TSTP Solution File: GEO012-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO012-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 20:34:16 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO012-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 04:39:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(between_type, type, (
% 0.20/0.49 between: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(c_type, type, (
% 0.20/0.49 c: $i)).
% 0.20/0.49 tff(b_type, type, (
% 0.20/0.49 b: $i)).
% 0.20/0.49 tff(d_type, type, (
% 0.20/0.49 d: $i)).
% 0.20/0.49 tff(a_type, type, (
% 0.20/0.49 a: $i)).
% 0.20/0.49 tff(colinear_type, type, (
% 0.20/0.49 colinear: ( $i * $i * $i ) > $o)).
% 0.20/0.49 tff(insertion_type, type, (
% 0.20/0.49 insertion: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.49 tff(extension_type, type, (
% 0.20/0.49 extension: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.49 tff(1,assumption,(~colinear(b, c, d)), introduced(assumption)).
% 0.20/0.49 tff(2,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i] : refl(((~between(W, V, U)) | colinear(U, V, W)) <=> ((~between(W, V, U)) | colinear(U, V, W)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.49 tff(4,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(5,axiom,(![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c2_1')).
% 0.20/0.49 tff(6,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.49 tff(7,plain,(
% 0.20/0.49 ![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.20/0.49 inference(skolemize,[status(sab)],[6])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.49 tff(9,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(d, c, b)) | colinear(b, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(d, c, b)) | colinear(b, c, d))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | ((~between(d, c, b)) | colinear(b, c, d))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : ((~between(W, V, U)) | colinear(U, V, W))) | (~between(d, c, b)) | colinear(b, c, d)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 (~between(d, c, b)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.20/0.49 tff(13,plain,
% 0.20/0.49 (^[Z: $i, Y: $i, X: $i] : refl(((~between(Z, X, Y)) | colinear(X, Y, Z)) <=> ((~between(Z, X, Y)) | colinear(X, Y, Z)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(16,axiom,(![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax','colinearity3')).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.49 tff(18,plain,(
% 0.20/0.49 ![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 0.20/0.49 inference(skolemize,[status(sab)],[17])).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | ((~between(d, b, c)) | colinear(b, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | (~between(d, b, c)) | colinear(b, c, d))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | ((~between(d, b, c)) | colinear(b, c, d))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | (~between(d, b, c)) | colinear(b, c, d)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 (~between(d, b, c)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[22, 19, 1])).
% 0.20/0.49 tff(24,plain,
% 0.20/0.49 (^[Z: $i, Y: $i, X: $i] : refl(((~between(Y, Z, X)) | colinear(X, Y, Z)) <=> ((~between(Y, Z, X)) | colinear(X, Y, Z)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(27,axiom,(![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax','colinearity2')).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.49 tff(29,plain,(
% 0.20/0.49 ![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 0.20/0.49 inference(skolemize,[status(sab)],[28])).
% 0.20/0.49 tff(30,plain,
% 0.20/0.49 (![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.49 tff(31,plain,
% 0.20/0.49 (((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(c, d, b)) | colinear(b, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(c, d, b)) | colinear(b, c, d))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(32,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(c, d, b)) | colinear(b, c, d))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(c, d, b)) | colinear(b, c, d)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 (~between(c, d, b)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[33, 30, 1])).
% 0.20/0.49 tff(35,assumption,(between(a, d, b)), introduced(assumption)).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ((~between(U, V, W)) | (V = insertion(U, W, U, V))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.49 tff(38,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V))) <=> ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(39,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','i3')).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.49 tff(41,plain,(
% 0.20/0.49 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[40])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(a, d, b)) | (d = insertion(a, b, a, d)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(a, d, b)) | (d = insertion(a, b, a, d)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(a, d, b)) | (d = insertion(a, b, a, d)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(a, d, b)) | (d = insertion(a, b, a, d))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 (d = insertion(a, b, a, d)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[45, 42, 35])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 (insertion(a, b, a, d) = d),
% 0.20/0.49 inference(symmetry,[status(thm)],[46])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 (between(c, insertion(a, b, a, d), b) <=> between(c, d, b)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (between(c, d, b) <=> between(c, insertion(a, b, a, d), b)),
% 0.20/0.49 inference(symmetry,[status(thm)],[48])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 ((~between(c, d, b)) <=> (~between(c, insertion(a, b, a, d), b))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.49 tff(51,assumption,(~between(c, d, b)), introduced(assumption)).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 (~between(c, insertion(a, b, a, d), b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (between(a, insertion(a, b, a, d), b) <=> between(a, d, b)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 (between(a, d, b) <=> between(a, insertion(a, b, a, d), b)),
% 0.20/0.49 inference(symmetry,[status(thm)],[53])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (between(a, insertion(a, b, a, d), b)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[35, 54])).
% 0.20/0.49 tff(56,assumption,(~between(d, b, c)), introduced(assumption)).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))) <=> ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.49 tff(59,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 (^[W: $i, V: $i, U: $i, X: $i] : rewrite((((~between(U, V, W)) | (~between(U, W, X))) | between(V, W, X)) <=> ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(V, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.49 tff(62,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(V, W, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b5')).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.49 tff(65,plain,(
% 0.20/0.49 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[64])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (between(d, b, c) | (~between(a, d, b)) | (~between(a, b, c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | between(d, b, c) | (~between(a, d, b)) | (~between(a, b, c)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 (((~between(a, d, b)) | between(d, b, c) | (~between(a, b, c))) <=> (between(d, b, c) | (~between(a, d, b)) | (~between(a, b, c)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(a, d, b)) | between(d, b, c) | (~between(a, b, c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (between(d, b, c) | (~between(a, d, b)) | (~between(a, b, c))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.50 tff(70,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(a, d, b)) | between(d, b, c) | (~between(a, b, c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | between(d, b, c) | (~between(a, d, b)) | (~between(a, b, c)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(a, d, b)) | between(d, b, c) | (~between(a, b, c)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(72,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | between(d, b, c) | (~between(a, d, b)) | (~between(a, b, c))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.50 tff(73,plain,
% 0.20/0.50 (~between(a, b, c)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[72, 66, 35, 56])).
% 0.20/0.50 tff(74,assumption,(~between(d, c, b)), introduced(assumption)).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X)) <=> ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.50 tff(77,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(78,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~between(U, V, X)) | (~between(U, W, X))) | between(V, W, X)) <=> ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)))), (((((~between(U, V, X)) | (~between(U, W, X))) | between(V, W, X)) | between(W, V, X)) <=> (((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X))) | between(W, V, X)))), rewrite((((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X))) | between(W, V, X)) <=> ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))), (((((~between(U, V, X)) | (~between(U, W, X))) | between(V, W, X)) | between(W, V, X)) <=> ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(79,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, X)) | (~between(U, W, X))) | between(V, W, X)) | between(W, V, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.50 tff(80,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, X)) | (~between(U, W, X))) | between(V, W, X)) | between(W, V, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b14')).
% 0.20/0.50 tff(81,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.50 tff(82,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.50 tff(83,plain,(
% 0.20/0.50 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 0.20/0.50 inference(skolemize,[status(sab)],[82])).
% 0.20/0.50 tff(84,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.20/0.50 tff(85,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (between(d, c, b) | between(c, d, b) | (~between(a, d, b)) | (~between(a, c, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | between(d, c, b) | between(c, d, b) | (~between(a, d, b)) | (~between(a, c, b)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(86,plain,
% 0.20/0.50 (((~between(a, d, b)) | between(d, c, b) | (~between(a, c, b)) | between(c, d, b)) <=> (between(d, c, b) | between(c, d, b) | (~between(a, d, b)) | (~between(a, c, b)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(87,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(a, d, b)) | between(d, c, b) | (~between(a, c, b)) | between(c, d, b))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (between(d, c, b) | between(c, d, b) | (~between(a, d, b)) | (~between(a, c, b))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.50 tff(88,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(a, d, b)) | between(d, c, b) | (~between(a, c, b)) | between(c, d, b))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | between(d, c, b) | between(c, d, b) | (~between(a, d, b)) | (~between(a, c, b)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[87, 85])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(a, d, b)) | between(d, c, b) | (~between(a, c, b)) | between(c, d, b))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(90,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | between(d, c, b) | between(c, d, b) | (~between(a, d, b)) | (~between(a, c, b))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 (~between(a, c, b)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[90, 84, 35, 74, 51])).
% 0.20/0.50 tff(92,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | between(W, V, U)) <=> ((~between(U, V, W)) | between(W, V, U)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.50 tff(94,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(95,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1')).
% 0.20/0.50 tff(96,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.50 tff(97,plain,(
% 0.20/0.50 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.20/0.50 inference(skolemize,[status(sab)],[96])).
% 0.20/0.50 tff(98,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, c, a)) | between(a, c, b))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, c, a)) | between(a, c, b))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, c, a)) | between(a, c, b))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, c, a)) | between(a, c, b)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 (~between(b, c, a)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[101, 98, 91])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 (colinear(a, b, c) <=> colinear(a, b, c)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(104,axiom,(colinear(a, b, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abc_colinear')).
% 0.20/0.50 tff(105,plain,
% 0.20/0.50 (colinear(a, b, c)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.50 tff(106,plain,
% 0.20/0.50 (^[Z: $i, Y: $i, X: $i] : refl((between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) <=> (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(107,plain,
% 0.20/0.50 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.50 tff(108,plain,
% 0.20/0.50 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(109,plain,
% 0.20/0.50 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) <=> (between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))), (((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) <=> ((between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) | between(Z, X, Y)))), rewrite(((between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z))) | between(Z, X, Y)) <=> (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))), (((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) <=> (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(110,plain,
% 0.20/0.50 (![Z: $i, Y: $i, X: $i] : ((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y)) <=> ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.50 tff(111,axiom,(![Z: $i, Y: $i, X: $i] : ((((~colinear(X, Y, Z)) | between(X, Y, Z)) | between(Y, Z, X)) | between(Z, X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax','colinearity4')).
% 0.20/0.50 tff(112,plain,
% 0.20/0.50 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.50 tff(113,plain,
% 0.20/0.50 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.20/0.50 tff(114,plain,(
% 0.20/0.50 ![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[113])).
% 0.20/0.50 tff(115,plain,
% 0.20/0.50 (![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.20/0.50 tff(116,plain,
% 0.20/0.50 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(a, b, c)) | between(c, a, b) | between(b, c, a) | between(a, b, c))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, b, c)) | between(c, a, b) | between(b, c, a) | between(a, b, c))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(117,plain,
% 0.20/0.50 ((between(c, a, b) | between(b, c, a) | between(a, b, c) | (~colinear(a, b, c))) <=> ((~colinear(a, b, c)) | between(c, a, b) | between(b, c, a) | between(a, b, c))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(118,plain,
% 0.20/0.50 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(c, a, b) | between(b, c, a) | between(a, b, c) | (~colinear(a, b, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(a, b, c)) | between(c, a, b) | between(b, c, a) | between(a, b, c)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.50 tff(119,plain,
% 0.20/0.50 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(c, a, b) | between(b, c, a) | between(a, b, c) | (~colinear(a, b, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, b, c)) | between(c, a, b) | between(b, c, a) | between(a, b, c))),
% 0.20/0.50 inference(transitivity,[status(thm)],[118, 116])).
% 0.20/0.50 tff(120,plain,
% 0.20/0.50 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(c, a, b) | between(b, c, a) | between(a, b, c) | (~colinear(a, b, c)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(121,plain,
% 0.20/0.50 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, b, c)) | between(c, a, b) | between(b, c, a) | between(a, b, c)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 (between(c, a, b) | between(b, c, a) | between(a, b, c)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[121, 115, 105])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 (between(c, a, b)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[122, 102, 73])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))) <=> ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(125,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.50 tff(126,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(127,plain,
% 0.20/0.50 (^[W: $i, V: $i, U: $i, X: $i] : rewrite((((~between(U, V, X)) | (~between(V, W, X))) | between(U, W, X)) <=> ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(128,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, X)) | (~between(V, W, X))) | between(U, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.50 tff(129,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, X)) | (~between(V, W, X))) | between(U, W, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b8')).
% 0.20/0.50 tff(130,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.50 tff(131,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.20/0.50 tff(132,plain,(
% 0.20/0.50 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[131])).
% 0.20/0.50 tff(133,plain,
% 0.20/0.50 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.20/0.50 tff(134,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(c, a, b)) | (~between(a, insertion(a, b, a, d), b)) | between(c, insertion(a, b, a, d), b))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(c, a, b)) | (~between(a, insertion(a, b, a, d), b)) | between(c, insertion(a, b, a, d), b))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(135,plain,
% 0.20/0.50 (((~between(c, a, b)) | between(c, insertion(a, b, a, d), b) | (~between(a, insertion(a, b, a, d), b))) <=> ((~between(c, a, b)) | (~between(a, insertion(a, b, a, d), b)) | between(c, insertion(a, b, a, d), b))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(136,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(c, a, b)) | between(c, insertion(a, b, a, d), b) | (~between(a, insertion(a, b, a, d), b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(c, a, b)) | (~between(a, insertion(a, b, a, d), b)) | between(c, insertion(a, b, a, d), b)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[135])).
% 0.20/0.50 tff(137,plain,
% 0.20/0.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(c, a, b)) | between(c, insertion(a, b, a, d), b) | (~between(a, insertion(a, b, a, d), b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(c, a, b)) | (~between(a, insertion(a, b, a, d), b)) | between(c, insertion(a, b, a, d), b))),
% 0.20/0.50 inference(transitivity,[status(thm)],[136, 134])).
% 0.20/0.50 tff(138,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(c, a, b)) | between(c, insertion(a, b, a, d), b) | (~between(a, insertion(a, b, a, d), b)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(139,plain,
% 0.20/0.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(c, a, b)) | (~between(a, insertion(a, b, a, d), b)) | between(c, insertion(a, b, a, d), b)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[139, 133, 123, 55, 52])).
% 0.20/0.50 tff(141,plain,((~between(a, d, b)) | between(c, d, b) | between(d, b, c) | between(d, c, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(142,plain,
% 0.20/0.51 (~between(a, d, b)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[141, 34, 23, 12])).
% 0.20/0.51 tff(143,plain,
% 0.20/0.51 (^[Z: $i, Y: $i, X: $i] : refl(((~between(X, Y, Z)) | colinear(X, Y, Z)) <=> ((~between(X, Y, Z)) | colinear(X, Y, Z)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(144,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[143])).
% 0.20/0.51 tff(145,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(146,axiom,(![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax','colinearity1')).
% 0.20/0.51 tff(147,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.51 tff(148,plain,(
% 0.20/0.51 ![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 0.20/0.51 inference(skolemize,[status(sab)],[147])).
% 0.20/0.51 tff(149,plain,
% 0.20/0.51 (![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.20/0.51 tff(150,plain,
% 0.20/0.51 (((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(b, c, d)) | colinear(b, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(b, c, d)) | colinear(b, c, d))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(151,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(b, c, d)) | colinear(b, c, d))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(152,plain,
% 0.20/0.51 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(b, c, d)) | colinear(b, c, d)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.51 tff(153,plain,
% 0.20/0.51 (~between(b, c, d)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[152, 149, 1])).
% 0.20/0.51 tff(154,plain,
% 0.20/0.51 (^[W: $i, V: $i, U: $i] : refl(((~between(V, U, W)) | colinear(U, V, W)) <=> ((~between(V, U, W)) | colinear(U, V, W)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(155,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[154])).
% 0.20/0.51 tff(156,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(157,axiom,(![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c2_3')).
% 0.20/0.51 tff(158,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.51 tff(159,plain,(
% 0.20/0.51 ![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.20/0.51 inference(skolemize,[status(sab)],[158])).
% 0.20/0.51 tff(160,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.20/0.51 tff(161,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(c, b, d)) | colinear(b, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(c, b, d)) | colinear(b, c, d))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(162,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(c, b, d)) | colinear(b, c, d))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(163,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(c, b, d)) | colinear(b, c, d)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.51 tff(164,plain,
% 0.20/0.51 (~between(c, b, d)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[163, 160, 1])).
% 0.20/0.51 tff(165,assumption,(~between(a, d, b)), introduced(assumption)).
% 0.20/0.51 tff(166,assumption,(between(a, b, c)), introduced(assumption)).
% 0.20/0.51 tff(167,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(a, b, c)) | (b = insertion(a, c, a, b)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(a, b, c)) | (b = insertion(a, c, a, b)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(168,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(a, b, c)) | (b = insertion(a, c, a, b)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(169,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(a, b, c)) | (b = insertion(a, c, a, b))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.51 tff(170,plain,
% 0.20/0.51 (b = insertion(a, c, a, b)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[169, 42, 166])).
% 0.20/0.51 tff(171,plain,
% 0.20/0.51 (insertion(a, c, a, b) = b),
% 0.20/0.51 inference(symmetry,[status(thm)],[170])).
% 0.20/0.51 tff(172,plain,
% 0.20/0.51 (between(d, insertion(a, c, a, b), a) <=> between(d, b, a)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.51 tff(173,plain,
% 0.20/0.51 ((~between(d, insertion(a, c, a, b), a)) <=> (~between(d, b, a))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[172])).
% 0.20/0.51 tff(174,plain,
% 0.20/0.51 ((~(a = b)) <=> (~(a = b))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(175,axiom,(~(a = b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_not_b')).
% 0.20/0.51 tff(176,plain,
% 0.20/0.51 (~(a = b)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.51 tff(177,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(178,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[177])).
% 0.20/0.51 tff(179,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(180,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(181,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[180])).
% 0.20/0.51 tff(182,axiom,(![W: $i, V: $i, U: $i] : (((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_1')).
% 0.20/0.51 tff(183,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.51 tff(184,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.20/0.51 tff(185,plain,(
% 0.20/0.51 ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[184])).
% 0.20/0.51 tff(186,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.20/0.51 tff(187,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((a = b) | (~between(a, b, c)) | (c = extension(a, b, b, c)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (a = b) | (~between(a, b, c)) | (c = extension(a, b, b, c)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(188,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((a = b) | (~between(a, b, c)) | (c = extension(a, b, b, c)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(189,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (a = b) | (~between(a, b, c)) | (c = extension(a, b, b, c))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.20/0.51 tff(190,plain,
% 0.20/0.51 (c = extension(a, b, b, c)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[189, 186, 176, 166])).
% 0.20/0.51 tff(191,plain,
% 0.20/0.51 (extension(a, b, b, c) = c),
% 0.20/0.51 inference(symmetry,[status(thm)],[190])).
% 0.20/0.51 tff(192,plain,
% 0.20/0.51 (between(d, extension(a, b, b, c), insertion(a, c, a, b)) <=> between(d, c, b)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[191, 171])).
% 0.20/0.51 tff(193,plain,
% 0.20/0.51 (between(d, c, b) <=> between(d, extension(a, b, b, c), insertion(a, c, a, b))),
% 0.20/0.51 inference(symmetry,[status(thm)],[192])).
% 0.20/0.51 tff(194,plain,
% 0.20/0.51 ((~between(d, c, b)) <=> (~between(d, extension(a, b, b, c), insertion(a, c, a, b)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[193])).
% 0.20/0.51 tff(195,plain,
% 0.20/0.51 (~between(d, extension(a, b, b, c), insertion(a, c, a, b))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[74, 194])).
% 0.20/0.51 tff(196,plain,
% 0.20/0.51 (between(extension(a, b, b, c), d, insertion(a, c, a, b)) <=> between(c, d, b)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[191, 171])).
% 0.20/0.51 tff(197,plain,
% 0.20/0.51 (between(c, d, b) <=> between(extension(a, b, b, c), d, insertion(a, c, a, b))),
% 0.20/0.51 inference(symmetry,[status(thm)],[196])).
% 0.20/0.51 tff(198,plain,
% 0.20/0.51 ((~between(c, d, b)) <=> (~between(extension(a, b, b, c), d, insertion(a, c, a, b)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[197])).
% 0.20/0.51 tff(199,plain,
% 0.20/0.51 (~between(extension(a, b, b, c), d, insertion(a, c, a, b))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[51, 198])).
% 0.20/0.51 tff(200,plain,
% 0.20/0.51 (between(extension(a, b, b, c), insertion(a, c, a, b), a) <=> between(c, b, a)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[191, 171])).
% 0.20/0.51 tff(201,plain,
% 0.20/0.51 (between(c, b, a) <=> between(extension(a, b, b, c), insertion(a, c, a, b), a)),
% 0.20/0.51 inference(symmetry,[status(thm)],[200])).
% 0.20/0.51 tff(202,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(a, b, c)) | between(c, b, a))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(a, b, c)) | between(c, b, a))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(203,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(a, b, c)) | between(c, b, a))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(204,plain,
% 0.20/0.51 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(a, b, c)) | between(c, b, a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.51 tff(205,plain,
% 0.20/0.51 (between(c, b, a)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[204, 98, 166])).
% 0.20/0.51 tff(206,plain,
% 0.20/0.51 (between(extension(a, b, b, c), insertion(a, c, a, b), a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.20/0.51 tff(207,plain,
% 0.20/0.51 ((b = a) <=> (a = b)),
% 0.20/0.51 inference(commutativity,[status(thm)],[])).
% 0.20/0.51 tff(208,plain,
% 0.20/0.51 ((insertion(a, c, a, b) = a) <=> (b = a)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.51 tff(209,plain,
% 0.20/0.51 ((insertion(a, c, a, b) = a) <=> (a = b)),
% 0.20/0.51 inference(transitivity,[status(thm)],[208, 207])).
% 0.20/0.51 tff(210,plain,
% 0.20/0.51 ((a = b) <=> (insertion(a, c, a, b) = a)),
% 0.20/0.51 inference(symmetry,[status(thm)],[209])).
% 0.20/0.51 tff(211,plain,
% 0.20/0.51 ((~(a = b)) <=> (~(insertion(a, c, a, b) = a))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[210])).
% 0.20/0.51 tff(212,plain,
% 0.20/0.51 (~(insertion(a, c, a, b) = a)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[176, 211])).
% 0.20/0.51 tff(213,plain,
% 0.20/0.51 (^[W: $i, V: $i, U: $i, X: $i] : refl(((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W)) <=> ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(214,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[213])).
% 0.20/0.51 tff(215,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(216,plain,
% 0.20/0.51 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) <=> ((W = X) | (~between(U, W, X)) | (~between(V, W, X)))), (((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) <=> (((W = X) | (~between(U, W, X)) | (~between(V, W, X))) | between(U, V, W)))), rewrite((((W = X) | (~between(U, W, X)) | (~between(V, W, X))) | between(U, V, W)) <=> ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)))), (((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) <=> ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X))))), ((((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) | between(V, U, W)) <=> (((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X))) | between(V, U, W)))), rewrite((((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X))) | between(V, U, W)) <=> ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))), ((((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) | between(V, U, W)) <=> ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(217,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) | between(V, U, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[216])).
% 0.20/0.51 tff(218,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, W, X)) | (~between(V, W, X))) | (W = X)) | between(U, V, W)) | between(V, U, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7')).
% 0.20/0.51 tff(219,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.51 tff(220,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.20/0.51 tff(221,plain,(
% 0.20/0.51 ![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 0.20/0.51 inference(skolemize,[status(sab)],[220])).
% 0.20/0.51 tff(222,plain,
% 0.20/0.51 (![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.20/0.51 tff(223,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | ((~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), d, insertion(a, c, a, b)) | (~between(d, insertion(a, c, a, b), a)) | between(d, extension(a, b, b, c), insertion(a, c, a, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), d, insertion(a, c, a, b)) | (~between(d, insertion(a, c, a, b), a)) | between(d, extension(a, b, b, c), insertion(a, c, a, b)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(224,plain,
% 0.20/0.51 (((insertion(a, c, a, b) = a) | between(extension(a, b, b, c), d, insertion(a, c, a, b)) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (~between(d, insertion(a, c, a, b), a)) | between(d, extension(a, b, b, c), insertion(a, c, a, b))) <=> ((~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), d, insertion(a, c, a, b)) | (~between(d, insertion(a, c, a, b), a)) | between(d, extension(a, b, b, c), insertion(a, c, a, b)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(225,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | ((insertion(a, c, a, b) = a) | between(extension(a, b, b, c), d, insertion(a, c, a, b)) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (~between(d, insertion(a, c, a, b), a)) | between(d, extension(a, b, b, c), insertion(a, c, a, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | ((~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), d, insertion(a, c, a, b)) | (~between(d, insertion(a, c, a, b), a)) | between(d, extension(a, b, b, c), insertion(a, c, a, b))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[224])).
% 0.20/0.51 tff(226,plain,
% 0.20/0.51 (((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | ((insertion(a, c, a, b) = a) | between(extension(a, b, b, c), d, insertion(a, c, a, b)) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (~between(d, insertion(a, c, a, b), a)) | between(d, extension(a, b, b, c), insertion(a, c, a, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), d, insertion(a, c, a, b)) | (~between(d, insertion(a, c, a, b), a)) | between(d, extension(a, b, b, c), insertion(a, c, a, b)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[225, 223])).
% 0.20/0.52 tff(227,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | ((insertion(a, c, a, b) = a) | between(extension(a, b, b, c), d, insertion(a, c, a, b)) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (~between(d, insertion(a, c, a, b), a)) | between(d, extension(a, b, b, c), insertion(a, c, a, b)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(228,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((W = X) | between(U, V, W) | (~between(U, W, X)) | (~between(V, W, X)) | between(V, U, W))) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), d, insertion(a, c, a, b)) | (~between(d, insertion(a, c, a, b), a)) | between(d, extension(a, b, b, c), insertion(a, c, a, b))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.20/0.52 tff(229,plain,
% 0.20/0.52 ((~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), d, insertion(a, c, a, b)) | (~between(d, insertion(a, c, a, b), a)) | between(d, extension(a, b, b, c), insertion(a, c, a, b))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[228, 222])).
% 0.20/0.52 tff(230,plain,
% 0.20/0.52 (~between(d, insertion(a, c, a, b), a)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[229, 212, 206, 199, 195])).
% 0.20/0.52 tff(231,plain,
% 0.20/0.52 (~between(d, b, a)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[230, 173])).
% 0.20/0.52 tff(232,plain,
% 0.20/0.52 (between(insertion(a, c, a, b), a, d) <=> between(b, a, d)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.52 tff(233,plain,
% 0.20/0.52 ((~between(insertion(a, c, a, b), a, d)) <=> (~between(b, a, d))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[232])).
% 0.20/0.52 tff(234,plain,
% 0.20/0.52 (between(extension(a, b, b, c), insertion(a, c, a, b), d) <=> between(c, b, d)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[191, 171])).
% 0.20/0.52 tff(235,plain,
% 0.20/0.52 (between(c, b, d) <=> between(extension(a, b, b, c), insertion(a, c, a, b), d)),
% 0.20/0.52 inference(symmetry,[status(thm)],[234])).
% 0.20/0.52 tff(236,plain,
% 0.20/0.52 ((~between(c, b, d)) <=> (~between(extension(a, b, b, c), insertion(a, c, a, b), d))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[235])).
% 0.20/0.52 tff(237,assumption,(~between(c, b, d)), introduced(assumption)).
% 0.20/0.52 tff(238,plain,
% 0.20/0.52 (~between(extension(a, b, b, c), insertion(a, c, a, b), d)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.20/0.52 tff(239,plain,
% 0.20/0.52 (^[W: $i, V: $i, U: $i, X: $i] : refl((between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W)) <=> (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(240,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[239])).
% 0.20/0.52 tff(241,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(242,plain,
% 0.20/0.52 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~between(U, V, W)) | (~between(V, W, X))) | between(U, V, X)) <=> (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)))), (((((~between(U, V, W)) | (~between(V, W, X))) | between(U, V, X)) | (V = W)) <=> ((between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X))) | (V = W)))), rewrite(((between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X))) | (V = W)) <=> (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))), (((((~between(U, V, W)) | (~between(V, W, X))) | between(U, V, X)) | (V = W)) <=> (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(243,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, W)) | (~between(V, W, X))) | between(U, V, X)) | (V = W)) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[242])).
% 0.20/0.52 tff(244,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, W)) | (~between(V, W, X))) | between(U, V, X)) | (V = W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b7')).
% 0.20/0.52 tff(245,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.20/0.52 tff(246,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[245, 241])).
% 0.20/0.52 tff(247,plain,(
% 0.20/0.52 ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.20/0.52 inference(skolemize,[status(sab)],[246])).
% 0.20/0.52 tff(248,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[247, 240])).
% 0.20/0.52 tff(249,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | ((~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), insertion(a, c, a, b), d) | (~between(insertion(a, c, a, b), a, d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), insertion(a, c, a, b), d) | (~between(insertion(a, c, a, b), a, d)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(250,plain,
% 0.20/0.52 ((between(extension(a, b, b, c), insertion(a, c, a, b), d) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (~between(insertion(a, c, a, b), a, d)) | (insertion(a, c, a, b) = a)) <=> ((~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), insertion(a, c, a, b), d) | (~between(insertion(a, c, a, b), a, d)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(251,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (between(extension(a, b, b, c), insertion(a, c, a, b), d) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (~between(insertion(a, c, a, b), a, d)) | (insertion(a, c, a, b) = a))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | ((~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), insertion(a, c, a, b), d) | (~between(insertion(a, c, a, b), a, d))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[250])).
% 0.20/0.52 tff(252,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (between(extension(a, b, b, c), insertion(a, c, a, b), d) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (~between(insertion(a, c, a, b), a, d)) | (insertion(a, c, a, b) = a))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), insertion(a, c, a, b), d) | (~between(insertion(a, c, a, b), a, d)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[251, 249])).
% 0.20/0.52 tff(253,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (between(extension(a, b, b, c), insertion(a, c, a, b), d) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (~between(insertion(a, c, a, b), a, d)) | (insertion(a, c, a, b) = a))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(254,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), insertion(a, c, a, b), d) | (~between(insertion(a, c, a, b), a, d))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.20/0.52 tff(255,plain,
% 0.20/0.52 ((~between(extension(a, b, b, c), insertion(a, c, a, b), a)) | (insertion(a, c, a, b) = a) | between(extension(a, b, b, c), insertion(a, c, a, b), d) | (~between(insertion(a, c, a, b), a, d))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[254, 248])).
% 0.20/0.52 tff(256,plain,
% 0.20/0.52 (~between(insertion(a, c, a, b), a, d)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[255, 212, 238, 206])).
% 0.20/0.52 tff(257,plain,
% 0.20/0.52 (~between(b, a, d)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[256, 233])).
% 0.20/0.52 tff(258,plain,
% 0.20/0.52 (colinear(a, b, d) <=> colinear(a, b, d)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(259,axiom,(colinear(a, b, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abd_colinear')).
% 0.20/0.52 tff(260,plain,
% 0.20/0.52 (colinear(a, b, d)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.20/0.52 tff(261,plain,
% 0.20/0.52 (^[W: $i, V: $i, U: $i] : refl(((~colinear(U, V, W)) | colinear(V, U, W)) <=> ((~colinear(U, V, W)) | colinear(V, U, W)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(262,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W)) <=> ![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[261])).
% 0.20/0.52 tff(263,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W)) <=> ![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(264,axiom,(![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t10_5')).
% 0.20/0.52 tff(265,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.20/0.52 tff(266,plain,(
% 0.20/0.52 ![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))),
% 0.20/0.52 inference(skolemize,[status(sab)],[265])).
% 0.20/0.52 tff(267,plain,
% 0.20/0.52 (![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[266, 262])).
% 0.20/0.52 tff(268,plain,
% 0.20/0.52 (((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | ((~colinear(a, b, d)) | colinear(b, a, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | (~colinear(a, b, d)) | colinear(b, a, d))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(269,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | ((~colinear(a, b, d)) | colinear(b, a, d))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(270,plain,
% 0.20/0.52 ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | (~colinear(a, b, d)) | colinear(b, a, d)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.20/0.52 tff(271,plain,
% 0.20/0.52 (colinear(b, a, d)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[270, 267, 260])).
% 0.20/0.52 tff(272,plain,
% 0.20/0.52 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, b, a) | between(a, d, b) | between(b, a, d) | (~colinear(b, a, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(d, b, a) | between(a, d, b) | between(b, a, d) | (~colinear(b, a, d)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(273,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, b, a) | between(a, d, b) | between(b, a, d) | (~colinear(b, a, d)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(274,plain,
% 0.20/0.52 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(d, b, a) | between(a, d, b) | between(b, a, d) | (~colinear(b, a, d))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.52 tff(275,plain,
% 0.20/0.52 (between(d, b, a) | between(a, d, b) | between(b, a, d)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[274, 115, 271])).
% 0.20/0.53 tff(276,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[275, 257, 231, 165])).
% 0.20/0.53 tff(277,plain,((~between(a, b, c)) | between(a, d, b) | between(d, c, b) | between(c, d, b) | between(c, b, d)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(278,plain,
% 0.20/0.53 (~between(a, b, c)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[277, 142, 12, 34, 164])).
% 0.20/0.53 tff(279,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(c, b, a)) | between(a, b, c))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(c, b, a)) | between(a, b, c))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(280,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(c, b, a)) | between(a, b, c))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(281,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(c, b, a)) | between(a, b, c)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.20/0.53 tff(282,plain,
% 0.20/0.53 (~between(c, b, a)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[281, 98, 278])).
% 0.20/0.53 tff(283,plain,
% 0.20/0.53 (^[W: $i, V: $i, U: $i] : refl(((~between(U, W, V)) | colinear(U, V, W)) <=> ((~between(U, W, V)) | colinear(U, V, W)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(284,plain,
% 0.20/0.53 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[283])).
% 0.20/0.53 tff(285,plain,
% 0.20/0.53 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W)) <=> ![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(286,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c2_2')).
% 0.20/0.53 tff(287,plain,
% 0.20/0.53 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.20/0.53 tff(288,plain,(
% 0.20/0.53 ![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.20/0.53 inference(skolemize,[status(sab)],[287])).
% 0.20/0.53 tff(289,plain,
% 0.20/0.53 (![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[288, 284])).
% 0.20/0.53 tff(290,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(b, d, c)) | colinear(b, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(b, d, c)) | colinear(b, c, d))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(291,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(b, d, c)) | colinear(b, c, d))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(292,plain,
% 0.20/0.53 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(b, d, c)) | colinear(b, c, d)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.20/0.53 tff(293,plain,
% 0.20/0.53 (~between(b, d, c)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[292, 289, 1])).
% 0.20/0.53 tff(294,plain,
% 0.20/0.53 ((a = b) <=> (b = a)),
% 0.20/0.53 inference(symmetry,[status(thm)],[207])).
% 0.20/0.53 tff(295,plain,
% 0.20/0.53 ((~(a = b)) <=> (~(b = a))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[294])).
% 0.20/0.53 tff(296,plain,
% 0.20/0.53 (~(b = a)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[176, 295])).
% 0.20/0.53 tff(297,assumption,(between(b, a, d)), introduced(assumption)).
% 0.20/0.53 tff(298,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((d = extension(b, a, a, d)) | (b = a) | (~between(b, a, d)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (d = extension(b, a, a, d)) | (b = a) | (~between(b, a, d)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(299,plain,
% 0.20/0.53 (((b = a) | (~between(b, a, d)) | (d = extension(b, a, a, d))) <=> ((d = extension(b, a, a, d)) | (b = a) | (~between(b, a, d)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(300,plain,
% 0.20/0.53 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((b = a) | (~between(b, a, d)) | (d = extension(b, a, a, d)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((d = extension(b, a, a, d)) | (b = a) | (~between(b, a, d))))),
% 0.43/0.53 inference(monotonicity,[status(thm)],[299])).
% 0.43/0.53 tff(301,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((b = a) | (~between(b, a, d)) | (d = extension(b, a, a, d)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (d = extension(b, a, a, d)) | (b = a) | (~between(b, a, d)))),
% 0.43/0.53 inference(transitivity,[status(thm)],[300, 298])).
% 0.43/0.53 tff(302,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((b = a) | (~between(b, a, d)) | (d = extension(b, a, a, d)))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(303,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (d = extension(b, a, a, d)) | (b = a) | (~between(b, a, d))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.43/0.53 tff(304,plain,
% 0.43/0.53 ((d = extension(b, a, a, d)) | (b = a)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[303, 186, 297])).
% 0.43/0.53 tff(305,plain,
% 0.43/0.53 (d = extension(b, a, a, d)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[304, 296])).
% 0.43/0.53 tff(306,plain,
% 0.43/0.53 (extension(b, a, a, d) = d),
% 0.43/0.53 inference(symmetry,[status(thm)],[305])).
% 0.43/0.53 tff(307,plain,
% 0.43/0.53 (between(b, extension(b, a, a, d), c) <=> between(b, d, c)),
% 0.43/0.53 inference(monotonicity,[status(thm)],[306])).
% 0.43/0.53 tff(308,plain,
% 0.43/0.53 (between(b, d, c) <=> between(b, extension(b, a, a, d), c)),
% 0.43/0.53 inference(symmetry,[status(thm)],[307])).
% 0.43/0.53 tff(309,plain,
% 0.43/0.53 ((~between(b, d, c)) <=> (~between(b, extension(b, a, a, d), c))),
% 0.43/0.53 inference(monotonicity,[status(thm)],[308])).
% 0.43/0.53 tff(310,assumption,(~between(b, d, c)), introduced(assumption)).
% 0.43/0.53 tff(311,plain,
% 0.43/0.53 (~between(b, extension(b, a, a, d), c)),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.43/0.53 tff(312,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(b, a, d)) | (a = insertion(b, d, b, a)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(b, a, d)) | (a = insertion(b, d, b, a)))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(313,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(b, a, d)) | (a = insertion(b, d, b, a)))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(314,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(b, a, d)) | (a = insertion(b, d, b, a))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.43/0.53 tff(315,plain,
% 0.43/0.53 (a = insertion(b, d, b, a)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[314, 42, 297])).
% 0.43/0.53 tff(316,plain,
% 0.43/0.53 (insertion(b, d, b, a) = a),
% 0.43/0.53 inference(symmetry,[status(thm)],[315])).
% 0.43/0.53 tff(317,plain,
% 0.43/0.53 (between(b, insertion(b, d, b, a), c) <=> between(b, a, c)),
% 0.43/0.53 inference(monotonicity,[status(thm)],[316])).
% 0.43/0.53 tff(318,plain,
% 0.43/0.53 (between(b, a, c) <=> between(b, insertion(b, d, b, a), c)),
% 0.43/0.53 inference(symmetry,[status(thm)],[317])).
% 0.43/0.53 tff(319,assumption,(~between(c, b, a)), introduced(assumption)).
% 0.43/0.53 tff(320,plain,
% 0.43/0.53 (between(insertion(b, d, b, a), c, b) <=> between(a, c, b)),
% 0.43/0.53 inference(monotonicity,[status(thm)],[316])).
% 0.43/0.53 tff(321,plain,
% 0.43/0.53 ((~between(insertion(b, d, b, a), c, b)) <=> (~between(a, c, b))),
% 0.43/0.53 inference(monotonicity,[status(thm)],[320])).
% 0.43/0.53 tff(322,plain,
% 0.43/0.53 (between(d, insertion(b, d, b, a), b) <=> between(d, a, b)),
% 0.43/0.53 inference(monotonicity,[status(thm)],[316])).
% 0.43/0.53 tff(323,plain,
% 0.43/0.53 (between(d, a, b) <=> between(d, insertion(b, d, b, a), b)),
% 0.43/0.53 inference(symmetry,[status(thm)],[322])).
% 0.43/0.53 tff(324,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, a, d)) | between(d, a, b))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, a, d)) | between(d, a, b))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(325,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, a, d)) | between(d, a, b))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(326,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, a, d)) | between(d, a, b)),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.43/0.53 tff(327,plain,
% 0.43/0.53 (between(d, a, b)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[326, 98, 297])).
% 0.43/0.53 tff(328,plain,
% 0.43/0.53 (between(d, insertion(b, d, b, a), b)),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[327, 323])).
% 0.43/0.53 tff(329,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (between(d, c, b) | (~between(d, insertion(b, d, b, a), b)) | (~between(insertion(b, d, b, a), c, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | between(d, c, b) | (~between(d, insertion(b, d, b, a), b)) | (~between(insertion(b, d, b, a), c, b)))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(330,plain,
% 0.43/0.53 (((~between(d, insertion(b, d, b, a), b)) | between(d, c, b) | (~between(insertion(b, d, b, a), c, b))) <=> (between(d, c, b) | (~between(d, insertion(b, d, b, a), b)) | (~between(insertion(b, d, b, a), c, b)))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(331,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(d, insertion(b, d, b, a), b)) | between(d, c, b) | (~between(insertion(b, d, b, a), c, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (between(d, c, b) | (~between(d, insertion(b, d, b, a), b)) | (~between(insertion(b, d, b, a), c, b))))),
% 0.43/0.53 inference(monotonicity,[status(thm)],[330])).
% 0.43/0.53 tff(332,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(d, insertion(b, d, b, a), b)) | between(d, c, b) | (~between(insertion(b, d, b, a), c, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | between(d, c, b) | (~between(d, insertion(b, d, b, a), b)) | (~between(insertion(b, d, b, a), c, b)))),
% 0.43/0.53 inference(transitivity,[status(thm)],[331, 329])).
% 0.43/0.53 tff(333,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(d, insertion(b, d, b, a), b)) | between(d, c, b) | (~between(insertion(b, d, b, a), c, b)))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(334,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | between(d, c, b) | (~between(d, insertion(b, d, b, a), b)) | (~between(insertion(b, d, b, a), c, b))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.43/0.53 tff(335,plain,
% 0.43/0.53 ((~between(d, insertion(b, d, b, a), b)) | (~between(insertion(b, d, b, a), c, b))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[334, 133, 74])).
% 0.43/0.53 tff(336,plain,
% 0.43/0.53 (~between(insertion(b, d, b, a), c, b)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[335, 328])).
% 0.43/0.53 tff(337,plain,
% 0.43/0.53 (~between(a, c, b)),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[336, 321])).
% 0.43/0.53 tff(338,plain,
% 0.43/0.53 (((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | ((~colinear(a, b, c)) | colinear(b, a, c))) <=> ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | (~colinear(a, b, c)) | colinear(b, a, c))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(339,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | ((~colinear(a, b, c)) | colinear(b, a, c))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(340,plain,
% 0.43/0.53 ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | (~colinear(a, b, c)) | colinear(b, a, c)),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.43/0.53 tff(341,plain,
% 0.43/0.53 (colinear(b, a, c)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[340, 267, 105])).
% 0.43/0.53 tff(342,plain,
% 0.43/0.53 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(c, b, a) | between(a, c, b) | between(b, a, c) | (~colinear(b, a, c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(c, b, a) | between(a, c, b) | between(b, a, c) | (~colinear(b, a, c)))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(343,plain,
% 0.43/0.53 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(c, b, a) | between(a, c, b) | between(b, a, c) | (~colinear(b, a, c)))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(344,plain,
% 0.43/0.53 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | between(c, b, a) | between(a, c, b) | between(b, a, c) | (~colinear(b, a, c))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.43/0.53 tff(345,plain,
% 0.43/0.53 (between(c, b, a) | between(a, c, b) | between(b, a, c)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[344, 115, 341])).
% 0.43/0.53 tff(346,plain,
% 0.43/0.53 (between(b, a, c)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[345, 337, 319])).
% 0.43/0.53 tff(347,plain,
% 0.43/0.53 (between(b, insertion(b, d, b, a), c)),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[346, 318])).
% 0.43/0.53 tff(348,plain,
% 0.43/0.53 (between(b, insertion(b, d, b, a), extension(b, a, a, d)) <=> between(b, a, d)),
% 0.43/0.53 inference(monotonicity,[status(thm)],[316, 306])).
% 0.43/0.53 tff(349,plain,
% 0.43/0.53 (between(b, a, d) <=> between(b, insertion(b, d, b, a), extension(b, a, a, d))),
% 0.43/0.53 inference(symmetry,[status(thm)],[348])).
% 0.43/0.53 tff(350,plain,
% 0.43/0.53 (between(b, insertion(b, d, b, a), extension(b, a, a, d))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[297, 349])).
% 0.43/0.53 tff(351,plain,
% 0.43/0.53 (between(b, c, extension(b, a, a, d)) <=> between(b, c, d)),
% 0.43/0.53 inference(monotonicity,[status(thm)],[306])).
% 0.43/0.53 tff(352,plain,
% 0.43/0.53 (between(b, c, d) <=> between(b, c, extension(b, a, a, d))),
% 0.43/0.53 inference(symmetry,[status(thm)],[351])).
% 0.43/0.53 tff(353,plain,
% 0.43/0.53 ((~between(b, c, d)) <=> (~between(b, c, extension(b, a, a, d)))),
% 0.43/0.53 inference(monotonicity,[status(thm)],[352])).
% 0.43/0.53 tff(354,assumption,(~between(b, c, d)), introduced(assumption)).
% 0.43/0.53 tff(355,plain,
% 0.43/0.53 (~between(b, c, extension(b, a, a, d))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.43/0.53 tff(356,plain,
% 0.43/0.53 ((b = insertion(b, d, b, a)) <=> (b = a)),
% 0.43/0.53 inference(monotonicity,[status(thm)],[316])).
% 0.43/0.53 tff(357,plain,
% 0.43/0.53 ((b = insertion(b, d, b, a)) <=> (a = b)),
% 0.43/0.53 inference(transitivity,[status(thm)],[356, 207])).
% 0.43/0.53 tff(358,plain,
% 0.43/0.53 ((a = b) <=> (b = insertion(b, d, b, a))),
% 0.43/0.53 inference(symmetry,[status(thm)],[357])).
% 0.43/0.53 tff(359,plain,
% 0.43/0.53 ((~(a = b)) <=> (~(b = insertion(b, d, b, a)))),
% 0.43/0.53 inference(monotonicity,[status(thm)],[358])).
% 0.43/0.53 tff(360,plain,
% 0.43/0.53 (~(b = insertion(b, d, b, a))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[176, 359])).
% 0.43/0.53 tff(361,plain,
% 0.43/0.53 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W)))),
% 0.43/0.53 inference(bind,[status(th)],[])).
% 0.43/0.53 tff(362,plain,
% 0.43/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 0.43/0.53 inference(quant_intro,[status(thm)],[361])).
% 0.43/0.53 tff(363,plain,
% 0.43/0.53 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 0.43/0.53 inference(rewrite,[status(thm)],[])).
% 0.43/0.53 tff(364,plain,
% 0.43/0.53 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~between(U, V, W)) | (~between(U, V, X))) <=> ((~between(U, V, X)) | (~between(U, V, W)))), ((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) <=> (((~between(U, V, X)) | (~between(U, V, W))) | (U = V)))), rewrite((((~between(U, V, X)) | (~between(U, V, W))) | (U = V)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)))), ((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W))))), (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) <=> (((~between(U, V, X)) | (U = V) | (~between(U, V, W))) | between(U, W, X)))), rewrite((((~between(U, V, X)) | (U = V) | (~between(U, V, W))) | between(U, W, X)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X))), (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X)))), ((((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) | between(U, X, W)) <=> (((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X)) | between(U, X, W)))), rewrite((((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X)) | between(U, X, W)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))), ((((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) | between(U, X, W)) <=> ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))))),
% 0.43/0.54 inference(bind,[status(th)],[])).
% 0.43/0.54 tff(365,plain,
% 0.43/0.54 (![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) | between(U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 0.43/0.54 inference(quant_intro,[status(thm)],[364])).
% 0.43/0.54 tff(366,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((~between(U, V, W)) | (~between(U, V, X))) | (U = V)) | between(U, W, X)) | between(U, X, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b12')).
% 0.43/0.54 tff(367,plain,
% 0.43/0.54 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.43/0.54 tff(368,plain,
% 0.43/0.54 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[367, 363])).
% 0.43/0.54 tff(369,plain,(
% 0.43/0.54 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 0.43/0.54 inference(skolemize,[status(sab)],[368])).
% 0.43/0.54 tff(370,plain,
% 0.43/0.54 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[369, 362])).
% 0.43/0.54 tff(371,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((b = insertion(b, d, b, a)) | between(b, c, extension(b, a, a, d)) | (~between(b, insertion(b, d, b, a), c)) | (~between(b, insertion(b, d, b, a), extension(b, a, a, d))) | between(b, extension(b, a, a, d), c))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | (b = insertion(b, d, b, a)) | between(b, c, extension(b, a, a, d)) | (~between(b, insertion(b, d, b, a), c)) | (~between(b, insertion(b, d, b, a), extension(b, a, a, d))) | between(b, extension(b, a, a, d), c))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(372,plain,
% 0.43/0.54 (((~between(b, insertion(b, d, b, a), extension(b, a, a, d))) | (b = insertion(b, d, b, a)) | (~between(b, insertion(b, d, b, a), c)) | between(b, c, extension(b, a, a, d)) | between(b, extension(b, a, a, d), c)) <=> ((b = insertion(b, d, b, a)) | between(b, c, extension(b, a, a, d)) | (~between(b, insertion(b, d, b, a), c)) | (~between(b, insertion(b, d, b, a), extension(b, a, a, d))) | between(b, extension(b, a, a, d), c))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(373,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((~between(b, insertion(b, d, b, a), extension(b, a, a, d))) | (b = insertion(b, d, b, a)) | (~between(b, insertion(b, d, b, a), c)) | between(b, c, extension(b, a, a, d)) | between(b, extension(b, a, a, d), c))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((b = insertion(b, d, b, a)) | between(b, c, extension(b, a, a, d)) | (~between(b, insertion(b, d, b, a), c)) | (~between(b, insertion(b, d, b, a), extension(b, a, a, d))) | between(b, extension(b, a, a, d), c)))),
% 0.43/0.54 inference(monotonicity,[status(thm)],[372])).
% 0.43/0.54 tff(374,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((~between(b, insertion(b, d, b, a), extension(b, a, a, d))) | (b = insertion(b, d, b, a)) | (~between(b, insertion(b, d, b, a), c)) | between(b, c, extension(b, a, a, d)) | between(b, extension(b, a, a, d), c))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | (b = insertion(b, d, b, a)) | between(b, c, extension(b, a, a, d)) | (~between(b, insertion(b, d, b, a), c)) | (~between(b, insertion(b, d, b, a), extension(b, a, a, d))) | between(b, extension(b, a, a, d), c))),
% 0.43/0.54 inference(transitivity,[status(thm)],[373, 371])).
% 0.43/0.54 tff(375,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((~between(b, insertion(b, d, b, a), extension(b, a, a, d))) | (b = insertion(b, d, b, a)) | (~between(b, insertion(b, d, b, a), c)) | between(b, c, extension(b, a, a, d)) | between(b, extension(b, a, a, d), c))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(376,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | (b = insertion(b, d, b, a)) | between(b, c, extension(b, a, a, d)) | (~between(b, insertion(b, d, b, a), c)) | (~between(b, insertion(b, d, b, a), extension(b, a, a, d))) | between(b, extension(b, a, a, d), c)),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.43/0.54 tff(377,plain,
% 0.43/0.54 ((~between(b, insertion(b, d, b, a), c)) | (~between(b, insertion(b, d, b, a), extension(b, a, a, d))) | between(b, extension(b, a, a, d), c)),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[376, 370, 360, 355])).
% 0.43/0.54 tff(378,plain,
% 0.43/0.54 ($false),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[377, 350, 347, 311])).
% 0.43/0.54 tff(379,plain,((~between(b, a, d)) | between(b, d, c) | between(c, b, a) | between(b, c, d) | between(d, c, b)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.54 tff(380,plain,
% 0.43/0.54 (~between(b, a, d)),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[379, 293, 282, 153, 12])).
% 0.43/0.54 tff(381,plain,
% 0.43/0.54 (between(d, b, a)),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[275, 380, 142])).
% 0.43/0.54 tff(382,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(d, b, a)) | (b = insertion(d, a, d, b)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(d, b, a)) | (b = insertion(d, a, d, b)))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(383,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(d, b, a)) | (b = insertion(d, a, d, b)))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(384,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(d, b, a)) | (b = insertion(d, a, d, b))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.43/0.54 tff(385,plain,
% 0.43/0.54 (b = insertion(d, a, d, b)),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[384, 42, 381])).
% 0.43/0.54 tff(386,plain,
% 0.43/0.54 (insertion(d, a, d, b) = b),
% 0.43/0.54 inference(symmetry,[status(thm)],[385])).
% 0.43/0.54 tff(387,plain,
% 0.43/0.54 ((d = b) <=> (b = d)),
% 0.43/0.54 inference(commutativity,[status(thm)],[])).
% 0.43/0.54 tff(388,plain,
% 0.43/0.54 ((b = d) <=> (d = b)),
% 0.43/0.54 inference(symmetry,[status(thm)],[387])).
% 0.43/0.54 tff(389,plain,
% 0.43/0.54 ((~(b = d)) <=> (~(d = b))),
% 0.43/0.54 inference(monotonicity,[status(thm)],[388])).
% 0.43/0.54 tff(390,plain,
% 0.43/0.54 (^[Z: $i, Y: $i, X: $i] : refl(((~(X = Y)) | colinear(X, Z, Y)) <=> ((~(X = Y)) | colinear(X, Z, Y)))),
% 0.43/0.54 inference(bind,[status(th)],[])).
% 0.43/0.54 tff(391,plain,
% 0.43/0.54 (![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y))),
% 0.43/0.54 inference(quant_intro,[status(thm)],[390])).
% 0.43/0.54 tff(392,plain,
% 0.43/0.54 (![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(393,axiom,(![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c3_4')).
% 0.43/0.54 tff(394,plain,
% 0.43/0.54 (![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.43/0.54 tff(395,plain,(
% 0.43/0.54 ![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y))),
% 0.43/0.54 inference(skolemize,[status(sab)],[394])).
% 0.43/0.54 tff(396,plain,
% 0.43/0.54 (![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[395, 391])).
% 0.43/0.54 tff(397,plain,
% 0.43/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y))) | ((~(b = d)) | colinear(b, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y))) | (~(b = d)) | colinear(b, c, d))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(398,plain,
% 0.43/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y))) | ((~(b = d)) | colinear(b, c, d))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(399,plain,
% 0.43/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~(X = Y)) | colinear(X, Z, Y))) | (~(b = d)) | colinear(b, c, d)),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.43/0.54 tff(400,plain,
% 0.43/0.54 (~(b = d)),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[399, 396, 1])).
% 0.43/0.54 tff(401,plain,
% 0.43/0.54 (~(d = b)),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[400, 389])).
% 0.43/0.54 tff(402,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((d = b) | (a = extension(d, b, b, a)) | (~between(d, b, a)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (d = b) | (a = extension(d, b, b, a)) | (~between(d, b, a)))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(403,plain,
% 0.43/0.54 (((d = b) | (~between(d, b, a)) | (a = extension(d, b, b, a))) <=> ((d = b) | (a = extension(d, b, b, a)) | (~between(d, b, a)))),
% 0.43/0.54 inference(rewrite,[status(thm)],[])).
% 0.43/0.54 tff(404,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((d = b) | (~between(d, b, a)) | (a = extension(d, b, b, a)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((d = b) | (a = extension(d, b, b, a)) | (~between(d, b, a))))),
% 0.43/0.54 inference(monotonicity,[status(thm)],[403])).
% 0.43/0.54 tff(405,plain,
% 0.43/0.54 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((d = b) | (~between(d, b, a)) | (a = extension(d, b, b, a)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (d = b) | (a = extension(d, b, b, a)) | (~between(d, b, a)))),
% 0.43/0.54 inference(transitivity,[status(thm)],[404, 402])).
% 0.43/0.54 tff(406,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((d = b) | (~between(d, b, a)) | (a = extension(d, b, b, a)))),
% 0.43/0.54 inference(quant_inst,[status(thm)],[])).
% 0.43/0.54 tff(407,plain,
% 0.43/0.54 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (d = b) | (a = extension(d, b, b, a)) | (~between(d, b, a))),
% 0.43/0.54 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.43/0.54 tff(408,plain,
% 0.43/0.54 ((d = b) | (a = extension(d, b, b, a))),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[407, 186, 381])).
% 0.43/0.54 tff(409,plain,
% 0.43/0.54 (a = extension(d, b, b, a)),
% 0.43/0.54 inference(unit_resolution,[status(thm)],[408, 401])).
% 0.43/0.54 tff(410,plain,
% 0.43/0.54 (extension(d, b, b, a) = a),
% 0.43/0.54 inference(symmetry,[status(thm)],[409])).
% 0.43/0.54 tff(411,plain,
% 0.43/0.54 (between(extension(d, b, b, a), insertion(d, a, d, b), d) <=> between(a, b, d)),
% 0.43/0.54 inference(monotonicity,[status(thm)],[410, 386])).
% 0.46/0.54 tff(412,plain,
% 0.46/0.54 (between(a, b, d) <=> between(extension(d, b, b, a), insertion(d, a, d, b), d)),
% 0.46/0.54 inference(symmetry,[status(thm)],[411])).
% 0.46/0.54 tff(413,plain,
% 0.46/0.54 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, b, a)) | between(a, b, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, b, a)) | between(a, b, d))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(414,plain,
% 0.46/0.54 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, b, a)) | between(a, b, d))),
% 0.46/0.54 inference(quant_inst,[status(thm)],[])).
% 0.46/0.54 tff(415,plain,
% 0.46/0.54 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, b, a)) | between(a, b, d)),
% 0.46/0.54 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.46/0.54 tff(416,plain,
% 0.46/0.54 (between(a, b, d)),
% 0.46/0.54 inference(unit_resolution,[status(thm)],[415, 98, 381])).
% 0.46/0.54 tff(417,plain,
% 0.46/0.54 (between(extension(d, b, b, a), insertion(d, a, d, b), d)),
% 0.46/0.54 inference(modus_ponens,[status(thm)],[416, 412])).
% 0.46/0.54 tff(418,plain,
% 0.46/0.54 (between(extension(d, b, b, a), c, d) <=> between(a, c, d)),
% 0.46/0.54 inference(monotonicity,[status(thm)],[410])).
% 0.46/0.54 tff(419,plain,
% 0.46/0.54 (between(a, c, d) <=> between(extension(d, b, b, a), c, d)),
% 0.46/0.54 inference(symmetry,[status(thm)],[418])).
% 0.46/0.54 tff(420,plain,
% 0.46/0.54 ((~between(a, c, d)) <=> (~between(extension(d, b, b, a), c, d))),
% 0.46/0.54 inference(monotonicity,[status(thm)],[419])).
% 0.46/0.54 tff(421,plain,
% 0.46/0.54 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X))) <=> ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X))))),
% 0.46/0.54 inference(bind,[status(th)],[])).
% 0.46/0.54 tff(422,plain,
% 0.46/0.54 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 0.46/0.54 inference(quant_intro,[status(thm)],[421])).
% 0.46/0.54 tff(423,plain,
% 0.46/0.54 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(424,plain,
% 0.46/0.54 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~between(U, V, X)) | (~between(U, W, X))) | between(U, V, W)) <=> ((~between(U, V, X)) | between(U, V, W) | (~between(U, W, X)))), (((((~between(U, V, X)) | (~between(U, W, X))) | between(U, V, W)) | between(U, W, V)) <=> (((~between(U, V, X)) | between(U, V, W) | (~between(U, W, X))) | between(U, W, V)))), rewrite((((~between(U, V, X)) | between(U, V, W) | (~between(U, W, X))) | between(U, W, V)) <=> ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))), (((((~between(U, V, X)) | (~between(U, W, X))) | between(U, V, W)) | between(U, W, V)) <=> ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))))),
% 0.46/0.54 inference(bind,[status(th)],[])).
% 0.46/0.54 tff(425,plain,
% 0.46/0.54 (![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, X)) | (~between(U, W, X))) | between(U, V, W)) | between(U, W, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 0.46/0.54 inference(quant_intro,[status(thm)],[424])).
% 0.46/0.54 tff(426,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((((~between(U, V, X)) | (~between(U, W, X))) | between(U, V, W)) | between(U, W, V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t9')).
% 0.46/0.54 tff(427,plain,
% 0.46/0.54 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 0.46/0.54 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.46/0.54 tff(428,plain,
% 0.46/0.54 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 0.46/0.54 inference(modus_ponens,[status(thm)],[427, 423])).
% 0.46/0.54 tff(429,plain,(
% 0.46/0.54 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 0.46/0.55 inference(skolemize,[status(sab)],[428])).
% 0.46/0.55 tff(430,plain,
% 0.46/0.55 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[429, 422])).
% 0.46/0.55 tff(431,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | (between(d, c, b) | between(d, b, c) | (~between(d, c, a)) | (~between(d, b, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | between(d, c, b) | between(d, b, c) | (~between(d, c, a)) | (~between(d, b, a)))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(432,plain,
% 0.46/0.55 (((~between(d, b, a)) | between(d, c, b) | between(d, b, c) | (~between(d, c, a))) <=> (between(d, c, b) | between(d, b, c) | (~between(d, c, a)) | (~between(d, b, a)))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(433,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(d, b, a)) | between(d, c, b) | between(d, b, c) | (~between(d, c, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | (between(d, c, b) | between(d, b, c) | (~between(d, c, a)) | (~between(d, b, a))))),
% 0.46/0.55 inference(monotonicity,[status(thm)],[432])).
% 0.46/0.55 tff(434,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(d, b, a)) | between(d, c, b) | between(d, b, c) | (~between(d, c, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | between(d, c, b) | between(d, b, c) | (~between(d, c, a)) | (~between(d, b, a)))),
% 0.46/0.55 inference(transitivity,[status(thm)],[433, 431])).
% 0.46/0.55 tff(435,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(d, b, a)) | between(d, c, b) | between(d, b, c) | (~between(d, c, a)))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(436,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | between(d, c, b) | between(d, b, c) | (~between(d, c, a)) | (~between(d, b, a))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.46/0.55 tff(437,plain,
% 0.46/0.55 (~between(d, c, a)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[436, 430, 381, 12, 23])).
% 0.46/0.55 tff(438,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(a, c, d)) | between(d, c, a))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(a, c, d)) | between(d, c, a))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(439,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(a, c, d)) | between(d, c, a))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(440,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(a, c, d)) | between(d, c, a)),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.46/0.55 tff(441,plain,
% 0.46/0.55 (~between(a, c, d)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[440, 98, 437])).
% 0.46/0.55 tff(442,plain,
% 0.46/0.55 (~between(extension(d, b, b, a), c, d)),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[441, 420])).
% 0.46/0.55 tff(443,plain,
% 0.46/0.55 (between(extension(d, b, b, a), c, insertion(d, a, d, b)) <=> between(a, c, b)),
% 0.46/0.55 inference(monotonicity,[status(thm)],[410, 386])).
% 0.46/0.55 tff(444,plain,
% 0.46/0.55 (between(a, c, b) <=> between(extension(d, b, b, a), c, insertion(d, a, d, b))),
% 0.46/0.55 inference(symmetry,[status(thm)],[443])).
% 0.46/0.55 tff(445,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (between(d, b, c) | (~between(b, a, c)) | (b = a) | (~between(d, b, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | between(d, b, c) | (~between(b, a, c)) | (b = a) | (~between(d, b, a)))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(446,plain,
% 0.46/0.55 ((between(d, b, c) | (~between(d, b, a)) | (~between(b, a, c)) | (b = a)) <=> (between(d, b, c) | (~between(b, a, c)) | (b = a) | (~between(d, b, a)))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(447,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (between(d, b, c) | (~between(d, b, a)) | (~between(b, a, c)) | (b = a))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (between(d, b, c) | (~between(b, a, c)) | (b = a) | (~between(d, b, a))))),
% 0.46/0.55 inference(monotonicity,[status(thm)],[446])).
% 0.46/0.55 tff(448,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (between(d, b, c) | (~between(d, b, a)) | (~between(b, a, c)) | (b = a))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | between(d, b, c) | (~between(b, a, c)) | (b = a) | (~between(d, b, a)))),
% 0.46/0.55 inference(transitivity,[status(thm)],[447, 445])).
% 0.46/0.55 tff(449,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (between(d, b, c) | (~between(d, b, a)) | (~between(b, a, c)) | (b = a))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(450,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | between(d, b, c) | (~between(b, a, c)) | (b = a) | (~between(d, b, a))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.46/0.55 tff(451,plain,
% 0.46/0.55 ((~between(b, a, c)) | (b = a)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[450, 248, 381, 23])).
% 0.46/0.55 tff(452,plain,
% 0.46/0.55 (~between(b, a, c)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[451, 296])).
% 0.46/0.55 tff(453,plain,
% 0.46/0.55 (between(a, c, b)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[345, 452, 282])).
% 0.46/0.55 tff(454,plain,
% 0.46/0.55 (between(extension(d, b, b, a), c, insertion(d, a, d, b))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[453, 444])).
% 0.46/0.55 tff(455,plain,
% 0.46/0.55 (^[W: $i, V: $i, U: $i, X: $i] : refl((between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X))) <=> (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X))))),
% 0.46/0.55 inference(bind,[status(th)],[])).
% 0.46/0.55 tff(456,plain,
% 0.46/0.55 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 0.46/0.55 inference(quant_intro,[status(thm)],[455])).
% 0.46/0.55 tff(457,plain,
% 0.46/0.55 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(458,plain,
% 0.46/0.55 (^[W: $i, V: $i, U: $i, X: $i] : rewrite((((~between(U, V, W)) | (~between(U, W, X))) | between(U, V, X)) <=> (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X))))),
% 0.46/0.55 inference(bind,[status(th)],[])).
% 0.46/0.55 tff(459,plain,
% 0.46/0.55 (![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(U, V, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 0.46/0.55 inference(quant_intro,[status(thm)],[458])).
% 0.46/0.55 tff(460,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(U, V, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b9')).
% 0.46/0.55 tff(461,plain,
% 0.46/0.55 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.46/0.55 tff(462,plain,
% 0.46/0.55 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[461, 457])).
% 0.46/0.55 tff(463,plain,(
% 0.46/0.55 ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 0.46/0.55 inference(skolemize,[status(sab)],[462])).
% 0.46/0.55 tff(464,plain,
% 0.46/0.55 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[463, 456])).
% 0.46/0.55 tff(465,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(extension(d, b, b, a), c, d) | (~between(extension(d, b, b, a), c, insertion(d, a, d, b))) | (~between(extension(d, b, b, a), insertion(d, a, d, b), d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(extension(d, b, b, a), c, d) | (~between(extension(d, b, b, a), c, insertion(d, a, d, b))) | (~between(extension(d, b, b, a), insertion(d, a, d, b), d)))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(466,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(extension(d, b, b, a), c, d) | (~between(extension(d, b, b, a), c, insertion(d, a, d, b))) | (~between(extension(d, b, b, a), insertion(d, a, d, b), d)))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(467,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(extension(d, b, b, a), c, d) | (~between(extension(d, b, b, a), c, insertion(d, a, d, b))) | (~between(extension(d, b, b, a), insertion(d, a, d, b), d))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.46/0.55 tff(468,plain,
% 0.46/0.55 (between(extension(d, b, b, a), c, d) | (~between(extension(d, b, b, a), c, insertion(d, a, d, b))) | (~between(extension(d, b, b, a), insertion(d, a, d, b), d))),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[467, 464])).
% 0.46/0.55 tff(469,plain,
% 0.46/0.55 ($false),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[468, 454, 442, 417])).
% 0.46/0.55 tff(470,plain,(colinear(b, c, d)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.55 tff(471,plain,
% 0.46/0.55 (((~colinear(a, c, d)) | (~colinear(b, c, d))) <=> ((~colinear(a, c, d)) | (~colinear(b, c, d)))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(472,axiom,((~colinear(a, c, d)) | (~colinear(b, c, d))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_colinearity')).
% 0.46/0.55 tff(473,plain,
% 0.46/0.55 ((~colinear(a, c, d)) | (~colinear(b, c, d))),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.46/0.55 tff(474,plain,
% 0.46/0.55 (~colinear(a, c, d)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[473, 470])).
% 0.46/0.55 tff(475,plain,
% 0.46/0.55 (((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(a, c, d)) | colinear(a, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(a, c, d)) | colinear(a, c, d))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(476,plain,
% 0.46/0.55 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | ((~between(a, c, d)) | colinear(a, c, d))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(477,plain,
% 0.46/0.55 ((~![Z: $i, Y: $i, X: $i] : ((~between(X, Y, Z)) | colinear(X, Y, Z))) | (~between(a, c, d)) | colinear(a, c, d)),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.46/0.55 tff(478,plain,
% 0.46/0.55 (~between(a, c, d)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[477, 149, 474])).
% 0.46/0.55 tff(479,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(c, a, d)) | colinear(a, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(c, a, d)) | colinear(a, c, d))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(480,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | ((~between(c, a, d)) | colinear(a, c, d))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(481,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i] : ((~between(V, U, W)) | colinear(U, V, W))) | (~between(c, a, d)) | colinear(a, c, d)),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.46/0.55 tff(482,plain,
% 0.46/0.55 (~between(c, a, d)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[481, 160, 474])).
% 0.46/0.55 tff(483,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(a, d, c)) | colinear(a, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(a, d, c)) | colinear(a, c, d))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(484,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | ((~between(a, d, c)) | colinear(a, c, d))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(485,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i] : ((~between(U, W, V)) | colinear(U, V, W))) | (~between(a, d, c)) | colinear(a, c, d)),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.46/0.55 tff(486,plain,
% 0.46/0.55 (~between(a, d, c)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[485, 289, 474])).
% 0.46/0.55 tff(487,plain,
% 0.46/0.55 (((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | ((~between(d, a, c)) | colinear(a, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | (~between(d, a, c)) | colinear(a, c, d))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(488,plain,
% 0.46/0.55 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | ((~between(d, a, c)) | colinear(a, c, d))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(489,plain,
% 0.46/0.55 ((~![Z: $i, Y: $i, X: $i] : ((~between(Z, X, Y)) | colinear(X, Y, Z))) | (~between(d, a, c)) | colinear(a, c, d)),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.46/0.55 tff(490,plain,
% 0.46/0.55 (~between(d, a, c)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[489, 19, 474])).
% 0.46/0.55 tff(491,assumption,(between(b, a, c)), introduced(assumption)).
% 0.46/0.55 tff(492,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, d, c)) | (~between(b, a, c)) | between(d, a, c) | between(a, d, c))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (~between(b, d, c)) | (~between(b, a, c)) | between(d, a, c) | between(a, d, c))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(493,plain,
% 0.46/0.55 (((~between(b, a, c)) | between(a, d, c) | (~between(b, d, c)) | between(d, a, c)) <=> ((~between(b, d, c)) | (~between(b, a, c)) | between(d, a, c) | between(a, d, c))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(494,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, a, c)) | between(a, d, c) | (~between(b, d, c)) | between(d, a, c))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, d, c)) | (~between(b, a, c)) | between(d, a, c) | between(a, d, c)))),
% 0.46/0.55 inference(monotonicity,[status(thm)],[493])).
% 0.46/0.55 tff(495,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, a, c)) | between(a, d, c) | (~between(b, d, c)) | between(d, a, c))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (~between(b, d, c)) | (~between(b, a, c)) | between(d, a, c) | between(a, d, c))),
% 0.46/0.55 inference(transitivity,[status(thm)],[494, 492])).
% 0.46/0.55 tff(496,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, a, c)) | between(a, d, c) | (~between(b, d, c)) | between(d, a, c))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(497,plain,
% 0.46/0.55 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (~between(b, d, c)) | (~between(b, a, c)) | between(d, a, c) | between(a, d, c)),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.46/0.55 tff(498,plain,
% 0.46/0.55 (~between(b, d, c)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[497, 84, 491, 486, 490])).
% 0.46/0.55 tff(499,plain,
% 0.46/0.55 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(b, c, d)) | (~between(b, a, c)) | between(a, c, d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(b, c, d)) | (~between(b, a, c)) | between(a, c, d))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(500,plain,
% 0.46/0.56 (((~between(b, a, c)) | between(a, c, d) | (~between(b, c, d))) <=> ((~between(b, c, d)) | (~between(b, a, c)) | between(a, c, d))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(501,plain,
% 0.46/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(b, a, c)) | between(a, c, d) | (~between(b, c, d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(b, c, d)) | (~between(b, a, c)) | between(a, c, d)))),
% 0.46/0.56 inference(monotonicity,[status(thm)],[500])).
% 0.46/0.56 tff(502,plain,
% 0.46/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(b, a, c)) | between(a, c, d) | (~between(b, c, d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(b, c, d)) | (~between(b, a, c)) | between(a, c, d))),
% 0.46/0.56 inference(transitivity,[status(thm)],[501, 499])).
% 0.46/0.56 tff(503,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(b, a, c)) | between(a, c, d) | (~between(b, c, d)))),
% 0.46/0.56 inference(quant_inst,[status(thm)],[])).
% 0.46/0.56 tff(504,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(b, c, d)) | (~between(b, a, c)) | between(a, c, d)),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.46/0.56 tff(505,plain,
% 0.46/0.56 (~between(b, c, d)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[504, 66, 491, 478])).
% 0.46/0.56 tff(506,plain,
% 0.46/0.56 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, c, b)) | between(b, c, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, c, b)) | between(b, c, d))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(507,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, c, b)) | between(b, c, d))),
% 0.46/0.56 inference(quant_inst,[status(thm)],[])).
% 0.46/0.56 tff(508,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, c, b)) | between(b, c, d)),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.46/0.56 tff(509,plain,
% 0.46/0.56 (~between(d, c, b)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[508, 98, 505])).
% 0.46/0.56 tff(510,plain,
% 0.46/0.56 (((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | ((~colinear(b, c, d)) | colinear(c, b, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | (~colinear(b, c, d)) | colinear(c, b, d))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(511,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | ((~colinear(b, c, d)) | colinear(c, b, d))),
% 0.46/0.56 inference(quant_inst,[status(thm)],[])).
% 0.46/0.56 tff(512,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i] : ((~colinear(U, V, W)) | colinear(V, U, W))) | (~colinear(b, c, d)) | colinear(c, b, d)),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.46/0.56 tff(513,plain,
% 0.46/0.56 (colinear(c, b, d)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[512, 267, 470])).
% 0.46/0.56 tff(514,plain,
% 0.46/0.56 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(c, b, d)) | between(c, b, d) | between(b, d, c) | between(d, c, b))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(c, b, d)) | between(c, b, d) | between(b, d, c) | between(d, c, b))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(515,plain,
% 0.46/0.56 ((between(d, c, b) | between(b, d, c) | between(c, b, d) | (~colinear(c, b, d))) <=> ((~colinear(c, b, d)) | between(c, b, d) | between(b, d, c) | between(d, c, b))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(516,plain,
% 0.46/0.56 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, c, b) | between(b, d, c) | between(c, b, d) | (~colinear(c, b, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(c, b, d)) | between(c, b, d) | between(b, d, c) | between(d, c, b)))),
% 0.46/0.56 inference(monotonicity,[status(thm)],[515])).
% 0.46/0.56 tff(517,plain,
% 0.46/0.56 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, c, b) | between(b, d, c) | between(c, b, d) | (~colinear(c, b, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(c, b, d)) | between(c, b, d) | between(b, d, c) | between(d, c, b))),
% 0.46/0.56 inference(transitivity,[status(thm)],[516, 514])).
% 0.46/0.56 tff(518,plain,
% 0.46/0.56 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, c, b) | between(b, d, c) | between(c, b, d) | (~colinear(c, b, d)))),
% 0.46/0.56 inference(quant_inst,[status(thm)],[])).
% 0.46/0.56 tff(519,plain,
% 0.46/0.56 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(c, b, d)) | between(c, b, d) | between(b, d, c) | between(d, c, b)),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.46/0.56 tff(520,plain,
% 0.46/0.56 (between(c, b, d) | between(b, d, c) | between(d, c, b)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[519, 115, 513])).
% 0.46/0.56 tff(521,plain,
% 0.46/0.56 (between(c, b, d)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[520, 509, 498])).
% 0.46/0.56 tff(522,plain,
% 0.46/0.56 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(b, a, c)) | (a = insertion(b, c, b, a)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(b, a, c)) | (a = insertion(b, c, b, a)))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(523,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(b, a, c)) | (a = insertion(b, c, b, a)))),
% 0.46/0.56 inference(quant_inst,[status(thm)],[])).
% 0.46/0.56 tff(524,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(b, a, c)) | (a = insertion(b, c, b, a))),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.46/0.56 tff(525,plain,
% 0.46/0.56 (a = insertion(b, c, b, a)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[524, 42, 491])).
% 0.46/0.56 tff(526,plain,
% 0.46/0.56 (insertion(b, c, b, a) = a),
% 0.46/0.56 inference(symmetry,[status(thm)],[525])).
% 0.46/0.56 tff(527,plain,
% 0.46/0.56 (between(c, insertion(b, c, b, a), b) <=> between(c, a, b)),
% 0.46/0.56 inference(monotonicity,[status(thm)],[526])).
% 0.46/0.56 tff(528,plain,
% 0.46/0.56 (between(c, a, b) <=> between(c, insertion(b, c, b, a), b)),
% 0.46/0.56 inference(symmetry,[status(thm)],[527])).
% 0.46/0.56 tff(529,plain,
% 0.46/0.56 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, a, c)) | between(c, a, b))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, a, c)) | between(c, a, b))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(530,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, a, c)) | between(c, a, b))),
% 0.46/0.56 inference(quant_inst,[status(thm)],[])).
% 0.46/0.56 tff(531,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, a, c)) | between(c, a, b)),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.46/0.56 tff(532,plain,
% 0.46/0.56 (between(c, a, b)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[531, 98, 491])).
% 0.46/0.56 tff(533,plain,
% 0.46/0.56 (between(c, insertion(b, c, b, a), b)),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[532, 528])).
% 0.46/0.56 tff(534,plain,
% 0.46/0.56 (between(c, insertion(b, c, b, a), d) <=> between(c, a, d)),
% 0.46/0.56 inference(monotonicity,[status(thm)],[526])).
% 0.46/0.56 tff(535,plain,
% 0.46/0.56 (between(c, a, d) <=> between(c, insertion(b, c, b, a), d)),
% 0.46/0.56 inference(symmetry,[status(thm)],[534])).
% 0.46/0.56 tff(536,plain,
% 0.46/0.56 ((~between(c, a, d)) <=> (~between(c, insertion(b, c, b, a), d))),
% 0.46/0.56 inference(monotonicity,[status(thm)],[535])).
% 0.46/0.56 tff(537,plain,
% 0.46/0.56 (~between(c, insertion(b, c, b, a), d)),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[482, 536])).
% 0.46/0.56 tff(538,plain,
% 0.46/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | ((~between(c, b, d)) | (~between(c, insertion(b, c, b, a), b)) | between(c, insertion(b, c, b, a), d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (~between(c, b, d)) | (~between(c, insertion(b, c, b, a), b)) | between(c, insertion(b, c, b, a), d))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(539,plain,
% 0.46/0.56 ((between(c, insertion(b, c, b, a), d) | (~between(c, insertion(b, c, b, a), b)) | (~between(c, b, d))) <=> ((~between(c, b, d)) | (~between(c, insertion(b, c, b, a), b)) | between(c, insertion(b, c, b, a), d))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(540,plain,
% 0.46/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(c, insertion(b, c, b, a), d) | (~between(c, insertion(b, c, b, a), b)) | (~between(c, b, d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | ((~between(c, b, d)) | (~between(c, insertion(b, c, b, a), b)) | between(c, insertion(b, c, b, a), d)))),
% 0.46/0.56 inference(monotonicity,[status(thm)],[539])).
% 0.46/0.56 tff(541,plain,
% 0.46/0.56 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(c, insertion(b, c, b, a), d) | (~between(c, insertion(b, c, b, a), b)) | (~between(c, b, d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (~between(c, b, d)) | (~between(c, insertion(b, c, b, a), b)) | between(c, insertion(b, c, b, a), d))),
% 0.46/0.56 inference(transitivity,[status(thm)],[540, 538])).
% 0.46/0.56 tff(542,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(c, insertion(b, c, b, a), d) | (~between(c, insertion(b, c, b, a), b)) | (~between(c, b, d)))),
% 0.46/0.56 inference(quant_inst,[status(thm)],[])).
% 0.46/0.56 tff(543,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (~between(c, b, d)) | (~between(c, insertion(b, c, b, a), b)) | between(c, insertion(b, c, b, a), d)),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.46/0.56 tff(544,plain,
% 0.46/0.56 ((~between(c, b, d)) | (~between(c, insertion(b, c, b, a), b)) | between(c, insertion(b, c, b, a), d)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[543, 464])).
% 0.46/0.56 tff(545,plain,
% 0.46/0.56 ($false),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[544, 537, 533, 521])).
% 0.46/0.56 tff(546,plain,(~between(b, a, c)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.56 tff(547,assumption,(~between(b, a, d)), introduced(assumption)).
% 0.46/0.56 tff(548,assumption,(between(c, b, a)), introduced(assumption)).
% 0.46/0.56 tff(549,plain,
% 0.46/0.56 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(c, b, a)) | (b = insertion(c, a, c, b)))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(c, b, a)) | (b = insertion(c, a, c, b)))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(550,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | ((~between(c, b, a)) | (b = insertion(c, a, c, b)))),
% 0.46/0.56 inference(quant_inst,[status(thm)],[])).
% 0.46/0.56 tff(551,plain,
% 0.46/0.56 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | (V = insertion(U, W, U, V)))) | (~between(c, b, a)) | (b = insertion(c, a, c, b))),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[550, 549])).
% 0.46/0.56 tff(552,plain,
% 0.46/0.56 (b = insertion(c, a, c, b)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[551, 42, 548])).
% 0.46/0.56 tff(553,plain,
% 0.46/0.56 (insertion(c, a, c, b) = b),
% 0.46/0.56 inference(symmetry,[status(thm)],[552])).
% 0.46/0.56 tff(554,plain,
% 0.46/0.56 (between(a, insertion(c, a, c, b), c) <=> between(a, b, c)),
% 0.46/0.56 inference(monotonicity,[status(thm)],[553])).
% 0.46/0.56 tff(555,plain,
% 0.46/0.56 (between(a, b, c) <=> between(a, insertion(c, a, c, b), c)),
% 0.46/0.56 inference(symmetry,[status(thm)],[554])).
% 0.46/0.56 tff(556,plain,
% 0.46/0.56 (between(a, b, c)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[281, 98, 548])).
% 0.46/0.56 tff(557,plain,
% 0.46/0.56 (between(a, insertion(c, a, c, b), c)),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.46/0.57 tff(558,plain,
% 0.46/0.57 ((a = insertion(c, a, c, b)) <=> (a = b)),
% 0.46/0.57 inference(monotonicity,[status(thm)],[553])).
% 0.46/0.57 tff(559,plain,
% 0.46/0.57 ((a = b) <=> (a = insertion(c, a, c, b))),
% 0.46/0.57 inference(symmetry,[status(thm)],[558])).
% 0.46/0.57 tff(560,plain,
% 0.46/0.57 ((~(a = b)) <=> (~(a = insertion(c, a, c, b)))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[559])).
% 0.46/0.57 tff(561,plain,
% 0.46/0.57 (~(a = insertion(c, a, c, b))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[176, 560])).
% 0.46/0.57 tff(562,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(563,plain,
% 0.46/0.57 (((a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), c)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))) <=> ((~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(564,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), c)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[563])).
% 0.46/0.57 tff(565,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), c)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 0.46/0.57 inference(transitivity,[status(thm)],[564, 562])).
% 0.46/0.57 tff(566,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), c)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(567,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[566, 565])).
% 0.46/0.57 tff(568,plain,
% 0.46/0.57 ((~between(a, insertion(c, a, c, b), c)) | (a = insertion(c, a, c, b)) | (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[567, 186])).
% 0.46/0.57 tff(569,plain,
% 0.46/0.57 (c = extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[568, 561, 557])).
% 0.46/0.57 tff(570,plain,
% 0.46/0.57 (extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c) = c),
% 0.46/0.57 inference(symmetry,[status(thm)],[569])).
% 0.46/0.57 tff(571,plain,
% 0.46/0.57 (between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) <=> between(a, b, c)),
% 0.46/0.57 inference(monotonicity,[status(thm)],[553, 570])).
% 0.46/0.57 tff(572,plain,
% 0.46/0.57 (between(a, b, c) <=> between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 0.46/0.57 inference(symmetry,[status(thm)],[571])).
% 0.46/0.57 tff(573,plain,
% 0.46/0.57 (between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[556, 572])).
% 0.46/0.57 tff(574,plain,
% 0.46/0.57 (between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) <=> between(a, d, c)),
% 0.46/0.57 inference(monotonicity,[status(thm)],[570])).
% 0.46/0.57 tff(575,plain,
% 0.46/0.57 (between(a, d, c) <=> between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 0.46/0.57 inference(symmetry,[status(thm)],[574])).
% 0.46/0.57 tff(576,plain,
% 0.46/0.57 ((~between(a, d, c)) <=> (~between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[575])).
% 0.46/0.57 tff(577,plain,
% 0.46/0.57 (~between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[486, 576])).
% 0.46/0.57 tff(578,plain,
% 0.46/0.57 (between(a, insertion(c, a, c, b), d) <=> between(a, b, d)),
% 0.46/0.57 inference(monotonicity,[status(thm)],[553])).
% 0.46/0.57 tff(579,plain,
% 0.46/0.57 (between(a, b, d) <=> between(a, insertion(c, a, c, b), d)),
% 0.46/0.57 inference(symmetry,[status(thm)],[578])).
% 0.46/0.57 tff(580,plain,
% 0.46/0.57 (((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(c, d, a)) | colinear(a, c, d))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(c, d, a)) | colinear(a, c, d))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(581,plain,
% 0.46/0.57 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | ((~between(c, d, a)) | colinear(a, c, d))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(582,plain,
% 0.46/0.57 ((~![Z: $i, Y: $i, X: $i] : ((~between(Y, Z, X)) | colinear(X, Y, Z))) | (~between(c, d, a)) | colinear(a, c, d)),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.46/0.57 tff(583,plain,
% 0.46/0.57 (~between(c, d, a)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[582, 30, 474])).
% 0.46/0.57 tff(584,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(b, d, a)) | between(c, d, a) | (~between(c, b, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(b, d, a)) | between(c, d, a) | (~between(c, b, a)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(585,plain,
% 0.46/0.57 (((~between(c, b, a)) | between(c, d, a) | (~between(b, d, a))) <=> ((~between(b, d, a)) | between(c, d, a) | (~between(c, b, a)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(586,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(c, b, a)) | between(c, d, a) | (~between(b, d, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(b, d, a)) | between(c, d, a) | (~between(c, b, a))))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[585])).
% 0.46/0.57 tff(587,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(c, b, a)) | between(c, d, a) | (~between(b, d, a)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(b, d, a)) | between(c, d, a) | (~between(c, b, a)))),
% 0.46/0.57 inference(transitivity,[status(thm)],[586, 584])).
% 0.46/0.57 tff(588,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | ((~between(c, b, a)) | between(c, d, a) | (~between(b, d, a)))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(589,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, X) | (~between(V, W, X)))) | (~between(b, d, a)) | between(c, d, a) | (~between(c, b, a))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.46/0.57 tff(590,plain,
% 0.46/0.57 (~between(b, d, a)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[589, 133, 548, 583])).
% 0.46/0.57 tff(591,plain,
% 0.46/0.57 (between(d, a, insertion(c, a, c, b)) <=> between(d, a, b)),
% 0.46/0.57 inference(monotonicity,[status(thm)],[553])).
% 0.46/0.57 tff(592,plain,
% 0.46/0.57 ((~between(d, a, insertion(c, a, c, b))) <=> (~between(d, a, b))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[591])).
% 0.46/0.57 tff(593,plain,
% 0.46/0.57 (between(insertion(c, a, c, b), a, d) <=> between(b, a, d)),
% 0.46/0.57 inference(monotonicity,[status(thm)],[553])).
% 0.46/0.57 tff(594,plain,
% 0.46/0.57 (between(b, a, d) <=> between(insertion(c, a, c, b), a, d)),
% 0.46/0.57 inference(symmetry,[status(thm)],[593])).
% 0.46/0.57 tff(595,plain,
% 0.46/0.57 ((~between(b, a, d)) <=> (~between(insertion(c, a, c, b), a, d))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[594])).
% 0.46/0.57 tff(596,plain,
% 0.46/0.57 (~between(insertion(c, a, c, b), a, d)),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[547, 595])).
% 0.46/0.57 tff(597,plain,
% 0.46/0.57 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, a, insertion(c, a, c, b))) | between(insertion(c, a, c, b), a, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, a, insertion(c, a, c, b))) | between(insertion(c, a, c, b), a, d))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(598,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, a, insertion(c, a, c, b))) | between(insertion(c, a, c, b), a, d))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(599,plain,
% 0.46/0.57 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, a, insertion(c, a, c, b))) | between(insertion(c, a, c, b), a, d)),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[598, 597])).
% 0.46/0.57 tff(600,plain,
% 0.46/0.57 ((~between(d, a, insertion(c, a, c, b))) | between(insertion(c, a, c, b), a, d)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[599, 98])).
% 0.46/0.57 tff(601,plain,
% 0.46/0.57 (~between(d, a, insertion(c, a, c, b))),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[600, 596])).
% 0.46/0.57 tff(602,plain,
% 0.46/0.57 (~between(d, a, b)),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[601, 592])).
% 0.46/0.57 tff(603,plain,
% 0.46/0.57 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(604,plain,
% 0.46/0.57 ((between(d, a, b) | between(b, d, a) | between(a, b, d) | (~colinear(a, b, d))) <=> ((~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(605,plain,
% 0.46/0.57 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, a, b) | between(b, d, a) | between(a, b, d) | (~colinear(a, b, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d)))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[604])).
% 0.46/0.57 tff(606,plain,
% 0.46/0.57 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, a, b) | between(b, d, a) | between(a, b, d) | (~colinear(a, b, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d))),
% 0.46/0.57 inference(transitivity,[status(thm)],[605, 603])).
% 0.46/0.57 tff(607,plain,
% 0.46/0.57 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, a, b) | between(b, d, a) | between(a, b, d) | (~colinear(a, b, d)))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(608,plain,
% 0.46/0.57 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(a, b, d)) | between(d, a, b) | between(b, d, a) | between(a, b, d)),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.46/0.57 tff(609,plain,
% 0.46/0.57 (between(d, a, b) | between(b, d, a) | between(a, b, d)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[608, 115, 260])).
% 0.46/0.57 tff(610,plain,
% 0.46/0.57 (between(a, b, d)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[609, 602, 590])).
% 0.46/0.57 tff(611,plain,
% 0.46/0.57 (between(a, insertion(c, a, c, b), d)),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[610, 579])).
% 0.46/0.57 tff(612,plain,
% 0.46/0.57 (between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) <=> between(a, c, d)),
% 0.46/0.58 inference(monotonicity,[status(thm)],[570])).
% 0.46/0.58 tff(613,plain,
% 0.46/0.58 (between(a, c, d) <=> between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d)),
% 0.46/0.58 inference(symmetry,[status(thm)],[612])).
% 0.46/0.58 tff(614,plain,
% 0.46/0.58 ((~between(a, c, d)) <=> (~between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[613])).
% 0.46/0.58 tff(615,plain,
% 0.46/0.58 (~between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d)),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[478, 614])).
% 0.46/0.58 tff(616,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | (a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(617,plain,
% 0.46/0.58 (((~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))) | (a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d)) <=> ((a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(618,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))) | (a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[617])).
% 0.46/0.58 tff(619,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))) | (a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | (a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))))),
% 0.46/0.58 inference(transitivity,[status(thm)],[618, 616])).
% 0.46/0.58 tff(620,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | ((~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c))) | (a = insertion(c, a, c, b)) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(621,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | (U = V) | (~between(U, V, W)) | between(U, W, X) | between(U, X, W))) | (a = insertion(c, a, c, b)) | between(a, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c), d) | (~between(a, insertion(c, a, c, b), d)) | between(a, d, extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)) | (~between(a, insertion(c, a, c, b), extension(a, insertion(c, a, c, b), insertion(c, a, c, b), c)))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[620, 619])).
% 0.46/0.58 tff(622,plain,
% 0.46/0.58 ($false),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[621, 370, 561, 615, 611, 577, 573])).
% 0.46/0.58 tff(623,plain,((~between(c, b, a)) | between(b, a, d)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.58 tff(624,plain,
% 0.46/0.58 (~between(c, b, a)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[623, 547])).
% 0.46/0.58 tff(625,plain,
% 0.46/0.58 (between(a, c, b)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[345, 624, 546])).
% 0.46/0.58 tff(626,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(a, d, b)) | (~between(a, c, b)) | between(a, d, c) | between(a, c, d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | (~between(a, d, b)) | (~between(a, c, b)) | between(a, d, c) | between(a, c, d))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(627,plain,
% 0.46/0.58 (((~between(a, c, b)) | between(a, d, c) | between(a, c, d) | (~between(a, d, b))) <=> ((~between(a, d, b)) | (~between(a, c, b)) | between(a, d, c) | between(a, c, d))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(628,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(a, c, b)) | between(a, d, c) | between(a, c, d) | (~between(a, d, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(a, d, b)) | (~between(a, c, b)) | between(a, d, c) | between(a, c, d)))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[627])).
% 0.46/0.58 tff(629,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(a, c, b)) | between(a, d, c) | between(a, c, d) | (~between(a, d, b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | (~between(a, d, b)) | (~between(a, c, b)) | between(a, d, c) | between(a, c, d))),
% 0.46/0.58 inference(transitivity,[status(thm)],[628, 626])).
% 0.46/0.58 tff(630,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | ((~between(a, c, b)) | between(a, d, c) | between(a, c, d) | (~between(a, d, b)))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(631,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(U, W, V) | between(U, V, W) | (~between(U, W, X)))) | (~between(a, d, b)) | (~between(a, c, b)) | between(a, d, c) | between(a, c, d)),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.46/0.58 tff(632,plain,
% 0.46/0.58 (~between(a, d, b)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[631, 430, 625, 486, 478])).
% 0.46/0.58 tff(633,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, a, b)) | between(b, a, d))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, a, b)) | between(b, a, d))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(634,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(d, a, b)) | between(b, a, d))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(635,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(d, a, b)) | between(b, a, d)),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[634, 633])).
% 0.46/0.58 tff(636,plain,
% 0.46/0.58 (~between(d, a, b)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[635, 98, 547])).
% 0.46/0.58 tff(637,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | ((~between(a, c, b)) | (~between(a, b, d)) | between(a, c, d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (~between(a, c, b)) | (~between(a, b, d)) | between(a, c, d))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(638,plain,
% 0.46/0.58 ((between(a, c, d) | (~between(a, c, b)) | (~between(a, b, d))) <=> ((~between(a, c, b)) | (~between(a, b, d)) | between(a, c, d))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(639,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(a, c, d) | (~between(a, c, b)) | (~between(a, b, d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | ((~between(a, c, b)) | (~between(a, b, d)) | between(a, c, d)))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[638])).
% 0.46/0.58 tff(640,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(a, c, d) | (~between(a, c, b)) | (~between(a, b, d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (~between(a, c, b)) | (~between(a, b, d)) | between(a, c, d))),
% 0.46/0.58 inference(transitivity,[status(thm)],[639, 637])).
% 0.46/0.58 tff(641,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(a, c, d) | (~between(a, c, b)) | (~between(a, b, d)))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(642,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (~between(a, c, b)) | (~between(a, b, d)) | between(a, c, d)),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[641, 640])).
% 0.46/0.58 tff(643,plain,
% 0.46/0.58 (~between(a, b, d)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[642, 464, 625, 478])).
% 0.46/0.58 tff(644,plain,
% 0.46/0.58 (between(b, d, a)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[609, 643, 636])).
% 0.46/0.58 tff(645,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, d, a)) | between(a, d, b))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, d, a)) | between(a, d, b))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(646,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(b, d, a)) | between(a, d, b))),
% 0.46/0.58 inference(quant_inst,[status(thm)],[])).
% 0.46/0.58 tff(647,plain,
% 0.46/0.58 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(b, d, a)) | between(a, d, b)),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.46/0.58 tff(648,plain,
% 0.46/0.58 ($false),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[647, 98, 644, 632])).
% 0.46/0.58 tff(649,plain,(between(b, a, d)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.58 tff(650,plain,
% 0.46/0.58 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(651,plain,
% 0.46/0.59 (((~between(b, a, d)) | between(a, c, d) | (~between(b, c, d)) | between(c, a, d)) <=> ((~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(652,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, a, d)) | between(a, c, d) | (~between(b, c, d)) | between(c, a, d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[651])).
% 0.46/0.59 tff(653,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, a, d)) | between(a, c, d) | (~between(b, c, d)) | between(c, a, d))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d)))),
% 0.46/0.59 inference(transitivity,[status(thm)],[652, 650])).
% 0.46/0.59 tff(654,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | ((~between(b, a, d)) | between(a, c, d) | (~between(b, c, d)) | between(c, a, d))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(655,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, X)) | between(V, W, X) | (~between(U, W, X)) | between(W, V, X))) | (~between(b, c, d)) | between(c, a, d) | between(a, c, d) | (~between(b, a, d))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.46/0.59 tff(656,plain,
% 0.46/0.59 (~between(b, c, d)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[655, 84, 649, 482, 478])).
% 0.46/0.59 tff(657,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(b, a, c) | (~between(b, d, c)) | (~between(b, a, d)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(b, a, c) | (~between(b, d, c)) | (~between(b, a, d)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(658,plain,
% 0.46/0.59 ((between(b, a, c) | (~between(b, a, d)) | (~between(b, d, c))) <=> (between(b, a, c) | (~between(b, d, c)) | (~between(b, a, d)))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(659,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(b, a, c) | (~between(b, a, d)) | (~between(b, d, c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(b, a, c) | (~between(b, d, c)) | (~between(b, a, d))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[658])).
% 0.46/0.59 tff(660,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(b, a, c) | (~between(b, a, d)) | (~between(b, d, c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(b, a, c) | (~between(b, d, c)) | (~between(b, a, d)))),
% 0.46/0.59 inference(transitivity,[status(thm)],[659, 657])).
% 0.46/0.59 tff(661,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(b, a, c) | (~between(b, a, d)) | (~between(b, d, c)))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(662,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | between(b, a, c) | (~between(b, d, c)) | (~between(b, a, d))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.46/0.59 tff(663,plain,
% 0.46/0.59 (~between(b, d, c)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[662, 464, 546, 649])).
% 0.46/0.59 tff(664,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(c, d, b)) | between(b, d, c))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(c, d, b)) | between(b, d, c))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(665,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(c, d, b)) | between(b, d, c))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(666,plain,
% 0.46/0.59 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(c, d, b)) | between(b, d, c)),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.46/0.59 tff(667,plain,
% 0.46/0.59 (~between(c, d, b)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[666, 98, 663])).
% 0.46/0.59 tff(668,plain,
% 0.46/0.59 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(b, c, d)) | between(d, b, c) | between(b, c, d) | between(c, d, b))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(b, c, d)) | between(d, b, c) | between(b, c, d) | between(c, d, b))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(669,plain,
% 0.46/0.59 ((between(d, b, c) | between(c, d, b) | between(b, c, d) | (~colinear(b, c, d))) <=> ((~colinear(b, c, d)) | between(d, b, c) | between(b, c, d) | between(c, d, b))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(670,plain,
% 0.46/0.59 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, b, c) | between(c, d, b) | between(b, c, d) | (~colinear(b, c, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | ((~colinear(b, c, d)) | between(d, b, c) | between(b, c, d) | between(c, d, b)))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[669])).
% 0.46/0.59 tff(671,plain,
% 0.46/0.59 (((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, b, c) | between(c, d, b) | between(b, c, d) | (~colinear(b, c, d)))) <=> ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(b, c, d)) | between(d, b, c) | between(b, c, d) | between(c, d, b))),
% 0.46/0.59 inference(transitivity,[status(thm)],[670, 668])).
% 0.46/0.59 tff(672,plain,
% 0.46/0.59 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (between(d, b, c) | between(c, d, b) | between(b, c, d) | (~colinear(b, c, d)))),
% 0.46/0.59 inference(quant_inst,[status(thm)],[])).
% 0.46/0.59 tff(673,plain,
% 0.46/0.59 ((~![Z: $i, Y: $i, X: $i] : (between(Z, X, Y) | between(Y, Z, X) | between(X, Y, Z) | (~colinear(X, Y, Z)))) | (~colinear(b, c, d)) | between(d, b, c) | between(b, c, d) | between(c, d, b)),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.46/0.59 tff(674,plain,
% 0.46/0.59 (between(d, b, c) | between(b, c, d) | between(c, d, b)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[673, 115, 470])).
% 0.46/0.59 tff(675,plain,
% 0.46/0.59 (between(d, b, c)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[674, 667, 656])).
% 0.46/0.59 tff(676,plain,
% 0.46/0.59 (a = insertion(b, d, b, a)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[314, 42, 649])).
% 0.46/0.59 tff(677,plain,
% 0.46/0.59 (insertion(b, d, b, a) = a),
% 0.46/0.59 inference(symmetry,[status(thm)],[676])).
% 0.46/0.59 tff(678,plain,
% 0.46/0.59 (between(d, insertion(b, d, b, a), b) <=> between(d, a, b)),
% 0.46/0.59 inference(monotonicity,[status(thm)],[677])).
% 0.46/0.59 tff(679,plain,
% 0.46/0.59 (between(d, a, b) <=> between(d, insertion(b, d, b, a), b)),
% 0.46/0.59 inference(symmetry,[status(thm)],[678])).
% 0.46/0.59 tff(680,plain,
% 0.46/0.59 (between(d, a, b)),
% 0.46/0.59 inference(unit_resolution,[status(thm)],[326, 98, 649])).
% 0.46/0.59 tff(681,plain,
% 0.46/0.59 (between(d, insertion(b, d, b, a), b)),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.46/0.59 tff(682,plain,
% 0.46/0.59 (between(d, insertion(b, d, b, a), c) <=> between(d, a, c)),
% 0.46/0.59 inference(monotonicity,[status(thm)],[677])).
% 0.46/0.59 tff(683,plain,
% 0.46/0.59 (between(d, a, c) <=> between(d, insertion(b, d, b, a), c)),
% 0.46/0.59 inference(symmetry,[status(thm)],[682])).
% 0.46/0.59 tff(684,plain,
% 0.46/0.59 ((~between(d, a, c)) <=> (~between(d, insertion(b, d, b, a), c))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[683])).
% 0.46/0.59 tff(685,plain,
% 0.46/0.59 (~between(d, insertion(b, d, b, a), c)),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[490, 684])).
% 0.46/0.59 tff(686,plain,
% 0.46/0.59 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | ((~between(d, b, c)) | between(d, insertion(b, d, b, a), c) | (~between(d, insertion(b, d, b, a), b)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (~between(d, b, c)) | between(d, insertion(b, d, b, a), c) | (~between(d, insertion(b, d, b, a), b)))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(687,plain,
% 0.46/0.60 ((between(d, insertion(b, d, b, a), c) | (~between(d, insertion(b, d, b, a), b)) | (~between(d, b, c))) <=> ((~between(d, b, c)) | between(d, insertion(b, d, b, a), c) | (~between(d, insertion(b, d, b, a), b)))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(688,plain,
% 0.46/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(d, insertion(b, d, b, a), c) | (~between(d, insertion(b, d, b, a), b)) | (~between(d, b, c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | ((~between(d, b, c)) | between(d, insertion(b, d, b, a), c) | (~between(d, insertion(b, d, b, a), b))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[687])).
% 0.46/0.60 tff(689,plain,
% 0.46/0.60 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(d, insertion(b, d, b, a), c) | (~between(d, insertion(b, d, b, a), b)) | (~between(d, b, c)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (~between(d, b, c)) | between(d, insertion(b, d, b, a), c) | (~between(d, insertion(b, d, b, a), b)))),
% 0.46/0.60 inference(transitivity,[status(thm)],[688, 686])).
% 0.46/0.60 tff(690,plain,
% 0.46/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (between(d, insertion(b, d, b, a), c) | (~between(d, insertion(b, d, b, a), b)) | (~between(d, b, c)))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.60 tff(691,plain,
% 0.46/0.60 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(U, W, X)))) | (~between(d, b, c)) | between(d, insertion(b, d, b, a), c) | (~between(d, insertion(b, d, b, a), b))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.46/0.60 tff(692,plain,
% 0.46/0.60 ((~between(d, b, c)) | between(d, insertion(b, d, b, a), c) | (~between(d, insertion(b, d, b, a), b))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[691, 464])).
% 0.46/0.60 tff(693,plain,
% 0.46/0.60 ($false),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[692, 685, 681, 675])).
% 0.46/0.60 % SZS output end Proof
%------------------------------------------------------------------------------