% 0.96/0.85  tff(41,plain,
% 0.96/0.85      ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) | between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))),
% 0.96/0.85      inference(quant_inst,[status(thm)],[])).
% 0.96/0.85  tff(42,plain,
% 0.96/0.85      ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) | between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[41, 40])).
% 0.96/0.85  tff(43,plain,
% 0.96/0.85      ((~between(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) | between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)),
% 0.96/0.85      inference(unit_resolution,[status(thm)],[42, 39])).
% 0.96/0.85  tff(44,plain,
% 0.96/0.85      (between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)),
% 0.96/0.85      inference(unit_resolution,[status(thm)],[43, 32])).
% 0.96/0.85  tff(45,plain,
% 0.96/0.85      ((reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) <=> (reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(commutativity,[status(thm)],[])).
% 0.96/0.85  tff(46,plain,
% 0.96/0.85      ((extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) <=> (reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.85      inference(monotonicity,[status(thm)],[20])).
% 0.96/0.85  tff(47,plain,
% 0.96/0.85      ((extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) <=> (reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(transitivity,[status(thm)],[46, 45])).
% 0.96/0.85  tff(48,plain,
% 0.96/0.85      ((reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))) <=> (extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.85      inference(symmetry,[status(thm)],[47])).
% 0.96/0.85  tff(49,plain,
% 0.96/0.85      ((~(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) <=> (~(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(monotonicity,[status(thm)],[48])).
% 0.96/0.85  tff(50,plain,
% 0.96/0.85      ((v = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) <=> (v = x)),
% 0.96/0.85      inference(monotonicity,[status(thm)],[10])).
% 0.96/0.85  tff(51,plain,
% 0.96/0.85      ((v = x) <=> (v = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.85      inference(symmetry,[status(thm)],[50])).
% 0.96/0.85  tff(52,plain,
% 0.96/0.85      ((~(v = x)) <=> (~(v = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(monotonicity,[status(thm)],[51])).
% 0.96/0.85  tff(53,plain,
% 0.96/0.85      ((~(v = x)) <=> (~(v = x))),
% 0.96/0.85      inference(rewrite,[status(thm)],[])).
% 0.96/0.85  tff(54,axiom,(~(v = x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_v_is_x')).
% 0.96/0.85  tff(55,plain,
% 0.96/0.85      (~(v = x)),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[54, 53])).
% 0.96/0.85  tff(56,plain,
% 0.96/0.85      (~(v = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[55, 52])).
% 0.96/0.85  tff(57,plain,
% 0.96/0.85      (^[V: $i, U: $i] : refl(((~(V = reflection(U, V))) | (U = V)) <=> ((~(V = reflection(U, V))) | (U = V)))),
% 0.96/0.85      inference(bind,[status(th)],[])).
% 0.96/0.85  tff(58,plain,
% 0.96/0.85      (![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V)) <=> ![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))),
% 0.96/0.85      inference(quant_intro,[status(thm)],[57])).
% 0.96/0.85  tff(59,plain,
% 0.96/0.85      (![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V)) <=> ![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))),
% 0.96/0.85      inference(rewrite,[status(thm)],[])).
% 0.96/0.85  tff(60,axiom,(![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','r4')).
% 0.96/0.85  tff(61,plain,
% 0.96/0.85      (![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[60, 59])).
% 0.96/0.85  tff(62,plain,(
% 0.96/0.85      ![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))),
% 0.96/0.85      inference(skolemize,[status(sab)],[61])).
% 0.96/0.85  tff(63,plain,
% 0.96/0.85      (![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[62, 58])).
% 0.96/0.85  tff(64,plain,
% 0.96/0.85      (((~![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))) | ((~(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) | (v = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) <=> ((~![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))) | (~(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) | (v = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(rewrite,[status(thm)],[])).
% 0.96/0.85  tff(65,plain,
% 0.96/0.85      ((~![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))) | ((~(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) | (v = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(quant_inst,[status(thm)],[])).
% 0.96/0.85  tff(66,plain,
% 0.96/0.85      ((~![V: $i, U: $i] : ((~(V = reflection(U, V))) | (U = V))) | (~(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) | (v = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[65, 64])).
% 0.96/0.85  tff(67,plain,
% 0.96/0.85      ((~(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) | (v = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.85      inference(unit_resolution,[status(thm)],[66, 63])).
% 0.96/0.85  tff(68,plain,
% 0.96/0.85      (~(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = reflection(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.85      inference(unit_resolution,[status(thm)],[67, 56])).
% 0.96/0.85  tff(69,plain,
% 0.96/0.85      (~(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[68, 49])).
% 0.96/0.85  tff(70,plain,
% 0.96/0.85      (^[W: $i, V: $i, U: $i] : refl(((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))) <=> ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))))),
% 0.96/0.85      inference(bind,[status(th)],[])).
% 0.96/0.85  tff(71,plain,
% 0.96/0.85      (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.96/0.85      inference(quant_intro,[status(thm)],[70])).
% 0.96/0.85  tff(72,plain,
% 0.96/0.85      (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.96/0.85      inference(rewrite,[status(thm)],[])).
% 0.96/0.85  tff(73,plain,
% 0.96/0.85      (^[W: $i, V: $i, U: $i] : rewrite((((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W))) <=> ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W))))),
% 0.96/0.85      inference(bind,[status(th)],[])).
% 0.96/0.85  tff(74,plain,
% 0.96/0.85      (![W: $i, V: $i, U: $i] : (((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.96/0.85      inference(quant_intro,[status(thm)],[73])).
% 0.96/0.85  tff(75,axiom,(![W: $i, V: $i, U: $i] : (((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_1')).
% 0.96/0.85  tff(76,plain,
% 0.96/0.85      (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[75, 74])).
% 0.96/0.85  tff(77,plain,
% 0.96/0.85      (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[76, 72])).
% 0.96/0.85  tff(78,plain,(
% 0.96/0.85      ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.96/0.85      inference(skolemize,[status(sab)],[77])).
% 0.96/0.85  tff(79,plain,
% 0.96/0.85      (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.96/0.85      inference(modus_ponens,[status(thm)],[78, 71])).
% 0.96/0.85  tff(80,plain,
% 0.96/0.85      (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((v = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) | (extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) | (~between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (v = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) | (extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) | (~between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))),
% 0.96/0.85      inference(rewrite,[status(thm)],[])).
% 0.96/0.85  tff(81,plain,
% 0.96/0.85      (((extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) | (~between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) | (v = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))) <=> ((v = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) | (extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) | (~between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))),
% 0.96/0.85      inference(rewrite,[status(thm)],[])).
% 0.96/0.85  tff(82,plain,
% 0.96/0.85      (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) | (~between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) | (v = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((v = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) | (extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) | (~between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))))),
% 0.96/0.86      inference(monotonicity,[status(thm)],[81])).
% 0.96/0.86  tff(83,plain,
% 0.96/0.86      (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) | (~between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) | (v = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (v = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) | (extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) | (~between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))),
% 0.96/0.86      inference(transitivity,[status(thm)],[82, 80])).
% 0.96/0.86  tff(84,plain,
% 0.96/0.86      ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) | (~between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) | (v = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))),
% 0.96/0.86      inference(quant_inst,[status(thm)],[])).
% 0.96/0.86  tff(85,plain,
% 0.96/0.86      ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (v = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) | (extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) | (~between(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[84, 83])).
% 0.96/0.86  tff(86,plain,
% 0.96/0.86      (v = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)),
% 0.96/0.86      inference(unit_resolution,[status(thm)],[85, 79, 69, 44])).
% 0.96/0.86  tff(87,plain,
% 0.96/0.86      (extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v) = v),
% 0.96/0.86      inference(symmetry,[status(thm)],[86])).
% 0.96/0.86  tff(88,plain,
% 0.96/0.86      (equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) <=> equidistant(v, v, v, x)),
% 0.96/0.86      inference(monotonicity,[status(thm)],[87, 87, 87, 10])).
% 0.96/0.86  tff(89,plain,
% 0.96/0.86      (equidistant(v, v, v, x) <=> equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.86      inference(symmetry,[status(thm)],[88])).
% 0.96/0.86  tff(90,plain,
% 0.96/0.86      ((lower_dimension_point_2 = lower_dimension_point_1) <=> (lower_dimension_point_1 = lower_dimension_point_2)),
% 0.96/0.86      inference(commutativity,[status(thm)],[])).
% 0.96/0.86  tff(91,plain,
% 0.96/0.86      ((lower_dimension_point_1 = lower_dimension_point_2) <=> (lower_dimension_point_2 = lower_dimension_point_1)),
% 0.96/0.86      inference(symmetry,[status(thm)],[90])).
% 0.96/0.86  tff(92,plain,
% 0.96/0.86      ((~(lower_dimension_point_1 = lower_dimension_point_2)) <=> (~(lower_dimension_point_2 = lower_dimension_point_1))),
% 0.96/0.86      inference(monotonicity,[status(thm)],[91])).
% 0.96/0.86  tff(93,plain,
% 0.96/0.86      ((~(lower_dimension_point_1 = lower_dimension_point_2)) <=> (~(lower_dimension_point_1 = lower_dimension_point_2))),
% 0.96/0.86      inference(rewrite,[status(thm)],[])).
% 0.96/0.86  tff(94,axiom,(~(lower_dimension_point_1 = lower_dimension_point_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','e2_1')).
% 0.96/0.86  tff(95,plain,
% 0.96/0.86      (~(lower_dimension_point_1 = lower_dimension_point_2)),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[94, 93])).
% 0.96/0.86  tff(96,plain,
% 0.96/0.86      (~(lower_dimension_point_2 = lower_dimension_point_1)),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[95, 92])).
% 0.96/0.86  tff(97,plain,
% 0.96/0.86      (^[V: $i, U: $i] : refl(between(U, V, V) <=> between(U, V, V))),
% 0.96/0.86      inference(bind,[status(th)],[])).
% 0.96/0.86  tff(98,plain,
% 0.96/0.86      (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 0.96/0.86      inference(quant_intro,[status(thm)],[97])).
% 0.96/0.86  tff(99,plain,
% 0.96/0.86      (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 0.96/0.86      inference(rewrite,[status(thm)],[])).
% 0.96/0.86  tff(100,axiom,(![V: $i, U: $i] : between(U, V, V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3')).
% 0.96/0.86  tff(101,plain,
% 0.96/0.86      (![V: $i, U: $i] : between(U, V, V)),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[100, 99])).
% 0.96/0.86  tff(102,plain,(
% 0.96/0.86      ![V: $i, U: $i] : between(U, V, V)),
% 0.96/0.86      inference(skolemize,[status(sab)],[101])).
% 0.96/0.86  tff(103,plain,
% 0.96/0.86      (![V: $i, U: $i] : between(U, V, V)),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[102, 98])).
% 0.96/0.86  tff(104,plain,
% 0.96/0.86      ((~![V: $i, U: $i] : between(U, V, V)) | between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1)),
% 0.96/0.86      inference(quant_inst,[status(thm)],[])).
% 0.96/0.86  tff(105,plain,
% 0.96/0.86      (between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1)),
% 0.96/0.86      inference(unit_resolution,[status(thm)],[104, 103])).
% 0.96/0.86  tff(106,plain,
% 0.96/0.86      (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((lower_dimension_point_2 = lower_dimension_point_1) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1)) | (lower_dimension_point_1 = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (lower_dimension_point_2 = lower_dimension_point_1) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1)) | (lower_dimension_point_1 = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)))),
% 0.96/0.86      inference(rewrite,[status(thm)],[])).
% 0.96/0.86  tff(107,plain,
% 0.96/0.86      ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((lower_dimension_point_2 = lower_dimension_point_1) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1)) | (lower_dimension_point_1 = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)))),
% 0.96/0.86      inference(quant_inst,[status(thm)],[])).
% 0.96/0.86  tff(108,plain,
% 0.96/0.86      ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (lower_dimension_point_2 = lower_dimension_point_1) | (~between(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1)) | (lower_dimension_point_1 = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1))),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[107, 106])).
% 0.96/0.86  tff(109,plain,
% 0.96/0.86      ((lower_dimension_point_2 = lower_dimension_point_1) | (lower_dimension_point_1 = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1))),
% 0.96/0.86      inference(unit_resolution,[status(thm)],[108, 79, 105])).
% 0.96/0.86  tff(110,plain,
% 0.96/0.86      (lower_dimension_point_1 = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)),
% 0.96/0.86      inference(unit_resolution,[status(thm)],[109, 96])).
% 0.96/0.86  tff(111,plain,
% 0.96/0.86      (extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1) = lower_dimension_point_1),
% 0.96/0.86      inference(symmetry,[status(thm)],[110])).
% 0.96/0.86  tff(112,plain,
% 0.96/0.86      (between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w) <=> between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, w)),
% 0.96/0.86      inference(monotonicity,[status(thm)],[111])).
% 0.96/0.86  tff(113,plain,
% 0.96/0.86      (between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, w) <=> between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)),
% 0.96/0.86      inference(symmetry,[status(thm)],[112])).
% 0.96/0.86  tff(114,plain,
% 0.96/0.86      (^[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)))),
% 0.96/0.86      inference(bind,[status(th)],[])).
% 0.96/0.86  tff(115,plain,
% 0.96/0.86      (![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))),
% 0.96/0.86      inference(quant_intro,[status(thm)],[114])).
% 0.96/0.86  tff(116,plain,
% 0.96/0.86      (![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))),
% 0.96/0.86      inference(rewrite,[status(thm)],[])).
% 0.96/0.86  tff(117,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')).
% 0.96/0.86  tff(118,plain,
% 0.96/0.86      (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[117, 116])).
% 0.96/0.86  tff(119,plain,(
% 0.96/0.86      ![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 0.96/0.86      inference(skolemize,[status(sab)],[118])).
% 0.96/0.86  tff(120,plain,
% 0.96/0.86      (![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[119, 115])).
% 0.96/0.86  tff(121,plain,
% 0.96/0.86      ((~![V: $i, U: $i] : between(U, V, extension(U, V, lower_dimension_point_1, lower_dimension_point_2))) | between(w, lower_dimension_point_1, extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2))),
% 0.96/0.86      inference(quant_inst,[status(thm)],[])).
% 0.96/0.86  tff(122,plain,
% 0.96/0.86      (between(w, lower_dimension_point_1, extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2))),
% 0.96/0.86      inference(unit_resolution,[status(thm)],[121, 120])).
% 0.96/0.86  tff(123,plain,
% 0.96/0.86      (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(w, lower_dimension_point_1, extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, w))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(w, lower_dimension_point_1, extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, w))),
% 0.96/0.86      inference(rewrite,[status(thm)],[])).
% 0.96/0.86  tff(124,plain,
% 0.96/0.86      ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(w, lower_dimension_point_1, extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, w))),
% 0.96/0.86      inference(quant_inst,[status(thm)],[])).
% 0.96/0.86  tff(125,plain,
% 0.96/0.86      ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(w, lower_dimension_point_1, extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2))) | between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, w)),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[124, 123])).
% 0.96/0.86  tff(126,plain,
% 0.96/0.86      (between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), lower_dimension_point_1, w)),
% 0.96/0.86      inference(unit_resolution,[status(thm)],[125, 39, 122])).
% 0.96/0.86  tff(127,plain,
% 0.96/0.86      (between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[126, 113])).
% 0.96/0.86  tff(128,plain,
% 0.96/0.86      ((extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = lower_dimension_point_1) <=> (lower_dimension_point_1 = extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2))),
% 0.96/0.86      inference(commutativity,[status(thm)],[])).
% 0.96/0.86  tff(129,plain,
% 0.96/0.86      ((extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)) <=> (extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = lower_dimension_point_1)),
% 0.96/0.86      inference(monotonicity,[status(thm)],[111])).
% 0.96/0.86  tff(130,plain,
% 0.96/0.86      ((extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)) <=> (lower_dimension_point_1 = extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2))),
% 0.96/0.86      inference(transitivity,[status(thm)],[129, 128])).
% 0.96/0.86  tff(131,plain,
% 0.96/0.86      ((lower_dimension_point_1 = extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2)) <=> (extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1))),
% 0.96/0.86      inference(symmetry,[status(thm)],[130])).
% 0.96/0.86  tff(132,plain,
% 0.96/0.86      ((~(lower_dimension_point_1 = extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2))) <=> (~(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)))),
% 0.96/0.86      inference(monotonicity,[status(thm)],[131])).
% 0.96/0.86  tff(133,plain,
% 0.96/0.86      (^[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))))),
% 0.96/0.86      inference(bind,[status(th)],[])).
% 0.96/0.86  tff(134,plain,
% 0.96/0.86      (![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)))),
% 0.96/0.86      inference(quant_intro,[status(thm)],[133])).
% 0.96/0.86  tff(135,plain,
% 0.96/0.86      (![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)))),
% 0.96/0.86      inference(rewrite,[status(thm)],[])).
% 0.96/0.86  tff(136,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')).
% 0.96/0.86  tff(137,plain,
% 0.96/0.86      (![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[136, 135])).
% 0.96/0.86  tff(138,plain,(
% 0.96/0.86      ![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.96/0.86      inference(skolemize,[status(sab)],[137])).
% 0.96/0.86  tff(139,plain,
% 0.96/0.86      (![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[138, 134])).
% 0.96/0.86  tff(140,plain,
% 0.96/0.86      ((~![V: $i, U: $i] : (~(V = extension(U, V, lower_dimension_point_1, lower_dimension_point_2)))) | (~(lower_dimension_point_1 = extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2)))),
% 0.96/0.86      inference(quant_inst,[status(thm)],[])).
% 0.96/0.86  tff(141,plain,
% 0.96/0.86      (~(lower_dimension_point_1 = extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2))),
% 0.96/0.86      inference(unit_resolution,[status(thm)],[140, 139])).
% 0.96/0.86  tff(142,plain,
% 0.96/0.86      (~(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1))),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[141, 132])).
% 0.96/0.86  tff(143,plain,
% 0.96/0.86      (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (~between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (~between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)))),
% 0.96/0.86      inference(rewrite,[status(thm)],[])).
% 0.96/0.86  tff(144,plain,
% 0.96/0.86      (((extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)) | (~between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w))) <=> ((w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (~between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)))),
% 0.96/0.86      inference(rewrite,[status(thm)],[])).
% 0.96/0.86  tff(145,plain,
% 0.96/0.86      (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)) | (~between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (~between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1))))),
% 0.96/0.86      inference(monotonicity,[status(thm)],[144])).
% 0.96/0.86  tff(146,plain,
% 0.96/0.86      (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)) | (~between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (~between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)))),
% 0.96/0.86      inference(transitivity,[status(thm)],[145, 143])).
% 0.96/0.86  tff(147,plain,
% 0.96/0.86      ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1)) | (~between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)))),
% 0.96/0.86      inference(quant_inst,[status(thm)],[])).
% 0.96/0.86  tff(148,plain,
% 0.96/0.86      ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (~between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1))),
% 0.96/0.86      inference(modus_ponens,[status(thm)],[147, 146])).
% 0.96/0.86  tff(149,plain,
% 0.96/0.86      ((w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (~between(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) | (extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2) = extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1))),
% 0.96/0.86      inference(unit_resolution,[status(thm)],[148, 79])).
% 0.96/0.86  tff(150,plain,
% 0.96/0.86      (w = extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)),
% 0.96/0.86      inference(unit_resolution,[status(thm)],[149, 142, 127])).
% 0.96/0.86  tff(151,plain,
% 0.96/0.86      (extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w) = w),
% 0.96/0.87      inference(symmetry,[status(thm)],[150])).
% 0.96/0.87  tff(152,plain,
% 0.96/0.87      (equidistant(extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) <=> equidistant(w, v, w, v)),
% 0.96/0.87      inference(monotonicity,[status(thm)],[151, 87, 151, 87])).
% 0.96/0.87  tff(153,plain,
% 0.96/0.87      (equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) <=> equidistant(v, w, v, w)),
% 0.96/0.87      inference(monotonicity,[status(thm)],[87, 151, 87, 151])).
% 0.96/0.87  tff(154,plain,
% 0.96/0.87      (equidistant(v, w, v, w) <=> equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w))),
% 0.96/0.87      inference(symmetry,[status(thm)],[153])).
% 0.96/0.87  tff(155,assumption,(w = v), introduced(assumption)).
% 0.96/0.87  tff(156,plain,
% 0.96/0.87      (v = w),
% 0.96/0.87      inference(symmetry,[status(thm)],[155])).
% 0.96/0.87  tff(157,plain,
% 0.96/0.87      (equidistant(x, v, v, v) <=> equidistant(x, w, v, w)),
% 0.96/0.87      inference(monotonicity,[status(thm)],[156, 156])).
% 0.96/0.87  tff(158,plain,
% 0.96/0.87      (equidistant(x, w, v, w) <=> equidistant(x, v, v, v)),
% 0.96/0.87      inference(symmetry,[status(thm)],[157])).
% 0.96/0.87  tff(159,plain,
% 0.96/0.87      (equidistant(w, v, w, x) <=> equidistant(w, v, w, x)),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(160,axiom,(equidistant(w, v, w, x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','w_to_v_equals_w_to_x')).
% 0.96/0.87  tff(161,plain,
% 0.96/0.87      (equidistant(w, v, w, x)),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[160, 159])).
% 0.96/0.87  tff(162,plain,
% 0.96/0.87      (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)) <=> ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)))),
% 0.96/0.87      inference(bind,[status(th)],[])).
% 0.96/0.87  tff(163,plain,
% 0.96/0.87      (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 0.96/0.87      inference(quant_intro,[status(thm)],[162])).
% 0.96/0.87  tff(164,plain,
% 0.96/0.87      (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(165,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_5')).
% 0.96/0.87  tff(166,plain,
% 0.96/0.87      (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[165, 164])).
% 0.96/0.87  tff(167,plain,(
% 0.96/0.87      ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 0.96/0.87      inference(skolemize,[status(sab)],[166])).
% 0.96/0.87  tff(168,plain,
% 0.96/0.87      (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[167, 163])).
% 0.96/0.87  tff(169,plain,
% 0.96/0.87      (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(w, v, w, x)) | equidistant(x, w, v, w))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(w, v, w, x)) | equidistant(x, w, v, w))),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(170,plain,
% 0.96/0.87      ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(w, v, w, x)) | equidistant(x, w, v, w))),
% 0.96/0.87      inference(quant_inst,[status(thm)],[])).
% 0.96/0.87  tff(171,plain,
% 0.96/0.87      ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(w, v, w, x)) | equidistant(x, w, v, w)),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[170, 169])).
% 0.96/0.87  tff(172,plain,
% 0.96/0.87      (equidistant(x, w, v, w)),
% 0.96/0.87      inference(unit_resolution,[status(thm)],[171, 168, 161])).
% 0.96/0.87  tff(173,plain,
% 0.96/0.87      (equidistant(x, v, v, v)),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[172, 158])).
% 0.96/0.87  tff(174,plain,
% 0.96/0.87      ((x = v) <=> (v = x)),
% 0.96/0.87      inference(commutativity,[status(thm)],[])).
% 0.96/0.87  tff(175,plain,
% 0.96/0.87      ((v = x) <=> (x = v)),
% 0.96/0.87      inference(symmetry,[status(thm)],[174])).
% 0.96/0.87  tff(176,plain,
% 0.96/0.87      ((~(v = x)) <=> (~(x = v))),
% 0.96/0.87      inference(monotonicity,[status(thm)],[175])).
% 0.96/0.87  tff(177,plain,
% 0.96/0.87      (~(x = v)),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[55, 176])).
% 0.96/0.87  tff(178,plain,
% 0.96/0.87      (^[Z: $i, Y: $i, X: $i] : refl(((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ((~equidistant(X, Y, Z, Z)) | (X = Y)))),
% 0.96/0.87      inference(bind,[status(th)],[])).
% 0.96/0.87  tff(179,plain,
% 0.96/0.87      (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.96/0.87      inference(quant_intro,[status(thm)],[178])).
% 0.96/0.87  tff(180,plain,
% 0.96/0.87      (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(181,axiom,(![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax','identity_for_equidistance')).
% 0.96/0.87  tff(182,plain,
% 0.96/0.87      (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[181, 180])).
% 0.96/0.87  tff(183,plain,(
% 0.96/0.87      ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.96/0.87      inference(skolemize,[status(sab)],[182])).
% 0.96/0.87  tff(184,plain,
% 0.96/0.87      (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[183, 179])).
% 0.96/0.87  tff(185,plain,
% 0.96/0.87      (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(x, v, v, v)) | (x = v))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(x, v, v, v)) | (x = v))),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(186,plain,
% 0.96/0.87      ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(x, v, v, v)) | (x = v))),
% 0.96/0.87      inference(quant_inst,[status(thm)],[])).
% 0.96/0.87  tff(187,plain,
% 0.96/0.87      ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(x, v, v, v)) | (x = v)),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[186, 185])).
% 0.96/0.87  tff(188,plain,
% 0.96/0.87      (~equidistant(x, v, v, v)),
% 0.96/0.87      inference(unit_resolution,[status(thm)],[187, 184, 177])).
% 0.96/0.87  tff(189,plain,
% 0.96/0.87      ($false),
% 0.96/0.87      inference(unit_resolution,[status(thm)],[188, 173])).
% 0.96/0.87  tff(190,plain,(~(w = v)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.87  tff(191,plain,
% 0.96/0.87      (between(u, v, w) <=> between(u, v, w)),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(192,axiom,(between(u, v, w)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v_between_u_and_w')).
% 0.96/0.87  tff(193,plain,
% 0.96/0.87      (between(u, v, w)),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[192, 191])).
% 0.96/0.87  tff(194,plain,
% 0.96/0.87      (((~![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))),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(195,plain,
% 0.96/0.87      ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, v, w)) | between(w, v, u))),
% 0.96/0.87      inference(quant_inst,[status(thm)],[])).
% 0.96/0.87  tff(196,plain,
% 0.96/0.87      ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, v, w)) | between(w, v, u)),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[195, 194])).
% 0.96/0.87  tff(197,plain,
% 0.96/0.87      (between(w, v, u)),
% 0.96/0.87      inference(unit_resolution,[status(thm)],[196, 39, 193])).
% 0.96/0.87  tff(198,plain,
% 0.96/0.87      (((~![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)))),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(199,plain,
% 0.96/0.87      ((~![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)))),
% 0.96/0.87      inference(quant_inst,[status(thm)],[])).
% 0.96/0.87  tff(200,plain,
% 0.96/0.87      ((~![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))),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[199, 198])).
% 0.96/0.87  tff(201,plain,
% 0.96/0.87      ((w = v) | (u = extension(w, v, v, u))),
% 0.96/0.87      inference(unit_resolution,[status(thm)],[200, 79, 197])).
% 0.96/0.87  tff(202,plain,
% 0.96/0.87      (u = extension(w, v, v, u)),
% 0.96/0.87      inference(unit_resolution,[status(thm)],[201, 190])).
% 0.96/0.87  tff(203,plain,
% 0.96/0.87      (extension(w, v, v, u) = u),
% 0.96/0.87      inference(symmetry,[status(thm)],[202])).
% 0.96/0.87  tff(204,assumption,(u = v), introduced(assumption)).
% 0.96/0.87  tff(205,plain,
% 0.96/0.87      (extension(w, v, v, u) = v),
% 0.96/0.87      inference(transitivity,[status(thm)],[203, 204])).
% 0.96/0.87  tff(206,plain,
% 0.96/0.87      (equidistant(extension(w, v, v, u), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(w, v, v, u), extension(w, v, v, u)) <=> equidistant(u, x, v, u)),
% 0.96/0.87      inference(monotonicity,[status(thm)],[203, 10, 205, 203])).
% 0.96/0.87  tff(207,plain,
% 0.96/0.87      (equidistant(u, x, v, u) <=> equidistant(extension(w, v, v, u), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(w, v, v, u), extension(w, v, v, u))),
% 0.96/0.87      inference(symmetry,[status(thm)],[206])).
% 0.96/0.87  tff(208,plain,
% 0.96/0.87      (equidistant(u, v, u, x) <=> equidistant(u, v, u, x)),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(209,axiom,(equidistant(u, v, u, x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','u_to_v_equals_u_to_x')).
% 0.96/0.87  tff(210,plain,
% 0.96/0.87      (equidistant(u, v, u, x)),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[209, 208])).
% 0.96/0.87  tff(211,plain,
% 0.96/0.87      (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(W, X, V, U)) <=> ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U)))),
% 0.96/0.87      inference(bind,[status(th)],[])).
% 0.96/0.87  tff(212,plain,
% 0.96/0.87      (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 0.96/0.87      inference(quant_intro,[status(thm)],[211])).
% 0.96/0.87  tff(213,plain,
% 0.96/0.87      (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(214,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')).
% 0.96/0.87  tff(215,plain,
% 0.96/0.87      (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[214, 213])).
% 0.96/0.87  tff(216,plain,(
% 0.96/0.87      ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 0.96/0.87      inference(skolemize,[status(sab)],[215])).
% 0.96/0.87  tff(217,plain,
% 0.96/0.87      (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[216, 212])).
% 0.96/0.87  tff(218,plain,
% 0.96/0.87      (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(u, v, u, x)) | equidistant(u, x, v, u))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(u, v, u, x)) | equidistant(u, x, v, u))),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(219,plain,
% 0.96/0.87      ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | ((~equidistant(u, v, u, x)) | equidistant(u, x, v, u))),
% 0.96/0.87      inference(quant_inst,[status(thm)],[])).
% 0.96/0.87  tff(220,plain,
% 0.96/0.87      ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, V, U))) | (~equidistant(u, v, u, x)) | equidistant(u, x, v, u)),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[219, 218])).
% 0.96/0.87  tff(221,plain,
% 0.96/0.87      (equidistant(u, x, v, u)),
% 0.96/0.87      inference(unit_resolution,[status(thm)],[220, 217, 210])).
% 0.96/0.87  tff(222,plain,
% 0.96/0.87      (equidistant(extension(w, v, v, u), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(w, v, v, u), extension(w, v, v, u))),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[221, 207])).
% 0.96/0.87  tff(223,plain,
% 0.96/0.87      ((extension(w, v, v, u) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)) <=> (reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(w, v, v, u))),
% 0.96/0.87      inference(commutativity,[status(thm)],[])).
% 0.96/0.87  tff(224,plain,
% 0.96/0.87      ((reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(w, v, v, u)) <=> (extension(w, v, v, u) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.87      inference(symmetry,[status(thm)],[223])).
% 0.96/0.87  tff(225,plain,
% 0.96/0.87      ((reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(w, v, v, u)) <=> (x = v)),
% 0.96/0.87      inference(monotonicity,[status(thm)],[10, 205])).
% 0.96/0.87  tff(226,plain,
% 0.96/0.87      ((reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(w, v, v, u)) <=> (v = x)),
% 0.96/0.87      inference(transitivity,[status(thm)],[225, 174])).
% 0.96/0.87  tff(227,plain,
% 0.96/0.87      ((v = x) <=> (reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(w, v, v, u))),
% 0.96/0.87      inference(symmetry,[status(thm)],[226])).
% 0.96/0.87  tff(228,plain,
% 0.96/0.87      ((v = x) <=> (extension(w, v, v, u) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.87      inference(transitivity,[status(thm)],[227, 224])).
% 0.96/0.87  tff(229,plain,
% 0.96/0.87      ((~(v = x)) <=> (~(extension(w, v, v, u) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.87      inference(monotonicity,[status(thm)],[228])).
% 0.96/0.87  tff(230,plain,
% 0.96/0.87      (~(extension(w, v, v, u) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[55, 229])).
% 0.96/0.87  tff(231,plain,
% 0.96/0.87      (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(extension(w, v, v, u), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(w, v, v, u), extension(w, v, v, u))) | (extension(w, v, v, u) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(extension(w, v, v, u), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(w, v, v, u), extension(w, v, v, u))) | (extension(w, v, v, u) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(232,plain,
% 0.96/0.87      ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(extension(w, v, v, u), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(w, v, v, u), extension(w, v, v, u))) | (extension(w, v, v, u) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)))),
% 0.96/0.87      inference(quant_inst,[status(thm)],[])).
% 0.96/0.87  tff(233,plain,
% 0.96/0.87      ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(extension(w, v, v, u), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(w, v, v, u), extension(w, v, v, u))) | (extension(w, v, v, u) = reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[232, 231])).
% 0.96/0.87  tff(234,plain,
% 0.96/0.87      (~equidistant(extension(w, v, v, u), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(w, v, v, u), extension(w, v, v, u))),
% 0.96/0.87      inference(unit_resolution,[status(thm)],[233, 184, 230])).
% 0.96/0.87  tff(235,plain,
% 0.96/0.87      ($false),
% 0.96/0.87      inference(unit_resolution,[status(thm)],[234, 222])).
% 0.96/0.87  tff(236,plain,(~(u = v)), inference(lemma,lemma(discharge,[]))).
% 0.96/0.87  tff(237,plain,
% 0.96/0.87      (((~![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)))),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(238,plain,
% 0.96/0.87      (((u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w))) <=> ((~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))),
% 0.96/0.87      inference(rewrite,[status(thm)],[])).
% 0.96/0.87  tff(239,plain,
% 0.96/0.87      (((~![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))))),
% 0.96/0.87      inference(monotonicity,[status(thm)],[238])).
% 0.96/0.87  tff(240,plain,
% 0.96/0.87      (((~![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)))),
% 0.96/0.87      inference(transitivity,[status(thm)],[239, 237])).
% 0.96/0.87  tff(241,plain,
% 0.96/0.87      ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w)))),
% 0.96/0.87      inference(quant_inst,[status(thm)],[])).
% 0.96/0.87  tff(242,plain,
% 0.96/0.87      ((~![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))),
% 0.96/0.87      inference(modus_ponens,[status(thm)],[241, 240])).
% 0.96/0.87  tff(243,plain,
% 0.96/0.87      ((u = v) | (w = extension(u, v, v, w))),
% 0.96/0.87      inference(unit_resolution,[status(thm)],[242, 79, 193])).
% 0.96/0.87  tff(244,plain,
% 0.96/0.87      (w = extension(u, v, v, w)),
% 0.96/0.87      inference(unit_resolution,[status(thm)],[243, 236])).
% 0.96/0.87  tff(245,plain,
% 0.96/0.87      (extension(u, v, v, w) = w),
% 0.96/0.87      inference(symmetry,[status(thm)],[244])).
% 0.96/0.87  tff(246,plain,
% 0.96/0.87      (extension(extension(w, v, v, u), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) = extension(u, v, v, w)),
% 0.96/0.87      inference(monotonicity,[status(thm)],[203, 87, 87, 151])).
% 0.96/0.87  tff(247,plain,
% 0.96/0.87      (extension(extension(w, v, v, u), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) = w),
% 0.96/0.87      inference(transitivity,[status(thm)],[246, 245])).
% 0.96/0.87  tff(248,plain,
% 0.96/0.87      (equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, v, v, u), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) <=> equidistant(v, w, v, w)),
% 0.96/0.88      inference(monotonicity,[status(thm)],[87, 247, 87, 151])).
% 0.96/0.88  tff(249,plain,
% 0.96/0.88      (equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, v, v, u), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)) <=> equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w))),
% 0.96/0.88      inference(transitivity,[status(thm)],[248, 154])).
% 0.96/0.88  tff(250,plain,
% 0.96/0.88      (^[W: $i, V: $i, Y: $i, X: $i] : refl(equidistant(Y, extension(X, Y, W, V), W, V) <=> equidistant(Y, extension(X, Y, W, V), W, V))),
% 0.96/0.88      inference(bind,[status(th)],[])).
% 0.96/0.88  tff(251,plain,
% 0.96/0.88      (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V) <=> ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.96/0.88      inference(quant_intro,[status(thm)],[250])).
% 0.96/0.88  tff(252,plain,
% 0.96/0.88      (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V) <=> ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.96/0.88      inference(rewrite,[status(thm)],[])).
% 0.96/0.88  tff(253,axiom,(![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax','segment_construction2')).
% 0.96/0.88  tff(254,plain,
% 0.96/0.88      (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.96/0.88      inference(modus_ponens,[status(thm)],[253, 252])).
% 0.96/0.88  tff(255,plain,(
% 0.96/0.88      ![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.96/0.88      inference(skolemize,[status(sab)],[254])).
% 0.96/0.88  tff(256,plain,
% 0.96/0.88      (![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)),
% 0.96/0.88      inference(modus_ponens,[status(thm)],[255, 251])).
% 0.96/0.88  tff(257,plain,
% 0.96/0.88      ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, v, v, u), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w))),
% 0.96/0.88      inference(quant_inst,[status(thm)],[])).
% 0.96/0.88  tff(258,plain,
% 0.96/0.88      (equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, v, v, u), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w)), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w))),
% 0.96/0.88      inference(unit_resolution,[status(thm)],[257, 256])).
% 0.96/0.88  tff(259,plain,
% 0.96/0.88      (equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w))),
% 0.96/0.88      inference(modus_ponens,[status(thm)],[258, 249])).
% 0.96/0.88  tff(260,plain,
% 0.96/0.88      (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w))) | equidistant(extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w))) | equidistant(extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))),
% 0.96/0.88      inference(rewrite,[status(thm)],[])).
% 0.96/0.88  tff(261,plain,
% 0.96/0.88      ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w))) | equidistant(extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))),
% 0.96/0.88      inference(quant_inst,[status(thm)],[])).
% 0.96/0.88  tff(262,plain,
% 0.96/0.88      ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w))) | equidistant(extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))),
% 0.96/0.88      inference(modus_ponens,[status(thm)],[261, 260])).
% 0.96/0.88  tff(263,plain,
% 0.96/0.88      (equidistant(extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(w, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_2), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), extension(lower_dimension_point_2, lower_dimension_point_1, lower_dimension_point_1, lower_dimension_point_1), w), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))),
% 0.96/0.88      inference(unit_resolution,[status(thm)],[262, 168, 259])).
% 0.96/0.88  tff(264,plain,
% 0.96/0.88      (equidistant(w, v, w, v)),
% 0.96/0.88      inference(modus_ponens,[status(thm)],[263, 152])).
% 0.96/0.88  tff(265,plain,
% 0.96/0.88      (between(w, v, extension(w, v, v, u)) <=> between(w, v, u)),
% 0.96/0.88      inference(monotonicity,[status(thm)],[203])).
% 0.96/0.88  tff(266,plain,
% 0.96/0.88      (between(w, v, u) <=> between(w, v, extension(w, v, v, u))),
% 0.96/0.88      inference(symmetry,[status(thm)],[265])).
% 0.96/0.88  tff(267,plain,
% 0.96/0.88      (between(w, v, extension(w, v, v, u))),
% 0.96/0.88      inference(modus_ponens,[status(thm)],[197, 266])).
% 0.96/0.88  tff(268,plain,
% 0.96/0.88      (equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x) <=> equidistant(u, v, u, x)),
% 0.96/0.88      inference(monotonicity,[status(thm)],[203, 203])).
% 0.96/0.88  tff(269,plain,
% 0.96/0.88      (equidistant(u, v, u, x) <=> equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)),
% 0.96/0.88      inference(symmetry,[status(thm)],[268])).
% 0.96/0.88  tff(270,plain,
% 0.96/0.88      (equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)),
% 0.96/0.88      inference(modus_ponens,[status(thm)],[210, 269])).
% 0.96/0.88  tff(271,plain,
% 0.96/0.88      (extension(w, v, v, extension(w, v, v, u)) = extension(w, v, v, u)),
% 0.96/0.88      inference(monotonicity,[status(thm)],[203])).
% 0.96/0.88  tff(272,plain,
% 0.96/0.88      (extension(w, v, v, u) = extension(w, v, v, extension(w, v, v, u))),
% 0.96/0.88      inference(symmetry,[status(thm)],[271])).
% 0.96/0.88  tff(273,plain,
% 0.96/0.88      (equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u)) <=> equidistant(v, extension(w, v, v, extension(w, v, v, u)), v, extension(w, v, v, u))),
% 0.96/0.88      inference(monotonicity,[status(thm)],[272])).
% 0.96/0.88  tff(274,plain,
% 0.96/0.88      (equidistant(v, extension(w, v, v, extension(w, v, v, u)), v, extension(w, v, v, u)) <=> equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u))),
% 0.96/0.88      inference(symmetry,[status(thm)],[273])).
% 0.96/0.88  tff(275,plain,
% 0.96/0.88      ((~![W: $i, V: $i, Y: $i, X: $i] : equidistant(Y, extension(X, Y, W, V), W, V)) | equidistant(v, extension(w, v, v, extension(w, v, v, u)), v, extension(w, v, v, u))),
% 0.96/0.88      inference(quant_inst,[status(thm)],[])).
% 0.96/0.88  tff(276,plain,
% 0.96/0.88      (equidistant(v, extension(w, v, v, extension(w, v, v, u)), v, extension(w, v, v, u))),
% 0.96/0.88      inference(unit_resolution,[status(thm)],[275, 256])).
% 0.96/0.88  tff(277,plain,
% 0.96/0.88      (equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u))),
% 0.96/0.88      inference(modus_ponens,[status(thm)],[276, 274])).
% 0.96/0.88  tff(278,plain,
% 0.96/0.88      (^[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, V, U1, V1)) | (~equidistant(V, W, 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, V, U1, V1)) | (~equidistant(V, W, V1, W1))))),
% 0.96/0.88      inference(bind,[status(th)],[])).
% 0.96/0.88  tff(279,plain,
% 0.96/0.88      (![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, V, U1, V1)) | (~equidistant(V, W, V1, W1))) <=> ![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))),
% 0.96/0.88      inference(quant_intro,[status(thm)],[278])).
% 0.96/0.88  tff(280,plain,
% 0.96/0.88      (![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, V, U1, V1)) | (~equidistant(V, W, V1, W1))) <=> ![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))),
% 0.96/0.88      inference(rewrite,[status(thm)],[])).
% 0.96/0.88  tff(281,plain,
% 0.96/0.88      (^[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(V, W, V1, W1))) | (~equidistant(U, X, U1, X1))) <=> ((~equidistant(U, X, U1, X1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) <=> (((~equidistant(U, X, U1, X1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(W, X, W1, X1))))), rewrite((((~equidistant(U, X, U1, X1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(W, X, W1, X1))) <=> ((~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1)))), (((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~equidistant(U, X, U1, X1))) | (~equidistant(W, X, W1, X1))) <=> ((~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))))), ((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, 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, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))))), rewrite((((~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U, V, W))) <=> ((~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1)))), ((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, 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, V, U1, V1)) | (~equidistant(V, W, V1, W1))))), (((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, 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, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U1, V1, W1))))), rewrite((((~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | (~between(U1, V1, W1))) <=> ((~between(U1, V1, W1)) | (~between(U, V, W)) | (~equidistant(W, X, W1, X1)) | (~equidistant(U, X, U1, X1)) | (~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, W1)))), (((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, 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, V, U1, V1)) | (~equidistant(V, W, V1, W1))))), ((((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, 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, V, U1, V1)) | (~equidistant(V, W, V1, W1))) | 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, V, U1, V1)) | (~equidistant(V, W, 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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))), ((((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, 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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))))),
% 0.96/0.89      inference(bind,[status(th)],[])).
% 0.96/0.89  tff(282,plain,
% 0.96/0.89      (![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, 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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))),
% 0.96/0.89      inference(quant_intro,[status(thm)],[281])).
% 0.96/0.89  tff(283,axiom,(![W: $i, V: $i, V1: $i, W1: $i, U: $i, X: $i, U1: $i, X1: $i] : (((((((~equidistant(U, V, U1, V1)) | (~equidistant(V, W, V1, 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','d14')).
% 0.96/0.89  tff(284,plain,
% 0.96/0.89      (![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))),
% 0.96/0.89      inference(modus_ponens,[status(thm)],[283, 282])).
% 0.96/0.89  tff(285,plain,
% 0.96/0.89      (![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))),
% 0.96/0.89      inference(modus_ponens,[status(thm)],[284, 280])).
% 0.96/0.89  tff(286,plain,(
% 0.96/0.89      ![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))),
% 0.96/0.89      inference(skolemize,[status(sab)],[285])).
% 0.96/0.89  tff(287,plain,
% 0.96/0.89      (![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))),
% 0.96/0.89      inference(modus_ponens,[status(thm)],[286, 279])).
% 0.96/0.89  tff(288,plain,
% 0.96/0.89      (((~![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))) | ((~equidistant(w, v, w, x)) | (~equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u))) | equidistant(v, v, v, x) | (~equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)) | (~between(w, v, extension(w, v, v, u))) | (~equidistant(w, v, w, v)))) <=> ((~![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))) | (~equidistant(w, v, w, x)) | (~equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u))) | equidistant(v, v, v, x) | (~equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)) | (~between(w, v, extension(w, v, v, u))) | (~equidistant(w, v, w, v)))),
% 0.96/0.89      inference(rewrite,[status(thm)],[])).
% 0.96/0.89  tff(289,plain,
% 0.96/0.89      ((equidistant(v, v, v, x) | (~between(w, v, extension(w, v, v, u))) | (~between(w, v, extension(w, v, v, u))) | (~equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)) | (~equidistant(w, v, w, x)) | (~equidistant(w, v, w, v)) | (~equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u)))) <=> ((~equidistant(w, v, w, x)) | (~equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u))) | equidistant(v, v, v, x) | (~equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)) | (~between(w, v, extension(w, v, v, u))) | (~equidistant(w, v, w, v)))),
% 0.96/0.89      inference(rewrite,[status(thm)],[])).
% 0.96/0.89  tff(290,plain,
% 0.96/0.89      (((~![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))) | (equidistant(v, v, v, x) | (~between(w, v, extension(w, v, v, u))) | (~between(w, v, extension(w, v, v, u))) | (~equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)) | (~equidistant(w, v, w, x)) | (~equidistant(w, v, w, v)) | (~equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u))))) <=> ((~![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))) | ((~equidistant(w, v, w, x)) | (~equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u))) | equidistant(v, v, v, x) | (~equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)) | (~between(w, v, extension(w, v, v, u))) | (~equidistant(w, v, w, v))))),
% 0.96/0.89      inference(monotonicity,[status(thm)],[289])).
% 0.96/0.89  tff(291,plain,
% 0.96/0.89      (((~![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))) | (equidistant(v, v, v, x) | (~between(w, v, extension(w, v, v, u))) | (~between(w, v, extension(w, v, v, u))) | (~equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)) | (~equidistant(w, v, w, x)) | (~equidistant(w, v, w, v)) | (~equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u))))) <=> ((~![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))) | (~equidistant(w, v, w, x)) | (~equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u))) | equidistant(v, v, v, x) | (~equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)) | (~between(w, v, extension(w, v, v, u))) | (~equidistant(w, v, w, v)))),
% 0.96/0.89      inference(transitivity,[status(thm)],[290, 288])).
% 0.96/0.89  tff(292,plain,
% 0.96/0.89      ((~![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))) | (equidistant(v, v, v, x) | (~between(w, v, extension(w, v, v, u))) | (~between(w, v, extension(w, v, v, u))) | (~equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)) | (~equidistant(w, v, w, x)) | (~equidistant(w, v, w, v)) | (~equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u))))),
% 0.96/0.89      inference(quant_inst,[status(thm)],[])).
% 0.96/0.89  tff(293,plain,
% 0.96/0.89      ((~![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, V, U1, V1)) | (~equidistant(V, W, V1, W1)))) | (~equidistant(w, v, w, x)) | (~equidistant(v, extension(w, v, v, u), v, extension(w, v, v, u))) | equidistant(v, v, v, x) | (~equidistant(extension(w, v, v, u), v, extension(w, v, v, u), x)) | (~between(w, v, extension(w, v, v, u))) | (~equidistant(w, v, w, v))),
% 0.96/0.89      inference(modus_ponens,[status(thm)],[292, 291])).
% 0.96/0.89  tff(294,plain,
% 0.96/0.89      (equidistant(v, v, v, x) | (~between(w, v, extension(w, v, v, u))) | (~equidistant(w, v, w, v))),
% 0.96/0.89      inference(unit_resolution,[status(thm)],[293, 287, 161, 277, 270])).
% 0.96/0.89  tff(295,plain,
% 0.96/0.89      (equidistant(v, v, v, x) | (~equidistant(w, v, w, v))),
% 0.96/0.89      inference(unit_resolution,[status(thm)],[294, 267])).
% 0.96/0.89  tff(296,plain,
% 0.96/0.89      (equidistant(v, v, v, x)),
% 0.96/0.89      inference(unit_resolution,[status(thm)],[295, 264])).
% 0.96/0.89  tff(297,plain,
% 0.96/0.89      (equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))),
% 0.96/0.89      inference(modus_ponens,[status(thm)],[296, 89])).
% 0.96/0.89  tff(298,plain,
% 0.96/0.89      (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))) | equidistant(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))) | equidistant(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))),
% 0.96/0.89      inference(rewrite,[status(thm)],[])).
% 0.96/0.89  tff(299,plain,
% 0.96/0.89      ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))) | equidistant(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))),
% 0.96/0.89      inference(quant_inst,[status(thm)],[])).
% 0.96/0.89  tff(300,plain,
% 0.96/0.89      ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))) | equidistant(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))),
% 0.96/0.89      inference(modus_ponens,[status(thm)],[299, 298])).
% 0.96/0.89  tff(301,plain,
% 0.96/0.89      ((~equidistant(extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1))) | equidistant(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))),
% 0.96/0.90      inference(unit_resolution,[status(thm)],[300, 168])).
% 0.96/0.90  tff(302,plain,
% 0.96/0.90      (equidistant(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))),
% 0.96/0.90      inference(unit_resolution,[status(thm)],[301, 297])).
% 0.96/0.90  tff(303,plain,
% 0.96/0.90      ((reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) <=> (x = v)),
% 0.96/0.90      inference(monotonicity,[status(thm)],[10, 87])).
% 0.96/0.90  tff(304,plain,
% 0.96/0.90      ((reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)) <=> (v = x)),
% 0.96/0.90      inference(transitivity,[status(thm)],[303, 174])).
% 0.96/0.90  tff(305,plain,
% 0.96/0.90      ((v = x) <=> (reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))),
% 0.96/0.90      inference(symmetry,[status(thm)],[304])).
% 0.96/0.90  tff(306,plain,
% 0.96/0.90      ((~(v = x)) <=> (~(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))),
% 0.96/0.90      inference(monotonicity,[status(thm)],[305])).
% 0.96/0.90  tff(307,plain,
% 0.96/0.90      (~(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))),
% 0.96/0.90      inference(modus_ponens,[status(thm)],[55, 306])).
% 0.96/0.90  tff(308,plain,
% 0.96/0.90      (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))) | (reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))) | (reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))),
% 0.96/0.90      inference(rewrite,[status(thm)],[])).
% 0.96/0.90  tff(309,plain,
% 0.96/0.90      ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))) | (reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v)))),
% 0.96/0.90      inference(quant_inst,[status(thm)],[])).
% 0.96/0.90  tff(310,plain,
% 0.96/0.90      ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v), extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))) | (reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1) = extension(extension(v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v, reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1)), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), reflection(reflection(x, lower_dimension_point_1), lower_dimension_point_1), v))),
% 0.96/0.90      inference(modus_ponens,[status(thm)],[309, 308])).
% 0.96/0.90  tff(311,plain,
% 0.96/0.90      ($false),
% 0.96/0.90      inference(unit_resolution,[status(thm)],[310, 184, 307, 302])).
% 0.96/0.90  % SZS output end Proof
%------------------------------------------------------------------------------