%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO046-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 : Sat Jun 21 05:05:25 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO046-3 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:08:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(between_type, type, (
% 0.12/0.40 between: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(x_type, type, (
% 0.12/0.40 x: $i)).
% 0.12/0.40 tff(w_type, type, (
% 0.12/0.40 w: $i)).
% 0.12/0.40 tff(u_type, type, (
% 0.12/0.40 u: $i)).
% 0.12/0.40 tff(v_type, type, (
% 0.12/0.40 v: $i)).
% 0.12/0.40 tff(extension_type, type, (
% 0.12/0.40 extension: ( $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(1,assumption,(v = w), introduced(assumption)).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (w = v),
% 0.12/0.40 inference(symmetry,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (between(u, w, x) <=> between(u, v, x)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[2])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (between(u, v, x) <=> between(u, w, x)),
% 0.12/0.40 inference(symmetry,[status(thm)],[3])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (between(u, v, x) <=> between(u, v, x)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(6,axiom,(between(u, v, x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','v_between_u_and_x')).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (between(u, v, x)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (between(u, w, x)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 ((~between(u, w, x)) <=> (~between(u, w, x))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(10,axiom,(~between(u, w, x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_w_between_u_and_x')).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (~between(u, w, x)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.12/0.40 tff(13,plain,(~(v = w)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(14,assumption,(x = w), introduced(assumption)).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (w = x),
% 0.12/0.40 inference(symmetry,[status(thm)],[14])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (between(w, w, u) <=> between(x, w, u)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[15])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (between(x, w, u) <=> between(w, w, u)),
% 0.12/0.40 inference(symmetry,[status(thm)],[16])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 ((~between(x, w, u)) <=> (~between(w, w, u))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[17])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (^[W: $i, V: $i, U: $i] : refl(((~between(U, V, W)) | between(W, V, U)) <=> ((~between(U, V, W)) | between(W, V, U)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(22,axiom,(![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1')).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.40 tff(24,plain,(
% 0.12/0.40 ![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.12/0.40 inference(skolemize,[status(sab)],[23])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (((~![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(x, w, u)) | between(u, w, x))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(x, w, u)) | between(u, w, x)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (~between(x, w, u)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[28, 25, 11])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (~between(w, w, u)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[29, 18])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (^[V: $i, U: $i] : refl(between(U, U, V) <=> between(U, U, V))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (![V: $i, U: $i] : between(U, U, V) <=> ![V: $i, U: $i] : between(U, U, V)),
% 0.12/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (![V: $i, U: $i] : between(U, U, V) <=> ![V: $i, U: $i] : between(U, U, V)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(34,axiom,(![V: $i, U: $i] : between(U, U, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2')).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (![V: $i, U: $i] : between(U, U, V)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.40 tff(36,plain,(
% 0.12/0.40 ![V: $i, U: $i] : between(U, U, V)),
% 0.12/0.40 inference(skolemize,[status(sab)],[35])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (![V: $i, U: $i] : between(U, U, V)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((~![V: $i, U: $i] : between(U, U, V)) | between(w, w, u)),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (between(w, w, u)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[39, 30])).
% 0.12/0.40 tff(41,plain,(~(x = w)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (between(v, w, x) <=> between(v, w, x)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(43,axiom,(between(v, w, x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','w_between_v_and_x')).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (between(v, w, x)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (((~![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(v, w, x)) | between(x, w, v))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(v, w, x)) | between(x, w, v)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (between(x, w, v)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[47, 25, 44])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.40 tff(54,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')).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.12/0.40 tff(57,plain,(
% 0.12/0.40 ![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[56])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.12/0.40 tff(59,plain,
% 0.19/0.41 (((~![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 ((~![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)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (x = w) | (~between(x, w, v)) | (v = extension(x, w, w, v))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 ((x = w) | (v = extension(x, w, w, v))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[61, 58, 48])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (v = extension(x, w, w, v)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[62, 41])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (extension(x, w, w, v) = v),
% 0.19/0.41 inference(symmetry,[status(thm)],[63])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (between(w, extension(x, w, w, v), u) <=> between(w, v, u)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[64])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (between(w, v, u) <=> between(w, extension(x, w, w, v), u)),
% 0.19/0.41 inference(symmetry,[status(thm)],[65])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 ((~between(w, v, u)) <=> (~between(w, extension(x, w, w, v), u))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.41 tff(68,assumption,(~(v = w)), introduced(assumption)).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ((w = v) <=> (v = w)),
% 0.19/0.41 inference(commutativity,[status(thm)],[])).
% 0.19/0.41 tff(70,assumption,(w = v), introduced(assumption)).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (v = w),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[68, 71])).
% 0.19/0.41 tff(73,plain,((~(w = v)) | (v = w)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (~(w = v)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[73, 68])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (^[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)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.41 tff(80,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')).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.41 tff(83,plain,(
% 0.19/0.41 ![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.19/0.41 inference(skolemize,[status(sab)],[82])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (![W: $i, V: $i, U: $i, X: $i] : (between(U, V, X) | (~between(U, V, W)) | (~between(V, W, X)) | (V = W))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (((~![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ((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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (((~![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))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (((~![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)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[87, 85])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~![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))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~![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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 ((w = v) | (~between(w, v, u))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[90, 84, 48, 29])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (~between(w, v, u)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 74])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (~between(w, extension(x, w, w, v), u)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[92, 67])).
% 0.19/0.41 tff(94,assumption,(x = extension(u, v, v, x)), introduced(assumption)).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (extension(u, v, v, x) = x),
% 0.19/0.41 inference(symmetry,[status(thm)],[94])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (between(extension(u, v, v, x), extension(x, w, w, v), u) <=> between(x, v, u)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[95, 64])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (between(x, v, u) <=> between(extension(u, v, v, x), extension(x, w, w, v), u)),
% 0.19/0.41 inference(symmetry,[status(thm)],[96])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (((~![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | ((~between(u, v, x)) | between(x, v, u))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ((~![W: $i, V: $i, U: $i] : ((~between(U, V, W)) | between(W, V, U))) | (~between(u, v, x)) | between(x, v, u)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (between(x, v, u)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[100, 25, 7])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (between(extension(u, v, v, x), extension(x, w, w, v), u)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (between(extension(u, v, v, x), w, extension(x, w, w, v)) <=> between(x, w, v)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[95, 64])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (between(x, w, v) <=> between(extension(u, v, v, x), w, extension(x, w, w, v))),
% 0.19/0.41 inference(symmetry,[status(thm)],[103])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (between(extension(u, v, v, x), w, extension(x, w, w, v))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 104])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.41 tff(111,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')).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.19/0.41 tff(114,plain,(
% 0.19/0.41 ![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[113])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (((~![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), u)) | between(w, extension(x, w, w, 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), u)) | between(w, extension(x, w, w, v), u))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (((~between(extension(u, v, v, x), w, extension(x, w, w, v))) | between(w, extension(x, w, w, v), u) | (~between(extension(u, v, v, x), extension(x, w, w, 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), u)) | between(w, extension(x, w, w, v), u))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (((~![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), u) | (~between(extension(u, v, v, x), extension(x, w, w, 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), u)) | between(w, extension(x, w, w, v), u)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (((~![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), u) | (~between(extension(u, v, v, x), extension(x, w, w, 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), u)) | between(w, extension(x, w, w, v), u))),
% 0.19/0.42 inference(transitivity,[status(thm)],[118, 116])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 ((~![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), u) | (~between(extension(u, v, v, x), extension(x, w, w, v), u)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 ((~![W: $i, V: $i, U: $i, X: $i] : ((~between(U, V, W)) | between(V, W, X) | (~between(U, W, X)))) | (~between(extension(u, v, v, x), w, extension(x, w, w, v))) | (~between(extension(u, v, v, x), extension(x, w, w, v), u)) | between(w, extension(x, w, w, v), u)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (between(w, extension(x, w, w, v), u)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[121, 115, 105, 102])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[122, 93])).
% 0.19/0.42 tff(124,plain,((v = w) | (~(x = extension(u, v, v, x)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (~(x = extension(u, v, v, x))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[124, 13])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (((u = v) | (~between(u, v, x)) | (x = extension(u, v, v, x))) <=> ((~between(u, v, x)) | (u = v) | (x = extension(u, v, v, x)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (((~![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))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[127])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (((~![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)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[128, 126])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 ((~![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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 ((~![W: $i, V: $i, U: $i] : ((U = V) | (~between(U, V, W)) | (W = extension(U, V, V, W)))) | (~between(u, v, x)) | (u = v) | (x = extension(u, v, v, x))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 ((u = v) | (x = extension(u, v, v, x))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[131, 58, 7])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (u = v),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[132, 125])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (between(u, w, x) <=> between(v, w, x)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[133])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (between(v, w, x) <=> between(u, w, x)),
% 0.19/0.42 inference(symmetry,[status(thm)],[134])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (between(u, w, x)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 135])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[11, 136])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------