TSTP Solution File: GEO026-3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO026-3 : TPTP v8.1.0. Released v1.0.0.
% 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 20:34:22 EDT 2022
% Result : Unsatisfiable 165.78s 107.26s
% Output : Proof 165.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO026-3 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 04:59:17 EDT 2022
% 0.12/0.34 % 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.
% 165.78/107.26 % SZS status Unsatisfiable
% 165.78/107.26 % SZS output start Proof
% 165.78/107.26 tff(equidistant_type, type, (
% 165.78/107.26 equidistant: ( $i * $i * $i * $i ) > $o)).
% 165.78/107.26 tff(x_type, type, (
% 165.78/107.26 x: $i)).
% 165.78/107.26 tff(w_type, type, (
% 165.78/107.26 w: $i)).
% 165.78/107.26 tff(continuous_type, type, (
% 165.78/107.26 continuous: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 165.78/107.26 tff(v_type, type, (
% 165.78/107.26 v: $i)).
% 165.78/107.26 tff(between_type, type, (
% 165.78/107.26 between: ( $i * $i * $i ) > $o)).
% 165.78/107.26 tff(inner_pasch_type, type, (
% 165.78/107.26 inner_pasch: ( $i * $i * $i * $i * $i ) > $i)).
% 165.78/107.26 tff(u_type, type, (
% 165.78/107.26 u: $i)).
% 165.78/107.26 tff(euclid1_type, type, (
% 165.78/107.26 euclid1: ( $i * $i * $i * $i * $i ) > $i)).
% 165.78/107.26 tff(1,assumption,(~equidistant(w, x, x, x)), introduced(assumption)).
% 165.78/107.26 tff(2,plain,
% 165.78/107.26 ((x = w) <=> (w = x)),
% 165.78/107.26 inference(commutativity,[status(thm)],[])).
% 165.78/107.26 tff(3,plain,
% 165.78/107.26 ((w = x) <=> (x = w)),
% 165.78/107.26 inference(symmetry,[status(thm)],[2])).
% 165.78/107.26 tff(4,plain,
% 165.78/107.26 ((~(w = x)) <=> (~(x = w))),
% 165.78/107.26 inference(monotonicity,[status(thm)],[3])).
% 165.78/107.26 tff(5,plain,
% 165.78/107.26 ((~(w = x)) <=> (~(w = x))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(6,axiom,(~(w = x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_w_is_x')).
% 165.78/107.26 tff(7,plain,
% 165.78/107.26 (~(w = x)),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[6, 5])).
% 165.78/107.26 tff(8,plain,
% 165.78/107.26 (~(x = w)),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[7, 4])).
% 165.78/107.26 tff(9,plain,
% 165.78/107.26 (equidistant(v, w, v, x) <=> equidistant(v, w, v, x)),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(10,axiom,(equidistant(v, w, v, x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','v_to_w_equals_v_to_x')).
% 165.78/107.26 tff(11,plain,
% 165.78/107.26 (equidistant(v, w, v, x)),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[10, 9])).
% 165.78/107.26 tff(12,plain,
% 165.78/107.26 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)))),
% 165.78/107.26 inference(bind,[status(th)],[])).
% 165.78/107.26 tff(13,plain,
% 165.78/107.26 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 165.78/107.26 inference(quant_intro,[status(thm)],[12])).
% 165.78/107.26 tff(14,plain,
% 165.78/107.26 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(15,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2')).
% 165.78/107.26 tff(16,plain,
% 165.78/107.26 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[15, 14])).
% 165.78/107.26 tff(17,plain,(
% 165.78/107.26 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 165.78/107.26 inference(skolemize,[status(sab)],[16])).
% 165.78/107.26 tff(18,plain,
% 165.78/107.26 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[17, 13])).
% 165.78/107.26 tff(19,plain,
% 165.78/107.26 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(v, w, v, x)) | equidistant(v, x, v, w))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(v, w, v, x)) | equidistant(v, x, v, w))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(20,plain,
% 165.78/107.26 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(v, w, v, x)) | equidistant(v, x, v, w))),
% 165.78/107.26 inference(quant_inst,[status(thm)],[])).
% 165.78/107.26 tff(21,plain,
% 165.78/107.26 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(v, w, v, x)) | equidistant(v, x, v, w)),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[20, 19])).
% 165.78/107.26 tff(22,plain,
% 165.78/107.26 (equidistant(v, x, v, w)),
% 165.78/107.26 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 165.78/107.26 tff(23,plain,
% 165.78/107.26 (^[W: $i, V: $i, Z: $i, Y: $i, X: $i] : refl(((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))) <=> ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))))),
% 165.78/107.26 inference(bind,[status(th)],[])).
% 165.78/107.26 tff(24,plain,
% 165.78/107.26 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))),
% 165.78/107.26 inference(quant_intro,[status(thm)],[23])).
% 165.78/107.26 tff(25,plain,
% 165.78/107.26 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(26,plain,
% 165.78/107.26 (^[W: $i, V: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~equidistant(X, W, X, V)) | (~equidistant(Y, W, Y, V))) | (~equidistant(Z, W, Z, V))) <=> ((~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))), (((((~equidistant(X, W, X, V)) | (~equidistant(Y, W, Y, V))) | (~equidistant(Z, W, Z, V))) | between(X, Y, Z)) <=> (((~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))) | between(X, Y, Z)))), rewrite((((~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))) | between(X, Y, Z)) <=> (between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))), (((((~equidistant(X, W, X, V)) | (~equidistant(Y, W, Y, V))) | (~equidistant(Z, W, Z, V))) | between(X, Y, Z)) <=> (between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))))), ((((((~equidistant(X, W, X, V)) | (~equidistant(Y, W, Y, V))) | (~equidistant(Z, W, Z, V))) | between(X, Y, Z)) | between(Y, Z, X)) <=> ((between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))) | between(Y, Z, X)))), rewrite(((between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))) | between(Y, Z, X)) <=> (between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))), ((((((~equidistant(X, W, X, V)) | (~equidistant(Y, W, Y, V))) | (~equidistant(Z, W, Z, V))) | between(X, Y, Z)) | between(Y, Z, X)) <=> (between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))))), (((((((~equidistant(X, W, X, V)) | (~equidistant(Y, W, Y, V))) | (~equidistant(Z, W, Z, V))) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) <=> ((between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))) | between(Z, X, Y)))), rewrite(((between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))) | between(Z, X, Y)) <=> (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))), (((((((~equidistant(X, W, X, V)) | (~equidistant(Y, W, Y, V))) | (~equidistant(Z, W, Z, V))) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) <=> (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))))), ((((((((~equidistant(X, W, X, V)) | (~equidistant(Y, W, Y, V))) | (~equidistant(Z, W, Z, V))) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) | (W = V)) <=> ((between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))) | (W = V)))), rewrite(((between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V))) | (W = V)) <=> ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))), ((((((((~equidistant(X, W, X, V)) | (~equidistant(Y, W, Y, V))) | (~equidistant(Z, W, Z, V))) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) | (W = V)) <=> ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))))),
% 165.78/107.26 inference(bind,[status(th)],[])).
% 165.78/107.26 tff(27,plain,
% 165.78/107.26 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (((((((~equidistant(X, W, X, V)) | (~equidistant(Y, W, Y, V))) | (~equidistant(Z, W, Z, V))) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) | (W = V)) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))),
% 165.78/107.26 inference(quant_intro,[status(thm)],[26])).
% 165.78/107.26 tff(28,axiom,(![W: $i, V: $i, Z: $i, Y: $i, X: $i] : (((((((~equidistant(X, W, X, V)) | (~equidistant(Y, W, Y, V))) | (~equidistant(Z, W, Z, V))) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) | (W = V))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','upper_dimension')).
% 165.78/107.26 tff(29,plain,
% 165.78/107.26 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[28, 27])).
% 165.78/107.26 tff(30,plain,
% 165.78/107.26 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[29, 25])).
% 165.78/107.26 tff(31,plain,(
% 165.78/107.26 ![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))),
% 165.78/107.26 inference(skolemize,[status(sab)],[30])).
% 165.78/107.26 tff(32,plain,
% 165.78/107.26 (![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[31, 24])).
% 165.78/107.26 tff(33,plain,
% 165.78/107.26 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))) | ((x = w) | between(v, v, v) | (~equidistant(v, x, v, w)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))) | (x = w) | between(v, v, v) | (~equidistant(v, x, v, w)))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(34,plain,
% 165.78/107.26 (((x = w) | between(v, v, v) | between(v, v, v) | between(v, v, v) | (~equidistant(v, x, v, w)) | (~equidistant(v, x, v, w)) | (~equidistant(v, x, v, w))) <=> ((x = w) | between(v, v, v) | (~equidistant(v, x, v, w)))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(35,plain,
% 165.78/107.26 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))) | ((x = w) | between(v, v, v) | between(v, v, v) | between(v, v, v) | (~equidistant(v, x, v, w)) | (~equidistant(v, x, v, w)) | (~equidistant(v, x, v, w)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))) | ((x = w) | between(v, v, v) | (~equidistant(v, x, v, w))))),
% 165.78/107.26 inference(monotonicity,[status(thm)],[34])).
% 165.78/107.26 tff(36,plain,
% 165.78/107.26 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))) | ((x = w) | between(v, v, v) | between(v, v, v) | between(v, v, v) | (~equidistant(v, x, v, w)) | (~equidistant(v, x, v, w)) | (~equidistant(v, x, v, w)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))) | (x = w) | between(v, v, v) | (~equidistant(v, x, v, w)))),
% 165.78/107.26 inference(transitivity,[status(thm)],[35, 33])).
% 165.78/107.26 tff(37,plain,
% 165.78/107.26 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))) | ((x = w) | between(v, v, v) | between(v, v, v) | between(v, v, v) | (~equidistant(v, x, v, w)) | (~equidistant(v, x, v, w)) | (~equidistant(v, x, v, w)))),
% 165.78/107.26 inference(quant_inst,[status(thm)],[])).
% 165.78/107.26 tff(38,plain,
% 165.78/107.26 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i] : ((W = V) | between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~equidistant(Z, W, Z, V)) | (~equidistant(Y, W, Y, V)) | (~equidistant(X, W, X, V)))) | (x = w) | between(v, v, v) | (~equidistant(v, x, v, w))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[37, 36])).
% 165.78/107.26 tff(39,plain,
% 165.78/107.26 ((x = w) | between(v, v, v)),
% 165.78/107.26 inference(unit_resolution,[status(thm)],[38, 32, 22])).
% 165.78/107.26 tff(40,plain,
% 165.78/107.26 (between(v, v, v)),
% 165.78/107.26 inference(unit_resolution,[status(thm)],[39, 8])).
% 165.78/107.26 tff(41,plain,
% 165.78/107.26 (^[Y: $i, X: $i] : refl(equidistant(X, Y, Y, X) <=> equidistant(X, Y, Y, X))),
% 165.78/107.26 inference(bind,[status(th)],[])).
% 165.78/107.26 tff(42,plain,
% 165.78/107.26 (![Y: $i, X: $i] : equidistant(X, Y, Y, X) <=> ![Y: $i, X: $i] : equidistant(X, Y, Y, X)),
% 165.78/107.26 inference(quant_intro,[status(thm)],[41])).
% 165.78/107.26 tff(43,plain,
% 165.78/107.26 (![Y: $i, X: $i] : equidistant(X, Y, Y, X) <=> ![Y: $i, X: $i] : equidistant(X, Y, Y, X)),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(44,axiom,(![Y: $i, X: $i] : equidistant(X, Y, Y, X)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','reflexivity_for_equidistance')).
% 165.78/107.26 tff(45,plain,
% 165.78/107.26 (![Y: $i, X: $i] : equidistant(X, Y, Y, X)),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[44, 43])).
% 165.78/107.26 tff(46,plain,(
% 165.78/107.26 ![Y: $i, X: $i] : equidistant(X, Y, Y, X)),
% 165.78/107.26 inference(skolemize,[status(sab)],[45])).
% 165.78/107.26 tff(47,plain,
% 165.78/107.26 (![Y: $i, X: $i] : equidistant(X, Y, Y, X)),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[46, 42])).
% 165.78/107.26 tff(48,plain,
% 165.78/107.26 ((~![Y: $i, X: $i] : equidistant(X, Y, Y, X)) | equidistant(v, v, v, v)),
% 165.78/107.26 inference(quant_inst,[status(thm)],[])).
% 165.78/107.26 tff(49,plain,
% 165.78/107.26 (equidistant(v, v, v, v)),
% 165.78/107.26 inference(unit_resolution,[status(thm)],[48, 47])).
% 165.78/107.26 tff(50,plain,
% 165.78/107.26 (^[W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : refl(((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1))) <=> ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1))))),
% 165.78/107.26 inference(bind,[status(th)],[])).
% 165.78/107.26 tff(51,plain,
% 165.78/107.26 (![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1))) <=> ![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))),
% 165.78/107.26 inference(quant_intro,[status(thm)],[50])).
% 165.78/107.26 tff(52,plain,
% 165.78/107.26 (![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1))) <=> ![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(53,plain,
% 165.78/107.26 (^[W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1))) <=> ((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1)))), ((((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1))) | (~between(U, V, X))) <=> (((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1))) | (~between(U, V, X))))), rewrite((((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1))) | (~between(U, V, X))) <=> ((~equidistant(U, V, U, V1)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))), ((((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1))) | (~between(U, V, X))) <=> ((~equidistant(U, V, U, V1)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1))))), (((((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1))) | (~between(U, V, X))) | (~between(V, W, X))) <=> (((~equidistant(U, V, U, V1)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1))) | (~between(V, W, X))))), rewrite((((~equidistant(U, V, U, V1)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1))) | (~between(V, W, X))) <=> ((~equidistant(U, V, U, V1)) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))), (((((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1))) | (~between(U, V, X))) | (~between(V, W, X))) <=> ((~equidistant(U, V, U, V1)) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1))))), ((((((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1))) | (~between(U, V, X))) | (~between(V, W, X))) | between(V1, continuous(U, V, V1, W, X, X1), X1)) <=> (((~equidistant(U, V, U, V1)) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1))) | between(V1, continuous(U, V, V1, W, X, X1), X1)))), rewrite((((~equidistant(U, V, U, V1)) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1))) | between(V1, continuous(U, V, V1, W, X, X1), X1)) <=> ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))), ((((((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1))) | (~between(U, V, X))) | (~between(V, W, X))) | between(V1, continuous(U, V, V1, W, X, X1), X1)) <=> ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))))),
% 165.78/107.26 inference(bind,[status(th)],[])).
% 165.78/107.26 tff(54,plain,
% 165.78/107.26 (![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : (((((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1))) | (~between(U, V, X))) | (~between(V, W, X))) | between(V1, continuous(U, V, V1, W, X, X1), X1)) <=> ![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))),
% 165.78/107.26 inference(quant_intro,[status(thm)],[53])).
% 165.78/107.26 tff(55,axiom,(![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : (((((~equidistant(U, V, U, V1)) | (~equidistant(U, X, U, X1))) | (~between(U, V, X))) | (~between(V, W, X))) | between(V1, continuous(U, V, V1, W, X, X1), X1))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','continuity1')).
% 165.78/107.26 tff(56,plain,
% 165.78/107.26 (![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[55, 54])).
% 165.78/107.26 tff(57,plain,
% 165.78/107.26 (![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[56, 52])).
% 165.78/107.26 tff(58,plain,(
% 165.78/107.26 ![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))),
% 165.78/107.26 inference(skolemize,[status(sab)],[57])).
% 165.78/107.26 tff(59,plain,
% 165.78/107.26 (![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[58, 51])).
% 165.78/107.26 tff(60,plain,
% 165.78/107.26 (((~![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))) | ((~between(v, v, v)) | (~equidistant(v, v, v, v)) | between(v, continuous(v, v, v, v, v, v), v))) <=> ((~![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))) | (~between(v, v, v)) | (~equidistant(v, v, v, v)) | between(v, continuous(v, v, v, v, v, v), v))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(61,plain,
% 165.78/107.26 (((~equidistant(v, v, v, v)) | between(v, continuous(v, v, v, v, v, v), v) | (~between(v, v, v)) | (~between(v, v, v)) | (~equidistant(v, v, v, v))) <=> ((~between(v, v, v)) | (~equidistant(v, v, v, v)) | between(v, continuous(v, v, v, v, v, v), v))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(62,plain,
% 165.78/107.26 (((~![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))) | ((~equidistant(v, v, v, v)) | between(v, continuous(v, v, v, v, v, v), v) | (~between(v, v, v)) | (~between(v, v, v)) | (~equidistant(v, v, v, v)))) <=> ((~![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))) | ((~between(v, v, v)) | (~equidistant(v, v, v, v)) | between(v, continuous(v, v, v, v, v, v), v)))),
% 165.78/107.26 inference(monotonicity,[status(thm)],[61])).
% 165.78/107.26 tff(63,plain,
% 165.78/107.26 (((~![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))) | ((~equidistant(v, v, v, v)) | between(v, continuous(v, v, v, v, v, v), v) | (~between(v, v, v)) | (~between(v, v, v)) | (~equidistant(v, v, v, v)))) <=> ((~![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))) | (~between(v, v, v)) | (~equidistant(v, v, v, v)) | between(v, continuous(v, v, v, v, v, v), v))),
% 165.78/107.26 inference(transitivity,[status(thm)],[62, 60])).
% 165.78/107.26 tff(64,plain,
% 165.78/107.26 ((~![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))) | ((~equidistant(v, v, v, v)) | between(v, continuous(v, v, v, v, v, v), v) | (~between(v, v, v)) | (~between(v, v, v)) | (~equidistant(v, v, v, v)))),
% 165.78/107.26 inference(quant_inst,[status(thm)],[])).
% 165.78/107.26 tff(65,plain,
% 165.78/107.26 ((~![W: $i, V: $i, V1: $i, U: $i, X: $i, X1: $i] : ((~equidistant(U, V, U, V1)) | between(V1, continuous(U, V, V1, W, X, X1), X1) | (~between(V, W, X)) | (~between(U, V, X)) | (~equidistant(U, X, U, X1)))) | (~between(v, v, v)) | (~equidistant(v, v, v, v)) | between(v, continuous(v, v, v, v, v, v), v)),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[64, 63])).
% 165.78/107.26 tff(66,plain,
% 165.78/107.26 (between(v, continuous(v, v, v, v, v, v), v)),
% 165.78/107.26 inference(unit_resolution,[status(thm)],[65, 59, 49, 40])).
% 165.78/107.26 tff(67,plain,
% 165.78/107.26 (^[Y: $i, X: $i] : refl(((~between(X, Y, X)) | (X = Y)) <=> ((~between(X, Y, X)) | (X = Y)))),
% 165.78/107.26 inference(bind,[status(th)],[])).
% 165.78/107.26 tff(68,plain,
% 165.78/107.26 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y)) <=> ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 165.78/107.26 inference(quant_intro,[status(thm)],[67])).
% 165.78/107.26 tff(69,plain,
% 165.78/107.26 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y)) <=> ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(70,axiom,(![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','identity_for_betweeness')).
% 165.78/107.26 tff(71,plain,
% 165.78/107.26 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[70, 69])).
% 165.78/107.26 tff(72,plain,(
% 165.78/107.26 ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 165.78/107.26 inference(skolemize,[status(sab)],[71])).
% 165.78/107.26 tff(73,plain,
% 165.78/107.26 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[72, 68])).
% 165.78/107.26 tff(74,plain,
% 165.78/107.26 (((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(v, continuous(v, v, v, v, v, v), v)) | (v = continuous(v, v, v, v, v, v)))) <=> ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(v, continuous(v, v, v, v, v, v), v)) | (v = continuous(v, v, v, v, v, v)))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(75,plain,
% 165.78/107.26 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(v, continuous(v, v, v, v, v, v), v)) | (v = continuous(v, v, v, v, v, v)))),
% 165.78/107.26 inference(quant_inst,[status(thm)],[])).
% 165.78/107.26 tff(76,plain,
% 165.78/107.26 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(v, continuous(v, v, v, v, v, v), v)) | (v = continuous(v, v, v, v, v, v))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[75, 74])).
% 165.78/107.26 tff(77,plain,
% 165.78/107.26 (v = continuous(v, v, v, v, v, v)),
% 165.78/107.26 inference(unit_resolution,[status(thm)],[76, 73, 66])).
% 165.78/107.26 tff(78,plain,
% 165.78/107.26 (continuous(v, v, v, v, v, v) = v),
% 165.78/107.26 inference(symmetry,[status(thm)],[77])).
% 165.78/107.26 tff(79,plain,
% 165.78/107.26 (equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x) <=> equidistant(v, w, v, x)),
% 165.78/107.26 inference(monotonicity,[status(thm)],[78, 78])).
% 165.78/107.26 tff(80,plain,
% 165.78/107.26 (equidistant(v, w, v, x) <=> equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)),
% 165.78/107.26 inference(symmetry,[status(thm)],[79])).
% 165.78/107.26 tff(81,plain,
% 165.78/107.26 (equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[11, 80])).
% 165.78/107.26 tff(82,plain,
% 165.78/107.26 (equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x) <=> equidistant(v, x, v, x)),
% 165.78/107.26 inference(monotonicity,[status(thm)],[78, 78])).
% 165.78/107.26 tff(83,plain,
% 165.78/107.26 (equidistant(v, x, v, x) <=> equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)),
% 165.78/107.26 inference(symmetry,[status(thm)],[82])).
% 165.78/107.26 tff(84,plain,
% 165.78/107.26 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(V, U, W, X)) <=> ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X)))),
% 165.78/107.26 inference(bind,[status(th)],[])).
% 165.78/107.26 tff(85,plain,
% 165.78/107.26 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))),
% 165.78/107.26 inference(quant_intro,[status(thm)],[84])).
% 165.78/107.26 tff(86,plain,
% 165.78/107.26 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))),
% 165.78/107.26 inference(rewrite,[status(thm)],[])).
% 165.78/107.26 tff(87,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3')).
% 165.78/107.26 tff(88,plain,
% 165.78/107.26 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[87, 86])).
% 165.78/107.26 tff(89,plain,(
% 165.78/107.26 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))),
% 165.78/107.26 inference(skolemize,[status(sab)],[88])).
% 165.78/107.26 tff(90,plain,
% 165.78/107.26 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))),
% 165.78/107.26 inference(modus_ponens,[status(thm)],[89, 85])).
% 165.78/107.26 tff(91,plain,
% 165.78/107.26 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | ((~equidistant(v, w, v, x)) | equidistant(w, v, v, x))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | (~equidistant(v, w, v, x)) | equidistant(w, v, v, x))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(92,plain,
% 165.78/107.27 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | ((~equidistant(v, w, v, x)) | equidistant(w, v, v, x))),
% 165.78/107.27 inference(quant_inst,[status(thm)],[])).
% 165.78/107.27 tff(93,plain,
% 165.78/107.27 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, W, X))) | (~equidistant(v, w, v, x)) | equidistant(w, v, v, x)),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[92, 91])).
% 165.78/107.27 tff(94,plain,
% 165.78/107.27 (equidistant(w, v, v, x)),
% 165.78/107.27 inference(unit_resolution,[status(thm)],[93, 90, 11])).
% 165.78/107.27 tff(95,plain,
% 165.78/107.27 (^[W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : refl((equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V))) <=> (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V))))),
% 165.78/107.27 inference(bind,[status(th)],[])).
% 165.78/107.27 tff(96,plain,
% 165.78/107.27 (![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))),
% 165.78/107.27 inference(quant_intro,[status(thm)],[95])).
% 165.78/107.27 tff(97,plain,
% 165.78/107.27 (![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V))) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(98,plain,
% 165.78/107.27 (^[W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : trans(monotonicity(rewrite(((~equidistant(X, Y, Z, V)) | (~equidistant(X, Y, V2, W))) <=> ((~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))), ((((~equidistant(X, Y, Z, V)) | (~equidistant(X, Y, V2, W))) | equidistant(Z, V, V2, W)) <=> (((~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V))) | equidistant(Z, V, V2, W)))), rewrite((((~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V))) | equidistant(Z, V, V2, W)) <=> (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))), ((((~equidistant(X, Y, Z, V)) | (~equidistant(X, Y, V2, W))) | equidistant(Z, V, V2, W)) <=> (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))))),
% 165.78/107.27 inference(bind,[status(th)],[])).
% 165.78/107.27 tff(99,plain,
% 165.78/107.27 (![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (((~equidistant(X, Y, Z, V)) | (~equidistant(X, Y, V2, W))) | equidistant(Z, V, V2, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))),
% 165.78/107.27 inference(quant_intro,[status(thm)],[98])).
% 165.78/107.27 tff(100,axiom,(![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (((~equidistant(X, Y, Z, V)) | (~equidistant(X, Y, V2, W))) | equidistant(Z, V, V2, W))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','transitivity_for_equidistance')).
% 165.78/107.27 tff(101,plain,
% 165.78/107.27 (![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[100, 99])).
% 165.78/107.27 tff(102,plain,
% 165.78/107.27 (![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[101, 97])).
% 165.78/107.27 tff(103,plain,(
% 165.78/107.27 ![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))),
% 165.78/107.27 inference(skolemize,[status(sab)],[102])).
% 165.78/107.27 tff(104,plain,
% 165.78/107.27 (![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[103, 96])).
% 165.78/107.27 tff(105,plain,
% 165.78/107.27 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))) | ((~equidistant(w, v, v, x)) | equidistant(v, x, v, x))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))) | (~equidistant(w, v, v, x)) | equidistant(v, x, v, x))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(106,plain,
% 165.78/107.27 ((equidistant(v, x, v, x) | (~equidistant(w, v, v, x)) | (~equidistant(w, v, v, x))) <=> ((~equidistant(w, v, v, x)) | equidistant(v, x, v, x))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(107,plain,
% 165.78/107.27 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))) | (equidistant(v, x, v, x) | (~equidistant(w, v, v, x)) | (~equidistant(w, v, v, x)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))) | ((~equidistant(w, v, v, x)) | equidistant(v, x, v, x)))),
% 165.78/107.27 inference(monotonicity,[status(thm)],[106])).
% 165.78/107.27 tff(108,plain,
% 165.78/107.27 (((~![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))) | (equidistant(v, x, v, x) | (~equidistant(w, v, v, x)) | (~equidistant(w, v, v, x)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))) | (~equidistant(w, v, v, x)) | equidistant(v, x, v, x))),
% 165.78/107.27 inference(transitivity,[status(thm)],[107, 105])).
% 165.78/107.27 tff(109,plain,
% 165.78/107.27 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))) | (equidistant(v, x, v, x) | (~equidistant(w, v, v, x)) | (~equidistant(w, v, v, x)))),
% 165.78/107.27 inference(quant_inst,[status(thm)],[])).
% 165.78/107.27 tff(110,plain,
% 165.78/107.27 ((~![W: $i, V: $i, Z: $i, Y: $i, X: $i, V2: $i] : (equidistant(Z, V, V2, W) | (~equidistant(X, Y, V2, W)) | (~equidistant(X, Y, Z, V)))) | (~equidistant(w, v, v, x)) | equidistant(v, x, v, x)),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[109, 108])).
% 165.78/107.27 tff(111,plain,
% 165.78/107.27 (equidistant(v, x, v, x)),
% 165.78/107.27 inference(unit_resolution,[status(thm)],[110, 104, 94])).
% 165.78/107.27 tff(112,plain,
% 165.78/107.27 (equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[111, 83])).
% 165.78/107.27 tff(113,plain,
% 165.78/107.27 ((~(u = v)) <=> (~(u = v))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(114,axiom,(~(u = v)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','u_not_v')).
% 165.78/107.27 tff(115,plain,
% 165.78/107.27 (~(u = v)),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[114, 113])).
% 165.78/107.27 tff(116,plain,
% 165.78/107.27 (between(u, v, x) <=> between(u, v, x)),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(117,axiom,(between(u, v, x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','v_between_u_and_x')).
% 165.78/107.27 tff(118,plain,
% 165.78/107.27 (between(u, v, x)),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[117, 116])).
% 165.78/107.27 tff(119,plain,
% 165.78/107.27 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl(((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y))) <=> ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y))))),
% 165.78/107.27 inference(bind,[status(th)],[])).
% 165.78/107.27 tff(120,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))),
% 165.78/107.27 inference(quant_intro,[status(thm)],[119])).
% 165.78/107.27 tff(121,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(122,plain,
% 165.78/107.27 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~between(U, W, Y)) | (~between(V, W, X))) | (U = W)) <=> ((U = W) | (~between(V, W, X)) | (~between(U, W, Y)))), (((((~between(U, W, Y)) | (~between(V, W, X))) | (U = W)) | between(U, V, euclid1(U, V, W, X, Y))) <=> (((U = W) | (~between(V, W, X)) | (~between(U, W, Y))) | between(U, V, euclid1(U, V, W, X, Y))))), rewrite((((U = W) | (~between(V, W, X)) | (~between(U, W, Y))) | between(U, V, euclid1(U, V, W, X, Y))) <=> ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))), (((((~between(U, W, Y)) | (~between(V, W, X))) | (U = W)) | between(U, V, euclid1(U, V, W, X, Y))) <=> ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))))),
% 165.78/107.27 inference(bind,[status(th)],[])).
% 165.78/107.27 tff(123,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((~between(U, W, Y)) | (~between(V, W, X))) | (U = W)) | between(U, V, euclid1(U, V, W, X, Y))) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))),
% 165.78/107.27 inference(quant_intro,[status(thm)],[122])).
% 165.78/107.27 tff(124,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((((~between(U, W, Y)) | (~between(V, W, X))) | (U = W)) | between(U, V, euclid1(U, V, W, X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','euclid1')).
% 165.78/107.27 tff(125,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[124, 123])).
% 165.78/107.27 tff(126,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[125, 121])).
% 165.78/107.27 tff(127,plain,(
% 165.78/107.27 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))),
% 165.78/107.27 inference(skolemize,[status(sab)],[126])).
% 165.78/107.27 tff(128,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[127, 120])).
% 165.78/107.27 tff(129,plain,
% 165.78/107.27 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))) | ((u = v) | between(u, u, euclid1(u, u, v, x, x)) | (~between(u, v, x)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))) | (u = v) | between(u, u, euclid1(u, u, v, x, x)) | (~between(u, v, x)))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(130,plain,
% 165.78/107.27 (((u = v) | between(u, u, euclid1(u, u, v, x, x)) | (~between(u, v, x)) | (~between(u, v, x))) <=> ((u = v) | between(u, u, euclid1(u, u, v, x, x)) | (~between(u, v, x)))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(131,plain,
% 165.78/107.27 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))) | ((u = v) | between(u, u, euclid1(u, u, v, x, x)) | (~between(u, v, x)) | (~between(u, v, x)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))) | ((u = v) | between(u, u, euclid1(u, u, v, x, x)) | (~between(u, v, x))))),
% 165.78/107.27 inference(monotonicity,[status(thm)],[130])).
% 165.78/107.27 tff(132,plain,
% 165.78/107.27 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))) | ((u = v) | between(u, u, euclid1(u, u, v, x, x)) | (~between(u, v, x)) | (~between(u, v, x)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))) | (u = v) | between(u, u, euclid1(u, u, v, x, x)) | (~between(u, v, x)))),
% 165.78/107.27 inference(transitivity,[status(thm)],[131, 129])).
% 165.78/107.27 tff(133,plain,
% 165.78/107.27 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))) | ((u = v) | between(u, u, euclid1(u, u, v, x, x)) | (~between(u, v, x)) | (~between(u, v, x)))),
% 165.78/107.27 inference(quant_inst,[status(thm)],[])).
% 165.78/107.27 tff(134,plain,
% 165.78/107.27 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((U = W) | between(U, V, euclid1(U, V, W, X, Y)) | (~between(V, W, X)) | (~between(U, W, Y)))) | (u = v) | between(u, u, euclid1(u, u, v, x, x)) | (~between(u, v, x))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[133, 132])).
% 165.78/107.27 tff(135,plain,
% 165.78/107.27 (between(u, u, euclid1(u, u, v, x, x))),
% 165.78/107.27 inference(unit_resolution,[status(thm)],[134, 128, 118, 115])).
% 165.78/107.27 tff(136,plain,
% 165.78/107.27 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl(((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y)) <=> ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y)))),
% 165.78/107.27 inference(bind,[status(th)],[])).
% 165.78/107.27 tff(137,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 165.78/107.27 inference(quant_intro,[status(thm)],[136])).
% 165.78/107.27 tff(138,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(139,plain,
% 165.78/107.27 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : rewrite((((~between(U, V, W)) | (~between(Y, X, W))) | between(V, inner_pasch(U, V, W, X, Y), Y)) <=> ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y)))),
% 165.78/107.27 inference(bind,[status(th)],[])).
% 165.78/107.27 tff(140,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(Y, X, W))) | between(V, inner_pasch(U, V, W, X, Y), Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 165.78/107.27 inference(quant_intro,[status(thm)],[139])).
% 165.78/107.27 tff(141,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(Y, X, W))) | between(V, inner_pasch(U, V, W, X, Y), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','inner_pasch1')).
% 165.78/107.27 tff(142,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[141, 140])).
% 165.78/107.27 tff(143,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[142, 138])).
% 165.78/107.27 tff(144,plain,(
% 165.78/107.27 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 165.78/107.27 inference(skolemize,[status(sab)],[143])).
% 165.78/107.27 tff(145,plain,
% 165.78/107.27 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[144, 137])).
% 165.78/107.27 tff(146,plain,
% 165.78/107.27 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | (between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u) | (~between(u, u, euclid1(u, u, v, x, x))))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u) | (~between(u, u, euclid1(u, u, v, x, x))))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(147,plain,
% 165.78/107.27 (((~between(u, u, euclid1(u, u, v, x, x))) | (~between(u, u, euclid1(u, u, v, x, x))) | between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u)) <=> (between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u) | (~between(u, u, euclid1(u, u, v, x, x))))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(148,plain,
% 165.78/107.27 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | ((~between(u, u, euclid1(u, u, v, x, x))) | (~between(u, u, euclid1(u, u, v, x, x))) | between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | (between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u) | (~between(u, u, euclid1(u, u, v, x, x)))))),
% 165.78/107.27 inference(monotonicity,[status(thm)],[147])).
% 165.78/107.27 tff(149,plain,
% 165.78/107.27 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | ((~between(u, u, euclid1(u, u, v, x, x))) | (~between(u, u, euclid1(u, u, v, x, x))) | between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u) | (~between(u, u, euclid1(u, u, v, x, x))))),
% 165.78/107.27 inference(transitivity,[status(thm)],[148, 146])).
% 165.78/107.27 tff(150,plain,
% 165.78/107.27 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | ((~between(u, u, euclid1(u, u, v, x, x))) | (~between(u, u, euclid1(u, u, v, x, x))) | between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u))),
% 165.78/107.27 inference(quant_inst,[status(thm)],[])).
% 165.78/107.27 tff(151,plain,
% 165.78/107.27 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u) | (~between(u, u, euclid1(u, u, v, x, x)))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[150, 149])).
% 165.78/107.27 tff(152,plain,
% 165.78/107.27 (between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u)),
% 165.78/107.27 inference(unit_resolution,[status(thm)],[151, 145, 135])).
% 165.78/107.27 tff(153,plain,
% 165.78/107.27 (((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u)) | (u = inner_pasch(u, u, euclid1(u, u, v, x, x), u, u)))) <=> ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u)) | (u = inner_pasch(u, u, euclid1(u, u, v, x, x), u, u)))),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(154,plain,
% 165.78/107.27 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u)) | (u = inner_pasch(u, u, euclid1(u, u, v, x, x), u, u)))),
% 165.78/107.27 inference(quant_inst,[status(thm)],[])).
% 165.78/107.27 tff(155,plain,
% 165.78/107.27 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(u, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), u)) | (u = inner_pasch(u, u, euclid1(u, u, v, x, x), u, u))),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[154, 153])).
% 165.78/107.27 tff(156,plain,
% 165.78/107.27 (u = inner_pasch(u, u, euclid1(u, u, v, x, x), u, u)),
% 165.78/107.27 inference(unit_resolution,[status(thm)],[155, 73, 152])).
% 165.78/107.27 tff(157,plain,
% 165.78/107.27 (inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = u),
% 165.78/107.27 inference(symmetry,[status(thm)],[156])).
% 165.78/107.27 tff(158,plain,
% 165.78/107.27 (between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w) <=> between(u, v, w)),
% 165.78/107.27 inference(monotonicity,[status(thm)],[157, 78])).
% 165.78/107.27 tff(159,plain,
% 165.78/107.27 (between(u, v, w) <=> between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)),
% 165.78/107.27 inference(symmetry,[status(thm)],[158])).
% 165.78/107.27 tff(160,plain,
% 165.78/107.27 (between(u, v, w) <=> between(u, v, w)),
% 165.78/107.27 inference(rewrite,[status(thm)],[])).
% 165.78/107.27 tff(161,axiom,(between(u, v, w)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','v_between_u_and_w')).
% 165.78/107.27 tff(162,plain,
% 165.78/107.27 (between(u, v, w)),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[161, 160])).
% 165.78/107.27 tff(163,plain,
% 165.78/107.27 (between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)),
% 165.78/107.27 inference(modus_ponens,[status(thm)],[162, 159])).
% 165.78/107.27 tff(164,assumption,(~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v))), introduced(assumption)).
% 165.78/107.27 tff(165,plain,
% 165.78/107.27 (^[V: $i, U: $i] : refl(equidistant(U, V, U, V) <=> equidistant(U, V, U, V))),
% 165.78/107.27 inference(bind,[status(th)],[])).
% 165.78/107.27 tff(166,plain,
% 165.78/107.27 (![V: $i, U: $i] : equidistant(U, V, U, V) <=> ![V: $i, U: $i] : equidistant(U, V, U, V)),
% 165.78/107.28 inference(quant_intro,[status(thm)],[165])).
% 165.78/107.28 tff(167,plain,
% 165.78/107.28 (![V: $i, U: $i] : equidistant(U, V, U, V) <=> ![V: $i, U: $i] : equidistant(U, V, U, V)),
% 165.78/107.28 inference(rewrite,[status(thm)],[])).
% 165.78/107.28 tff(168,axiom,(![V: $i, U: $i] : equidistant(U, V, U, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1')).
% 165.78/107.28 tff(169,plain,
% 165.78/107.28 (![V: $i, U: $i] : equidistant(U, V, U, V)),
% 165.78/107.28 inference(modus_ponens,[status(thm)],[168, 167])).
% 165.78/107.28 tff(170,plain,(
% 165.78/107.28 ![V: $i, U: $i] : equidistant(U, V, U, V)),
% 165.78/107.28 inference(skolemize,[status(sab)],[169])).
% 165.78/107.28 tff(171,plain,
% 165.78/107.28 (![V: $i, U: $i] : equidistant(U, V, U, V)),
% 165.78/107.28 inference(modus_ponens,[status(thm)],[170, 166])).
% 165.78/107.28 tff(172,plain,
% 165.78/107.28 ((~![V: $i, U: $i] : equidistant(U, V, U, V)) | equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v))),
% 165.78/107.28 inference(quant_inst,[status(thm)],[])).
% 165.78/107.28 tff(173,plain,
% 165.78/107.28 ($false),
% 165.78/107.28 inference(unit_resolution,[status(thm)],[172, 171, 164])).
% 165.78/107.28 tff(174,plain,(equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v))), inference(lemma,lemma(discharge,[]))).
% 165.78/107.28 tff(175,assumption,(~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)), introduced(assumption)).
% 165.78/107.28 tff(176,plain,
% 165.78/107.28 ((~![V: $i, U: $i] : equidistant(U, V, U, V)) | equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)),
% 165.78/107.28 inference(quant_inst,[status(thm)],[])).
% 165.78/107.28 tff(177,plain,
% 165.78/107.28 ($false),
% 165.78/107.28 inference(unit_resolution,[status(thm)],[176, 171, 175])).
% 165.78/107.28 tff(178,plain,(equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)), inference(lemma,lemma(discharge,[]))).
% 165.78/107.28 tff(179,plain,
% 165.78/107.28 (between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x) <=> between(u, v, x)),
% 165.78/107.28 inference(monotonicity,[status(thm)],[157, 78])).
% 165.78/107.28 tff(180,plain,
% 165.78/107.28 (between(u, v, x) <=> between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)),
% 165.78/107.28 inference(symmetry,[status(thm)],[179])).
% 165.78/107.28 tff(181,plain,
% 165.78/107.28 (between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)),
% 165.78/107.28 inference(modus_ponens,[status(thm)],[118, 180])).
% 165.78/107.28 tff(182,plain,
% 165.78/107.28 ((inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)) <=> (u = v)),
% 165.78/107.28 inference(monotonicity,[status(thm)],[157, 78])).
% 165.78/107.28 tff(183,plain,
% 165.78/107.28 ((u = v) <=> (inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v))),
% 165.78/107.28 inference(symmetry,[status(thm)],[182])).
% 165.78/107.28 tff(184,plain,
% 165.78/107.28 ((~(u = v)) <=> (~(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)))),
% 165.78/107.28 inference(monotonicity,[status(thm)],[183])).
% 165.78/107.28 tff(185,plain,
% 165.78/107.28 (~(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v))),
% 165.78/107.28 inference(modus_ponens,[status(thm)],[115, 184])).
% 165.78/107.28 tff(186,plain,
% 165.78/107.28 (^[V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : refl((equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) <=> (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))),
% 165.78/107.28 inference(bind,[status(th)],[])).
% 165.78/107.28 tff(187,plain,
% 165.78/107.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) <=> ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 165.78/107.28 inference(quant_intro,[status(thm)],[186])).
% 165.78/107.28 tff(188,plain,
% 165.78/107.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) <=> ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 165.78/107.28 inference(rewrite,[status(thm)],[])).
% 165.78/107.28 tff(189,plain,
% 165.78/107.28 (^[V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) <=> ((~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) <=> (((~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~equidistant(Y, V, Y1, V1))))), rewrite((((~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~equidistant(Y, V, Y1, V1))) <=> ((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) <=> ((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), ((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) <=> (((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X, Y, Z))))), rewrite((((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X, Y, Z))) <=> ((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), ((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) <=> ((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), (((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) <=> (((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X1, Y1, Z1))))), rewrite((((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X1, Y1, Z1))) <=> ((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) <=> ((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) <=> (((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (X = Y)))), rewrite((((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (X = Y)) <=> ((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) <=> ((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), (((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1)) <=> (((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | equidistant(Z, V, Z1, V1)))), rewrite((((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | equidistant(Z, V, Z1, V1)) <=> (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1)) <=> (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))))),
% 165.78/107.28 inference(bind,[status(th)],[])).
% 165.78/107.28 tff(190,plain,
% 165.78/107.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1)) <=> ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 165.78/107.28 inference(quant_intro,[status(thm)],[189])).
% 165.78/107.28 tff(191,axiom,(![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','outer_five_segment')).
% 165.78/107.28 tff(192,plain,
% 165.78/107.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 165.78/107.28 inference(modus_ponens,[status(thm)],[191, 190])).
% 165.78/107.28 tff(193,plain,
% 165.78/107.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 165.78/107.28 inference(modus_ponens,[status(thm)],[192, 188])).
% 165.78/107.28 tff(194,plain,(
% 165.78/107.28 ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 165.78/107.28 inference(skolemize,[status(sab)],[193])).
% 165.78/107.28 tff(195,plain,
% 165.78/107.28 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 165.78/107.28 inference(modus_ponens,[status(thm)],[194, 187])).
% 165.78/107.28 tff(196,plain,
% 165.78/107.28 (((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | ((inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)) | equidistant(w, x, x, x) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v))))) <=> ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)) | equidistant(w, x, x, x) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v))))),
% 165.78/107.28 inference(rewrite,[status(thm)],[])).
% 165.78/107.28 tff(197,plain,
% 165.78/107.28 ((equidistant(w, x, x, x) | (inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)) | (~equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)) | (~equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v)))) <=> ((inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)) | equidistant(w, x, x, x) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v))))),
% 165.78/107.28 inference(rewrite,[status(thm)],[])).
% 165.78/107.28 tff(198,plain,
% 165.78/107.28 (((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (equidistant(w, x, x, x) | (inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)) | (~equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)) | (~equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v))))) <=> ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | ((inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)) | equidistant(w, x, x, x) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v)))))),
% 165.78/107.28 inference(monotonicity,[status(thm)],[197])).
% 165.78/107.28 tff(199,plain,
% 165.78/107.28 (((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (equidistant(w, x, x, x) | (inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)) | (~equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)) | (~equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v))))) <=> ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)) | equidistant(w, x, x, x) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v))))),
% 165.78/107.29 inference(transitivity,[status(thm)],[198, 196])).
% 165.78/107.29 tff(200,plain,
% 165.78/107.29 ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (equidistant(w, x, x, x) | (inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)) | (~equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)) | (~equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v))))),
% 165.78/107.29 inference(quant_inst,[status(thm)],[])).
% 165.78/107.29 tff(201,plain,
% 165.78/107.29 ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (inner_pasch(u, u, euclid1(u, u, v, x, x), u, u) = continuous(v, v, v, v, v, v)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x, inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), x)) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), x, continuous(v, v, v, v, v, v), x)) | (~equidistant(continuous(v, v, v, v, v, v), w, continuous(v, v, v, v, v, v), x)) | equidistant(w, x, x, x) | (~between(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), w)) | (~equidistant(inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v), inner_pasch(u, u, euclid1(u, u, v, x, x), u, u), continuous(v, v, v, v, v, v)))),
% 165.78/107.29 inference(modus_ponens,[status(thm)],[200, 199])).
% 165.78/107.29 tff(202,plain,
% 165.78/107.29 ($false),
% 165.78/107.29 inference(unit_resolution,[status(thm)],[201, 195, 185, 181, 178, 174, 163, 112, 81, 1])).
% 165.78/107.29 tff(203,plain,(equidistant(w, x, x, x)), inference(lemma,lemma(discharge,[]))).
% 165.78/107.29 tff(204,plain,
% 165.78/107.29 (^[Z: $i, Y: $i, X: $i] : refl(((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ((~equidistant(X, Y, Z, Z)) | (X = Y)))),
% 165.78/107.29 inference(bind,[status(th)],[])).
% 165.78/107.29 tff(205,plain,
% 165.78/107.29 (![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))),
% 165.78/107.29 inference(quant_intro,[status(thm)],[204])).
% 165.78/107.29 tff(206,plain,
% 165.78/107.29 (![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))),
% 165.78/107.29 inference(rewrite,[status(thm)],[])).
% 165.78/107.29 tff(207,axiom,(![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','identity_for_equidistance')).
% 165.78/107.29 tff(208,plain,
% 165.78/107.29 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 165.78/107.29 inference(modus_ponens,[status(thm)],[207, 206])).
% 165.78/107.29 tff(209,plain,(
% 165.78/107.29 ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 165.78/107.29 inference(skolemize,[status(sab)],[208])).
% 165.78/107.29 tff(210,plain,
% 165.78/107.29 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 165.78/107.29 inference(modus_ponens,[status(thm)],[209, 205])).
% 165.78/107.29 tff(211,plain,
% 165.78/107.29 (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(w, x, x, x)) | (w = x))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(w, x, x, x)) | (w = x))),
% 165.78/107.29 inference(rewrite,[status(thm)],[])).
% 165.78/107.29 tff(212,plain,
% 165.78/107.29 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(w, x, x, x)) | (w = x))),
% 165.78/107.29 inference(quant_inst,[status(thm)],[])).
% 165.78/107.29 tff(213,plain,
% 165.78/107.29 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(w, x, x, x)) | (w = x)),
% 165.78/107.29 inference(modus_ponens,[status(thm)],[212, 211])).
% 165.78/107.29 tff(214,plain,
% 165.78/107.29 ($false),
% 165.78/107.29 inference(unit_resolution,[status(thm)],[213, 210, 7, 203])).
% 165.78/107.29 % SZS output end Proof
%------------------------------------------------------------------------------