TSTP Solution File: GEO043-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO043-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 20:34:29 EDT 2022
% Result : Unsatisfiable 0.52s 0.57s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO043-3 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.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 04:53:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.52/0.57 % SZS status Unsatisfiable
% 0.52/0.57 % SZS output start Proof
% 0.52/0.57 tff(between_type, type, (
% 0.52/0.57 between: ( $i * $i * $i ) > $o)).
% 0.52/0.57 tff(extension_type, type, (
% 0.52/0.57 extension: ( $i * $i * $i * $i ) > $i)).
% 0.52/0.57 tff(u_type, type, (
% 0.52/0.57 u: $i)).
% 0.52/0.57 tff(w_type, type, (
% 0.52/0.57 w: $i)).
% 0.52/0.57 tff(x_type, type, (
% 0.52/0.57 x: $i)).
% 0.52/0.57 tff(reflection_type, type, (
% 0.52/0.57 reflection: ( $i * $i ) > $i)).
% 0.52/0.57 tff(v_type, type, (
% 0.52/0.57 v: $i)).
% 0.52/0.57 tff(inner_pasch_type, type, (
% 0.52/0.57 inner_pasch: ( $i * $i * $i * $i * $i ) > $i)).
% 0.52/0.57 tff(1,assumption,(x = w), introduced(assumption)).
% 0.52/0.57 tff(2,plain,
% 0.52/0.57 (w = x),
% 0.52/0.57 inference(symmetry,[status(thm)],[1])).
% 0.52/0.57 tff(3,assumption,(u = v), introduced(assumption)).
% 0.52/0.57 tff(4,plain,
% 0.52/0.57 (between(u, w, x) <=> between(v, w, x)),
% 0.52/0.57 inference(monotonicity,[status(thm)],[3])).
% 0.52/0.57 tff(5,plain,
% 0.52/0.57 (between(v, w, x) <=> between(u, w, x)),
% 0.52/0.57 inference(symmetry,[status(thm)],[4])).
% 0.52/0.57 tff(6,plain,
% 0.52/0.57 ((~between(v, w, x)) <=> (~between(u, w, x))),
% 0.52/0.57 inference(monotonicity,[status(thm)],[5])).
% 0.52/0.57 tff(7,plain,
% 0.52/0.57 ((~between(v, w, x)) <=> (~between(v, w, x))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(8,axiom,(~between(v, w, x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_w_between_v_and_x')).
% 0.52/0.57 tff(9,plain,
% 0.52/0.57 (~between(v, w, x)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.52/0.57 tff(10,plain,
% 0.52/0.57 (~between(u, w, x)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.52/0.57 tff(11,plain,
% 0.52/0.57 (between(u, w, x) <=> between(u, w, x)),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(12,axiom,(between(u, w, x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','w_between_u_and_x')).
% 0.52/0.57 tff(13,plain,
% 0.52/0.57 (between(u, w, x)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.52/0.57 tff(14,plain,
% 0.52/0.57 ($false),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[13, 10])).
% 0.52/0.57 tff(15,plain,(~(u = v)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.57 tff(16,plain,
% 0.52/0.57 (between(u, v, w) <=> between(u, v, w)),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(17,axiom,(between(u, v, w)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v_between_u_and_w')).
% 0.52/0.57 tff(18,plain,
% 0.52/0.57 (between(u, v, w)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.52/0.57 tff(19,plain,
% 0.52/0.57 (^[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))))),
% 0.52/0.57 inference(bind,[status(th)],[])).
% 0.52/0.57 tff(20,plain,
% 0.52/0.57 (![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)))),
% 0.52/0.57 inference(quant_intro,[status(thm)],[19])).
% 0.52/0.57 tff(21,plain,
% 0.52/0.57 (![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)))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(22,plain,
% 0.52/0.57 (^[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))))),
% 0.52/0.57 inference(bind,[status(th)],[])).
% 0.52/0.57 tff(23,plain,
% 0.52/0.57 (![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)))),
% 0.52/0.57 inference(quant_intro,[status(thm)],[22])).
% 0.52/0.57 tff(24,axiom,(![W: $i, V: $i, U: $i] : (((~between(U, V, W)) | (U = V)) | (W = extension(U, V, V, W)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_1')).
% 0.52/0.57 tff(25,plain,
% 0.52/0.57 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.52/0.57 tff(26,plain,
% 0.52/0.57 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.52/0.57 tff(27,plain,(
% 0.52/0.57 ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.52/0.57 inference(skolemize,[status(sab)],[26])).
% 0.52/0.57 tff(28,plain,
% 0.52/0.57 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.52/0.57 tff(29,plain,
% 0.52/0.57 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(30,plain,
% 0.52/0.57 (((u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w))) <=> ((~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(31,plain,
% 0.52/0.57 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w))))),
% 0.52/0.57 inference(monotonicity,[status(thm)],[30])).
% 0.52/0.57 tff(32,plain,
% 0.52/0.57 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w)))),
% 0.52/0.57 inference(transitivity,[status(thm)],[31, 29])).
% 0.52/0.57 tff(33,plain,
% 0.52/0.57 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u = v) | (~between(u, v, w)) | (w = extension(u, v, v, w)))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(34,plain,
% 0.52/0.57 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(u, v, w)) | (u = v) | (w = extension(u, v, v, w))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.52/0.57 tff(35,plain,
% 0.52/0.57 ((u = v) | (w = extension(u, v, v, w))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[34, 28, 18])).
% 0.52/0.57 tff(36,plain,
% 0.52/0.57 (w = extension(u, v, v, w)),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[35, 15])).
% 0.52/0.57 tff(37,plain,
% 0.52/0.57 (extension(u, v, v, w) = w),
% 0.52/0.57 inference(symmetry,[status(thm)],[36])).
% 0.52/0.57 tff(38,plain,
% 0.52/0.57 (extension(u, v, v, w) = x),
% 0.52/0.57 inference(transitivity,[status(thm)],[37, 2])).
% 0.52/0.57 tff(39,plain,
% 0.52/0.57 (between(v, extension(u, v, v, w), extension(u, v, v, w)) <=> between(v, w, x)),
% 0.52/0.57 inference(monotonicity,[status(thm)],[37, 38])).
% 0.52/0.57 tff(40,plain,
% 0.52/0.57 (between(v, w, x) <=> between(v, extension(u, v, v, w), extension(u, v, v, w))),
% 0.52/0.57 inference(symmetry,[status(thm)],[39])).
% 0.52/0.57 tff(41,plain,
% 0.52/0.57 ((~between(v, w, x)) <=> (~between(v, extension(u, v, v, w), extension(u, v, v, w)))),
% 0.52/0.57 inference(monotonicity,[status(thm)],[40])).
% 0.52/0.57 tff(42,plain,
% 0.52/0.57 (~between(v, extension(u, v, v, w), extension(u, v, v, w))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[9, 41])).
% 0.52/0.57 tff(43,plain,
% 0.52/0.57 (^[V: $i, U: $i] : refl(between(U, V, V) <=> between(U, V, V))),
% 0.52/0.57 inference(bind,[status(th)],[])).
% 0.52/0.57 tff(44,plain,
% 0.52/0.57 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 0.52/0.57 inference(quant_intro,[status(thm)],[43])).
% 0.52/0.57 tff(45,plain,
% 0.52/0.57 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(46,axiom,(![V: $i, U: $i] : between(U, V, V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3')).
% 0.52/0.57 tff(47,plain,
% 0.52/0.57 (![V: $i, U: $i] : between(U, V, V)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.52/0.57 tff(48,plain,(
% 0.52/0.57 ![V: $i, U: $i] : between(U, V, V)),
% 0.52/0.57 inference(skolemize,[status(sab)],[47])).
% 0.52/0.57 tff(49,plain,
% 0.52/0.57 (![V: $i, U: $i] : between(U, V, V)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.52/0.57 tff(50,plain,
% 0.52/0.57 ((~![V: $i, U: $i] : between(U, V, V)) | between(v, extension(u, v, v, w), extension(u, v, v, w))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(51,plain,
% 0.52/0.57 (between(v, extension(u, v, v, w), extension(u, v, v, w))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.52/0.57 tff(52,plain,
% 0.52/0.57 ($false),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[51, 42])).
% 0.52/0.57 tff(53,plain,(~(x = w)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.57 tff(54,plain,
% 0.52/0.57 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | between(W, V, U)) <=> ((~between(U, V, W)) | between(W, V, U)))),
% 0.52/0.58 inference(bind,[status(th)],[])).
% 0.52/0.58 tff(55,plain,
% 0.52/0.58 (![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))),
% 0.52/0.58 inference(quant_intro,[status(thm)],[54])).
% 0.52/0.58 tff(56,plain,
% 0.52/0.58 (![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))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(57,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1')).
% 0.52/0.58 tff(58,plain,
% 0.52/0.58 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.52/0.58 tff(59,plain,(
% 0.52/0.58 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.52/0.58 inference(skolemize,[status(sab)],[58])).
% 0.52/0.58 tff(60,plain,
% 0.52/0.58 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.52/0.58 tff(61,plain,
% 0.52/0.58 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, w, x)) | between(x, w, u))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, w, x)) | between(x, w, u))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(62,plain,
% 0.52/0.58 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, w, x)) | between(x, w, u))),
% 0.52/0.58 inference(quant_inst,[status(thm)],[])).
% 0.52/0.58 tff(63,plain,
% 0.52/0.58 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, w, x)) | between(x, w, u)),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.52/0.58 tff(64,plain,
% 0.52/0.58 (between(x, w, u)),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[63, 60, 13])).
% 0.52/0.58 tff(65,plain,
% 0.52/0.58 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((x = w) | (~between(x, w, u)) | (u = extension(x, w, w, u)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (x = w) | (~between(x, w, u)) | (u = extension(x, w, w, u)))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(66,plain,
% 0.52/0.58 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((x = w) | (~between(x, w, u)) | (u = extension(x, w, w, u)))),
% 0.52/0.58 inference(quant_inst,[status(thm)],[])).
% 0.52/0.58 tff(67,plain,
% 0.52/0.58 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (x = w) | (~between(x, w, u)) | (u = extension(x, w, w, u))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.52/0.58 tff(68,plain,
% 0.52/0.58 ((x = w) | (u = extension(x, w, w, u))),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[67, 28, 64])).
% 0.52/0.58 tff(69,plain,
% 0.52/0.58 (u = extension(x, w, w, u)),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[68, 53])).
% 0.52/0.58 tff(70,plain,
% 0.52/0.58 (extension(x, w, w, u) = u),
% 0.52/0.58 inference(symmetry,[status(thm)],[69])).
% 0.52/0.58 tff(71,plain,
% 0.52/0.58 (^[V: $i, U: $i] : refl((U = reflection(reflection(U, V), V)) <=> (U = reflection(reflection(U, V), V)))),
% 0.52/0.58 inference(bind,[status(th)],[])).
% 0.52/0.58 tff(72,plain,
% 0.52/0.58 (![V: $i, U: $i] : (U = reflection(reflection(U, V), V)) <=> ![V: $i, U: $i] : (U = reflection(reflection(U, V), V))),
% 0.52/0.58 inference(quant_intro,[status(thm)],[71])).
% 0.52/0.58 tff(73,plain,
% 0.52/0.58 (![V: $i, U: $i] : (U = reflection(reflection(U, V), V)) <=> ![V: $i, U: $i] : (U = reflection(reflection(U, V), V))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(74,axiom,(![V: $i, U: $i] : (U = reflection(reflection(U, V), V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','r6')).
% 0.52/0.58 tff(75,plain,
% 0.52/0.58 (![V: $i, U: $i] : (U = reflection(reflection(U, V), V))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.52/0.58 tff(76,plain,(
% 0.52/0.58 ![V: $i, U: $i] : (U = reflection(reflection(U, V), V))),
% 0.52/0.58 inference(skolemize,[status(sab)],[75])).
% 0.52/0.58 tff(77,plain,
% 0.52/0.58 (![V: $i, U: $i] : (U = reflection(reflection(U, V), V))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.52/0.58 tff(78,plain,
% 0.52/0.58 ((~![V: $i, U: $i] : (U = reflection(reflection(U, V), V))) | (v = reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)))),
% 0.52/0.58 inference(quant_inst,[status(thm)],[])).
% 0.52/0.58 tff(79,plain,
% 0.52/0.58 (v = reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w))),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.52/0.58 tff(80,plain,
% 0.52/0.58 (reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)) = v),
% 0.52/0.58 inference(symmetry,[status(thm)],[79])).
% 0.52/0.58 tff(81,plain,
% 0.52/0.58 (between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u)) <=> between(w, v, u)),
% 0.52/0.58 inference(monotonicity,[status(thm)],[37, 80, 70])).
% 0.52/0.58 tff(82,plain,
% 0.52/0.58 (between(w, v, u) <=> between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))),
% 0.52/0.58 inference(symmetry,[status(thm)],[81])).
% 0.52/0.58 tff(83,plain,
% 0.52/0.58 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, v, w)) | between(w, v, u))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, v, w)) | between(w, v, u))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(84,plain,
% 0.52/0.58 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, v, w)) | between(w, v, u))),
% 0.52/0.58 inference(quant_inst,[status(thm)],[])).
% 0.52/0.58 tff(85,plain,
% 0.52/0.58 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, v, w)) | between(w, v, u)),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.52/0.58 tff(86,plain,
% 0.52/0.58 (between(w, v, u)),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[85, 60, 18])).
% 0.52/0.58 tff(87,plain,
% 0.52/0.58 (between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.52/0.58 tff(88,plain,
% 0.52/0.58 (between(extension(u, v, v, w), v, extension(x, w, w, u)) <=> between(w, v, u)),
% 0.52/0.58 inference(monotonicity,[status(thm)],[37, 70])).
% 0.52/0.58 tff(89,plain,
% 0.52/0.58 (between(w, v, u) <=> between(extension(u, v, v, w), v, extension(x, w, w, u))),
% 0.52/0.58 inference(symmetry,[status(thm)],[88])).
% 0.52/0.58 tff(90,plain,
% 0.52/0.58 (between(extension(u, v, v, w), v, extension(x, w, w, u))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[86, 89])).
% 0.52/0.58 tff(91,plain,
% 0.52/0.58 (between(x, extension(u, v, v, w), extension(x, w, w, u)) <=> between(x, w, u)),
% 0.52/0.58 inference(monotonicity,[status(thm)],[37, 70])).
% 0.52/0.58 tff(92,plain,
% 0.52/0.58 (between(x, w, u) <=> between(x, extension(u, v, v, w), extension(x, w, w, u))),
% 0.52/0.58 inference(symmetry,[status(thm)],[91])).
% 0.52/0.58 tff(93,plain,
% 0.52/0.58 (between(x, extension(u, v, v, w), extension(x, w, w, u))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[64, 92])).
% 0.52/0.58 tff(94,plain,
% 0.52/0.58 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl(((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y)) <=> ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y)))),
% 0.52/0.58 inference(bind,[status(th)],[])).
% 0.52/0.58 tff(95,plain,
% 0.52/0.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 0.52/0.58 inference(quant_intro,[status(thm)],[94])).
% 0.52/0.58 tff(96,plain,
% 0.52/0.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(97,plain,
% 0.52/0.58 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : rewrite((((~between(U, V, W)) | (~between(Y, X, W))) | between(V, inner_pasch(U, V, W, X, Y), Y)) <=> ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y)))),
% 0.52/0.58 inference(bind,[status(th)],[])).
% 0.52/0.58 tff(98,plain,
% 0.52/0.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(Y, X, W))) | between(V, inner_pasch(U, V, W, X, Y), Y)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 0.52/0.58 inference(quant_intro,[status(thm)],[97])).
% 0.52/0.58 tff(99,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(Y, X, W))) | between(V, inner_pasch(U, V, W, X, Y), Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax','inner_pasch1')).
% 0.52/0.58 tff(100,plain,
% 0.52/0.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.52/0.58 tff(101,plain,
% 0.52/0.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.52/0.58 tff(102,plain,(
% 0.52/0.58 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 0.52/0.58 inference(skolemize,[status(sab)],[101])).
% 0.52/0.58 tff(103,plain,
% 0.52/0.58 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.52/0.58 tff(104,plain,
% 0.52/0.58 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | ((~between(extension(u, v, v, w), v, extension(x, w, w, u))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | between(extension(u, v, v, w), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)), extension(u, v, v, w)))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | (~between(extension(u, v, v, w), v, extension(x, w, w, u))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | between(extension(u, v, v, w), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)), extension(u, v, v, w)))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(105,plain,
% 0.52/0.58 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | ((~between(extension(u, v, v, w), v, extension(x, w, w, u))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | between(extension(u, v, v, w), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)), extension(u, v, v, w)))),
% 0.52/0.58 inference(quant_inst,[status(thm)],[])).
% 0.52/0.58 tff(106,plain,
% 0.52/0.58 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(V, inner_pasch(U, V, W, X, Y), Y))) | (~between(extension(u, v, v, w), v, extension(x, w, w, u))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | between(extension(u, v, v, w), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)), extension(u, v, v, w))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.52/0.58 tff(107,plain,
% 0.52/0.58 ((~between(extension(u, v, v, w), v, extension(x, w, w, u))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | between(extension(u, v, v, w), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)), extension(u, v, v, w))),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.52/0.58 tff(108,plain,
% 0.52/0.58 (between(extension(u, v, v, w), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)), extension(u, v, v, w))),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[107, 93, 90])).
% 0.52/0.58 tff(109,plain,
% 0.52/0.58 (^[Y: $i, X: $i] : refl(((~between(X, Y, X)) | (X = Y)) <=> ((~between(X, Y, X)) | (X = Y)))),
% 0.52/0.58 inference(bind,[status(th)],[])).
% 0.52/0.58 tff(110,plain,
% 0.52/0.58 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y)) <=> ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.52/0.58 inference(quant_intro,[status(thm)],[109])).
% 0.52/0.58 tff(111,plain,
% 0.52/0.58 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y)) <=> ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(112,axiom,(![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax','identity_for_betweeness')).
% 0.52/0.59 tff(113,plain,
% 0.52/0.59 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.52/0.59 tff(114,plain,(
% 0.52/0.59 ![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.52/0.59 inference(skolemize,[status(sab)],[113])).
% 0.52/0.59 tff(115,plain,
% 0.52/0.59 (![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.52/0.59 tff(116,plain,
% 0.52/0.59 (((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(extension(u, v, v, w), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)), extension(u, v, v, w))) | (extension(u, v, v, w) = inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w))))) <=> ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(extension(u, v, v, w), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)), extension(u, v, v, w))) | (extension(u, v, v, w) = inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w))))),
% 0.52/0.59 inference(rewrite,[status(thm)],[])).
% 0.52/0.59 tff(117,plain,
% 0.52/0.59 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | ((~between(extension(u, v, v, w), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)), extension(u, v, v, w))) | (extension(u, v, v, w) = inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w))))),
% 0.52/0.59 inference(quant_inst,[status(thm)],[])).
% 0.52/0.59 tff(118,plain,
% 0.52/0.59 ((~![Y: $i, X: $i] : ((~between(X, Y, X)) | (X = Y))) | (~between(extension(u, v, v, w), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)), extension(u, v, v, w))) | (extension(u, v, v, w) = inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.52/0.59 tff(119,plain,
% 0.52/0.59 (extension(u, v, v, w) = inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w))),
% 0.52/0.59 inference(unit_resolution,[status(thm)],[118, 115, 108])).
% 0.52/0.59 tff(120,plain,
% 0.52/0.59 (inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w)) = extension(u, v, v, w)),
% 0.52/0.59 inference(symmetry,[status(thm)],[119])).
% 0.52/0.59 tff(121,plain,
% 0.52/0.59 (inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)) = inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), v, extension(u, v, v, w))),
% 0.52/0.59 inference(monotonicity,[status(thm)],[80])).
% 0.52/0.59 tff(122,plain,
% 0.52/0.59 (inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)) = w),
% 0.52/0.59 inference(transitivity,[status(thm)],[121, 120, 37])).
% 0.52/0.59 tff(123,plain,
% 0.52/0.59 (between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x) <=> between(v, w, x)),
% 0.52/0.59 inference(monotonicity,[status(thm)],[80, 122])).
% 0.52/0.59 tff(124,plain,
% 0.52/0.59 (between(v, w, x) <=> between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x)),
% 0.52/0.59 inference(symmetry,[status(thm)],[123])).
% 0.52/0.59 tff(125,plain,
% 0.52/0.59 ((~between(v, w, x)) <=> (~between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x))),
% 0.52/0.59 inference(monotonicity,[status(thm)],[124])).
% 0.52/0.59 tff(126,plain,
% 0.52/0.59 (~between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x)),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[9, 125])).
% 0.55/0.59 tff(127,plain,
% 0.55/0.59 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : refl(((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U)) <=> ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U)))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(128,plain,
% 0.55/0.59 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))),
% 0.55/0.59 inference(quant_intro,[status(thm)],[127])).
% 0.55/0.59 tff(129,plain,
% 0.55/0.59 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(130,plain,
% 0.55/0.59 (^[W: $i, V: $i, Y: $i, U: $i, X: $i] : rewrite((((~between(U, V, W)) | (~between(Y, X, W))) | between(X, inner_pasch(U, V, W, X, Y), U)) <=> ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U)))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(131,plain,
% 0.55/0.59 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(Y, X, W))) | between(X, inner_pasch(U, V, W, X, Y), U)) <=> ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))),
% 0.55/0.59 inference(quant_intro,[status(thm)],[130])).
% 0.55/0.59 tff(132,axiom,(![W: $i, V: $i, Y: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(Y, X, W))) | between(X, inner_pasch(U, V, W, X, Y), U))), file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax','inner_pasch2')).
% 0.55/0.59 tff(133,plain,
% 0.55/0.59 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.55/0.59 tff(134,plain,
% 0.55/0.59 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.55/0.59 tff(135,plain,(
% 0.55/0.59 ![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))),
% 0.55/0.59 inference(skolemize,[status(sab)],[134])).
% 0.55/0.59 tff(136,plain,
% 0.55/0.59 (![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.55/0.59 tff(137,plain,
% 0.55/0.59 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))) | ((~between(x, extension(u, v, v, w), extension(x, w, w, u))) | (~between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))) | between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | (~between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))) | between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(138,plain,
% 0.55/0.59 (((~between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x)) <=> ((~between(x, extension(u, v, v, w), extension(x, w, w, u))) | (~between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))) | between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(139,plain,
% 0.55/0.59 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))) | ((~between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))) | ((~between(x, extension(u, v, v, w), extension(x, w, w, u))) | (~between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))) | between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x)))),
% 0.55/0.59 inference(monotonicity,[status(thm)],[138])).
% 0.55/0.59 tff(140,plain,
% 0.55/0.59 (((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))) | ((~between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x))) <=> ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | (~between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))) | between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x))),
% 0.55/0.59 inference(transitivity,[status(thm)],[139, 137])).
% 0.55/0.59 tff(141,plain,
% 0.55/0.59 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))) | ((~between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x))),
% 0.55/0.59 inference(quant_inst,[status(thm)],[])).
% 0.55/0.59 tff(142,plain,
% 0.55/0.59 ((~![W: $i, V: $i, Y: $i, U: $i, X: $i] : ((~between(Y, X, W)) | (~between(U, V, W)) | between(X, inner_pasch(U, V, W, X, Y), U))) | (~between(x, extension(u, v, v, w), extension(x, w, w, u))) | (~between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))) | between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x)),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.55/0.60 tff(143,plain,
% 0.55/0.60 ((~between(extension(u, v, v, w), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(x, w, w, u))) | between(reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), inner_pasch(x, extension(u, v, v, w), extension(x, w, w, u), reflection(reflection(v, extension(u, v, v, w)), extension(u, v, v, w)), extension(u, v, v, w)), x)),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[142, 136, 93])).
% 0.55/0.60 tff(144,plain,
% 0.55/0.60 ($false),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[143, 126, 87])).
% 0.55/0.60 % SZS output end Proof
%------------------------------------------------------------------------------