TSTP Solution File: GEO046-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO046-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 20:34:30 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO046-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 04:21:06 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(between_type, type, (
% 0.21/0.42 between: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(u_type, type, (
% 0.21/0.42 u: $i)).
% 0.21/0.42 tff(v_type, type, (
% 0.21/0.42 v: $i)).
% 0.21/0.42 tff(w_type, type, (
% 0.21/0.42 w: $i)).
% 0.21/0.42 tff(x_type, type, (
% 0.21/0.42 x: $i)).
% 0.21/0.42 tff(extension_type, type, (
% 0.21/0.42 extension: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.42 tff(1,assumption,(w = v), introduced(assumption)).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (between(u, w, x) <=> between(u, v, x)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[1])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (between(u, v, x) <=> between(u, w, x)),
% 0.21/0.42 inference(symmetry,[status(thm)],[2])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (between(u, v, x) <=> between(u, v, x)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(5,axiom,(between(u, v, x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v_between_u_and_x')).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (between(u, v, x)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (between(u, w, x)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 ((~between(u, w, x)) <=> (~between(u, w, x))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(9,axiom,(~between(u, w, x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_w_between_u_and_x')).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (~between(u, w, x)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.21/0.42 tff(12,plain,(~(w = v)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | between(W, V, U)) <=> ((~between(U, V, W)) | between(W, V, U)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(16,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1')).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.42 tff(18,plain,(
% 0.21/0.42 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.21/0.42 inference(skolemize,[status(sab)],[17])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(x, w, u)) | between(u, w, x))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(x, w, u)) | between(u, w, x))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(x, w, u)) | between(u, w, x))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(x, w, u)) | between(u, w, x)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (~between(x, w, u)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[22, 19, 10])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (between(v, w, x) <=> between(v, w, x)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(25,axiom,(between(v, w, x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','w_between_v_and_x')).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (between(v, w, x)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(v, w, x)) | between(x, w, v))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(v, w, x)) | between(x, w, v))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(v, w, x)) | between(x, w, v))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(v, w, x)) | between(x, w, v)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (between(x, w, v)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[29, 19, 26])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (^[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)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.42 tff(36,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/sandbox/benchmark/theBenchmark.p','b7')).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.42 tff(39,plain,(
% 0.21/0.42 ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.21/0.42 inference(skolemize,[status(sab)],[38])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | ((w = v) | between(x, w, u) | (~between(x, w, v)) | (~between(w, v, u)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (w = v) | between(x, w, u) | (~between(x, w, v)) | (~between(w, v, u)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 ((between(x, w, u) | (~between(x, w, v)) | (~between(w, v, u)) | (w = v)) <=> ((w = v) | between(x, w, u) | (~between(x, w, v)) | (~between(w, v, u)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (between(x, w, u) | (~between(x, w, v)) | (~between(w, v, u)) | (w = v))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | ((w = v) | between(x, w, u) | (~between(x, w, v)) | (~between(w, v, u))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[42])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (between(x, w, u) | (~between(x, w, v)) | (~between(w, v, u)) | (w = v))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (w = v) | between(x, w, u) | (~between(x, w, v)) | (~between(w, v, u)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[43, 41])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (between(x, w, u) | (~between(x, w, v)) | (~between(w, v, u)) | (w = v))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 ((~![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))) | (w = v) | between(x, w, u) | (~between(x, w, v)) | (~between(w, v, u))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 ((w = v) | (~between(w, v, u))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[46, 40, 30, 23])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (~between(w, v, u)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[47, 12])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, v, x)) | between(x, v, u))) <=> ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, v, x)) | between(x, v, u))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, v, x)) | between(x, v, u))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, v, x)) | between(x, v, u)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (between(x, v, u)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[51, 19, 6])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 ((v = x) <=> (x = v)),
% 0.21/0.43 inference(commutativity,[status(thm)],[])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 ((~(v = x)) <=> (~(x = v))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (^[W: $i, V: $i, U: $i, X: $i] : refl((between(V, W, X) | (~(U = X)) | (~between(U, W, X))) <=> (between(V, W, X) | (~(U = X)) | (~between(U, W, X))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(rewrite(((~between(U, W, X)) | (~(U = X))) <=> ((~(U = X)) | (~between(U, W, X)))), ((((~between(U, W, X)) | (~(U = X))) | between(V, W, X)) <=> (((~(U = X)) | (~between(U, W, X))) | between(V, W, X)))), rewrite((((~(U = X)) | (~between(U, W, X))) | between(V, W, X)) <=> (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))), ((((~between(U, W, X)) | (~(U = X))) | between(V, W, X)) <=> (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (![W: $i, V: $i, U: $i, X: $i] : (((~between(U, W, X)) | (~(U = X))) | between(V, W, X)) <=> ![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.43 tff(60,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, W, X)) | (~(U = X))) | between(V, W, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b1')).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 (![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.21/0.43 tff(63,plain,(
% 0.21/0.43 ![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[62])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u, w, x) | (~between(v, w, x)) | (~(v = x)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | between(u, w, x) | (~between(v, w, x)) | (~(v = x)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 ((between(u, w, x) | (~(v = x)) | (~between(v, w, x))) <=> (between(u, w, x) | (~between(v, w, x)) | (~(v = x)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u, w, x) | (~(v = x)) | (~between(v, w, x)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u, w, x) | (~between(v, w, x)) | (~(v = x))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[66])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u, w, x) | (~(v = x)) | (~between(v, w, x)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | between(u, w, x) | (~between(v, w, x)) | (~(v = x)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[67, 65])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | (between(u, w, x) | (~(v = x)) | (~between(v, w, x)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 ((~![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X)))) | between(u, w, x) | (~between(v, w, x)) | (~(v = x))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 (~(v = x)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[70, 64, 26, 10])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (~(x = v)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[71, 54])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.43 tff(78,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')).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.43 tff(81,plain,(
% 0.21/0.43 ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[80])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((x = v) | (~between(x, v, u)) | (u = extension(x, v, v, u)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (x = v) | (~between(x, v, u)) | (u = extension(x, v, v, u)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((x = v) | (~between(x, v, u)) | (u = extension(x, v, v, u)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (x = v) | (~between(x, v, u)) | (u = extension(x, v, v, u))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (u = extension(x, v, v, u)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[85, 82, 72, 52])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (extension(x, v, v, u) = u),
% 0.21/0.43 inference(symmetry,[status(thm)],[86])).
% 0.21/0.43 tff(88,assumption,(v = extension(x, w, w, v)), introduced(assumption)).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (extension(x, w, w, v) = v),
% 0.21/0.43 inference(symmetry,[status(thm)],[88])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (between(w, extension(x, w, w, v), extension(x, v, v, u)) <=> between(w, v, u)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[89, 87])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 (between(w, v, u) <=> between(w, extension(x, w, w, v), extension(x, v, v, u))),
% 0.21/0.43 inference(symmetry,[status(thm)],[90])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 ((~between(w, v, u)) <=> (~between(w, extension(x, w, w, v), extension(x, v, v, u)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[91])).
% 0.21/0.43 tff(93,assumption,(~between(w, v, u)), introduced(assumption)).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (~between(w, extension(x, w, w, v), extension(x, v, v, u))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.43 tff(95,assumption,(u = v), introduced(assumption)).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (v = u),
% 0.21/0.43 inference(symmetry,[status(thm)],[95])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (between(v, w, x) <=> between(u, w, x)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[96])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (between(u, w, x) <=> between(v, w, x)),
% 0.21/0.43 inference(symmetry,[status(thm)],[97])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 ((~between(u, w, x)) <=> (~between(v, w, x))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[98])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 (~between(v, w, x)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[10, 99])).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[26, 100])).
% 0.21/0.43 tff(102,plain,(~(u = v)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(u, v, x)) | (u = v) | (x = extension(u, v, v, x)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(u, v, x)) | (u = v) | (x = extension(u, v, v, x)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 (((u = v) | (~between(u, v, x)) | (x = extension(u, v, v, x))) <=> ((~between(u, v, x)) | (u = v) | (x = extension(u, v, v, x)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u = v) | (~between(u, v, x)) | (x = extension(u, v, v, x)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((~between(u, v, x)) | (u = v) | (x = extension(u, v, v, x))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[104])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u = v) | (~between(u, v, x)) | (x = extension(u, v, v, x)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(u, v, x)) | (u = v) | (x = extension(u, v, v, x)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[105, 103])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((u = v) | (~between(u, v, x)) | (x = extension(u, v, v, x)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(u, v, x)) | (u = v) | (x = extension(u, v, v, x))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 ((u = v) | (x = extension(u, v, v, x))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[108, 82, 6])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (x = extension(u, v, v, x)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[109, 102])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (extension(u, v, v, x) = x),
% 0.21/0.44 inference(symmetry,[status(thm)],[110])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 (between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u)) <=> between(x, v, u)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[111, 89, 87])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (between(x, v, u) <=> between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u))),
% 0.21/0.44 inference(symmetry,[status(thm)],[112])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[52, 113])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (between(extension(u, v, v, x), w, extension(x, w, w, v)) <=> between(x, w, v)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[111, 89])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (between(x, w, v) <=> between(extension(u, v, v, x), w, extension(x, w, w, v))),
% 0.21/0.44 inference(symmetry,[status(thm)],[115])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (between(extension(u, v, v, x), w, extension(x, w, w, v))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[30, 116])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[118])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[121])).
% 0.21/0.44 tff(123,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, V, W)) | (~between(U, W, X))) | between(V, W, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','b5')).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.21/0.44 tff(126,plain,(
% 0.21/0.44 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[125])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(u, v, v, x), w, extension(x, w, w, v))) | (~between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u))) | between(w, extension(x, w, w, v), extension(x, v, v, u)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(u, v, v, x), w, extension(x, w, w, v))) | (~between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u))) | between(w, extension(x, w, w, v), extension(x, v, v, u)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (((~between(extension(u, v, v, x), w, extension(x, w, w, v))) | between(w, extension(x, w, w, v), extension(x, v, v, u)) | (~between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u)))) <=> ((~between(extension(u, v, v, x), w, extension(x, w, w, v))) | (~between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u))) | between(w, extension(x, w, w, v), extension(x, v, v, u)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(u, v, v, x), w, extension(x, w, w, v))) | between(w, extension(x, w, w, v), extension(x, v, v, u)) | (~between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(u, v, v, x), w, extension(x, w, w, v))) | (~between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u))) | between(w, extension(x, w, w, v), extension(x, v, v, u))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[129])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 (((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(u, v, v, x), w, extension(x, w, w, v))) | between(w, extension(x, w, w, v), extension(x, v, v, u)) | (~between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(u, v, v, x), w, extension(x, w, w, v))) | (~between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u))) | between(w, extension(x, w, w, v), extension(x, v, v, u)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[130, 128])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | ((~between(extension(u, v, v, x), w, extension(x, w, w, v))) | between(w, extension(x, w, w, v), extension(x, v, v, u)) | (~between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(u, v, v, x), w, extension(x, w, w, v))) | (~between(extension(u, v, v, x), extension(x, w, w, v), extension(x, v, v, u))) | between(w, extension(x, w, w, v), extension(x, v, v, u))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 (between(w, extension(x, w, w, v), extension(x, v, v, u))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[133, 127, 117, 114])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[134, 94])).
% 0.21/0.44 tff(136,plain,(between(w, v, u) | (~(v = extension(x, w, w, v)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 (~(v = extension(x, w, w, v))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[136, 48])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 (((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((x = w) | (~between(x, w, v)) | (v = extension(x, w, w, v)))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (x = w) | (~between(x, w, v)) | (v = extension(x, w, w, v)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | ((x = w) | (~between(x, w, v)) | (v = extension(x, w, w, v)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (x = w) | (~between(x, w, v)) | (v = extension(x, w, w, v))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.45 tff(141,plain,
% 0.21/0.45 ((x = w) | (v = extension(x, w, w, v))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[140, 82, 30])).
% 0.21/0.45 tff(142,plain,
% 0.21/0.45 (x = w),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[141, 137])).
% 0.21/0.45 tff(143,plain,
% 0.21/0.45 (w = x),
% 0.21/0.45 inference(symmetry,[status(thm)],[142])).
% 0.21/0.45 tff(144,plain,
% 0.21/0.45 (between(w, v, u) <=> between(x, v, u)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[143])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 (between(x, v, u) <=> between(w, v, u)),
% 0.21/0.45 inference(symmetry,[status(thm)],[144])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 (between(w, v, u)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[52, 145])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[48, 146])).
% 0.21/0.45 % SZS output end Proof
%------------------------------------------------------------------------------