%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO026-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:05:22 AM UTC 2025
% Result : Unsatisfiable 10.34s 10.50s
% Output : Proof 10.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO026-3 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.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 14:05:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 10.34/10.50 % SZS status Unsatisfiable
% 10.34/10.50 % SZS output start Proof
% 10.34/10.50 tff(equidistant_type, type, (
% 10.34/10.50 equidistant: ( $i * $i * $i * $i ) > $o)).
% 10.34/10.50 tff(x_type, type, (
% 10.34/10.50 x: $i)).
% 10.34/10.50 tff(w_type, type, (
% 10.34/10.50 w: $i)).
% 10.34/10.50 tff(u_type, type, (
% 10.34/10.50 u: $i)).
% 10.34/10.50 tff(v_type, type, (
% 10.34/10.50 v: $i)).
% 10.34/10.50 tff(extension_type, type, (
% 10.34/10.50 extension: ( $i * $i * $i * $i ) > $i)).
% 10.34/10.50 tff(reflection_type, type, (
% 10.34/10.50 reflection: ( $i * $i ) > $i)).
% 10.34/10.50 tff(between_type, type, (
% 10.34/10.50 between: ( $i * $i * $i ) > $o)).
% 10.34/10.50 tff(1,assumption,(~equidistant(x, x, x, w)), introduced(assumption)).
% 10.34/10.50 tff(2,assumption,(~equidistant(x, x, w, x)), introduced(assumption)).
% 10.34/10.50 tff(3,assumption,(~equidistant(x, u, x, u)), introduced(assumption)).
% 10.34/10.50 tff(4,plain,
% 10.34/10.50 (^[V: $i, U: $i] : refl(equidistant(U, V, U, V) <=> equidistant(U, V, U, V))),
% 10.34/10.50 inference(bind,[status(th)],[])).
% 10.34/10.50 tff(5,plain,
% 10.34/10.50 (![V: $i, U: $i] : equidistant(U, V, U, V) <=> ![V: $i, U: $i] : equidistant(U, V, U, V)),
% 10.34/10.50 inference(quant_intro,[status(thm)],[4])).
% 10.34/10.50 tff(6,plain,
% 10.34/10.50 (![V: $i, U: $i] : equidistant(U, V, U, V) <=> ![V: $i, U: $i] : equidistant(U, V, U, V)),
% 10.34/10.50 inference(rewrite,[status(thm)],[])).
% 10.34/10.50 tff(7,axiom,(![V: $i, U: $i] : equidistant(U, V, U, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1')).
% 10.34/10.50 tff(8,plain,
% 10.34/10.50 (![V: $i, U: $i] : equidistant(U, V, U, V)),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[7, 6])).
% 10.34/10.50 tff(9,plain,(
% 10.34/10.50 ![V: $i, U: $i] : equidistant(U, V, U, V)),
% 10.34/10.50 inference(skolemize,[status(sab)],[8])).
% 10.34/10.50 tff(10,plain,
% 10.34/10.50 (![V: $i, U: $i] : equidistant(U, V, U, V)),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[9, 5])).
% 10.34/10.50 tff(11,plain,
% 10.34/10.50 ((~![V: $i, U: $i] : equidistant(U, V, U, V)) | equidistant(x, u, x, u)),
% 10.34/10.50 inference(quant_inst,[status(thm)],[])).
% 10.34/10.50 tff(12,plain,
% 10.34/10.50 ($false),
% 10.34/10.50 inference(unit_resolution,[status(thm)],[11, 10, 3])).
% 10.34/10.50 tff(13,plain,(equidistant(x, u, x, u)), inference(lemma,lemma(discharge,[]))).
% 10.34/10.50 tff(14,plain,
% 10.34/10.50 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)) <=> ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)))),
% 10.34/10.50 inference(bind,[status(th)],[])).
% 10.34/10.50 tff(15,plain,
% 10.34/10.50 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 10.34/10.50 inference(quant_intro,[status(thm)],[14])).
% 10.34/10.50 tff(16,plain,
% 10.34/10.50 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 10.34/10.50 inference(rewrite,[status(thm)],[])).
% 10.34/10.50 tff(17,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_5')).
% 10.34/10.50 tff(18,plain,
% 10.34/10.50 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[17, 16])).
% 10.34/10.50 tff(19,plain,(
% 10.34/10.50 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 10.34/10.50 inference(skolemize,[status(sab)],[18])).
% 10.34/10.50 tff(20,plain,
% 10.34/10.50 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[19, 15])).
% 10.34/10.50 tff(21,plain,
% 10.34/10.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(x, u, x, u)) | equidistant(u, x, u, x))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(x, u, x, u)) | equidistant(u, x, u, x))),
% 10.34/10.50 inference(rewrite,[status(thm)],[])).
% 10.34/10.50 tff(22,plain,
% 10.34/10.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(x, u, x, u)) | equidistant(u, x, u, x))),
% 10.34/10.50 inference(quant_inst,[status(thm)],[])).
% 10.34/10.50 tff(23,plain,
% 10.34/10.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(x, u, x, u)) | equidistant(u, x, u, x)),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[22, 21])).
% 10.34/10.50 tff(24,plain,
% 10.34/10.50 (equidistant(u, x, u, x)),
% 10.34/10.50 inference(unit_resolution,[status(thm)],[23, 20, 13])).
% 10.34/10.50 tff(25,assumption,(~equidistant(v, x, v, x)), introduced(assumption)).
% 10.34/10.50 tff(26,plain,
% 10.34/10.50 (equidistant(v, w, v, x) <=> equidistant(v, w, v, x)),
% 10.34/10.50 inference(rewrite,[status(thm)],[])).
% 10.34/10.50 tff(27,axiom,(equidistant(v, w, v, x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','v_to_w_equals_v_to_x')).
% 10.34/10.50 tff(28,plain,
% 10.34/10.50 (equidistant(v, w, v, x)),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[27, 26])).
% 10.34/10.50 tff(29,plain,
% 10.34/10.50 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)))),
% 10.34/10.50 inference(bind,[status(th)],[])).
% 10.34/10.50 tff(30,plain,
% 10.34/10.50 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 10.34/10.50 inference(quant_intro,[status(thm)],[29])).
% 10.34/10.50 tff(31,plain,
% 10.34/10.50 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 10.34/10.50 inference(rewrite,[status(thm)],[])).
% 10.34/10.50 tff(32,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2')).
% 10.34/10.50 tff(33,plain,
% 10.34/10.50 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[32, 31])).
% 10.34/10.50 tff(34,plain,(
% 10.34/10.50 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 10.34/10.50 inference(skolemize,[status(sab)],[33])).
% 10.34/10.50 tff(35,plain,
% 10.34/10.50 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[34, 30])).
% 10.34/10.50 tff(36,plain,
% 10.34/10.50 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(v, w, v, x)) | equidistant(v, x, v, w))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(v, w, v, x)) | equidistant(v, x, v, w))),
% 10.34/10.50 inference(rewrite,[status(thm)],[])).
% 10.34/10.50 tff(37,plain,
% 10.34/10.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(v, w, v, x)) | equidistant(v, x, v, w))),
% 10.34/10.50 inference(quant_inst,[status(thm)],[])).
% 10.34/10.50 tff(38,plain,
% 10.34/10.50 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(v, w, v, x)) | equidistant(v, x, v, w)),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[37, 36])).
% 10.34/10.50 tff(39,plain,
% 10.34/10.50 (equidistant(v, x, v, w)),
% 10.34/10.50 inference(unit_resolution,[status(thm)],[38, 35, 28])).
% 10.34/10.50 tff(40,plain,
% 10.34/10.50 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X))) <=> (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X))))),
% 10.34/10.50 inference(bind,[status(th)],[])).
% 10.34/10.50 tff(41,plain,
% 10.34/10.50 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 10.34/10.50 inference(quant_intro,[status(thm)],[40])).
% 10.34/10.50 tff(42,plain,
% 10.34/10.50 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 10.34/10.50 inference(rewrite,[status(thm)],[])).
% 10.34/10.50 tff(43,plain,
% 10.34/10.50 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : rewrite((((~equidistant(U, V, W, X)) | (~equidistant(W, X, Y, Z))) | equidistant(U, V, Y, Z)) <=> (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X))))),
% 10.34/10.50 inference(bind,[status(th)],[])).
% 10.34/10.50 tff(44,plain,
% 10.34/10.50 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((~equidistant(U, V, W, X)) | (~equidistant(W, X, Y, Z))) | equidistant(U, V, Y, Z)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 10.34/10.50 inference(quant_intro,[status(thm)],[43])).
% 10.34/10.50 tff(45,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (((~equidistant(U, V, W, X)) | (~equidistant(W, X, Y, Z))) | equidistant(U, V, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5')).
% 10.34/10.50 tff(46,plain,
% 10.34/10.50 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[45, 44])).
% 10.34/10.50 tff(47,plain,
% 10.34/10.50 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[46, 42])).
% 10.34/10.50 tff(48,plain,(
% 10.34/10.50 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 10.34/10.50 inference(skolemize,[status(sab)],[47])).
% 10.34/10.50 tff(49,plain,
% 10.34/10.50 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[48, 41])).
% 10.34/10.50 tff(50,plain,
% 10.34/10.50 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | ((~equidistant(v, w, v, x)) | (~equidistant(v, x, v, w)) | equidistant(v, x, v, x))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(v, w, v, x)) | (~equidistant(v, x, v, w)) | equidistant(v, x, v, x))),
% 10.34/10.50 inference(rewrite,[status(thm)],[])).
% 10.34/10.50 tff(51,plain,
% 10.34/10.50 ((equidistant(v, x, v, x) | (~equidistant(v, w, v, x)) | (~equidistant(v, x, v, w))) <=> ((~equidistant(v, w, v, x)) | (~equidistant(v, x, v, w)) | equidistant(v, x, v, x))),
% 10.34/10.50 inference(rewrite,[status(thm)],[])).
% 10.34/10.50 tff(52,plain,
% 10.34/10.50 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(v, x, v, x) | (~equidistant(v, w, v, x)) | (~equidistant(v, x, v, w)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | ((~equidistant(v, w, v, x)) | (~equidistant(v, x, v, w)) | equidistant(v, x, v, x)))),
% 10.34/10.50 inference(monotonicity,[status(thm)],[51])).
% 10.34/10.50 tff(53,plain,
% 10.34/10.50 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(v, x, v, x) | (~equidistant(v, w, v, x)) | (~equidistant(v, x, v, w)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(v, w, v, x)) | (~equidistant(v, x, v, w)) | equidistant(v, x, v, x))),
% 10.34/10.50 inference(transitivity,[status(thm)],[52, 50])).
% 10.34/10.50 tff(54,plain,
% 10.34/10.50 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(v, x, v, x) | (~equidistant(v, w, v, x)) | (~equidistant(v, x, v, w)))),
% 10.34/10.50 inference(quant_inst,[status(thm)],[])).
% 10.34/10.50 tff(55,plain,
% 10.34/10.50 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(v, w, v, x)) | (~equidistant(v, x, v, w)) | equidistant(v, x, v, x)),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[54, 53])).
% 10.34/10.50 tff(56,plain,
% 10.34/10.50 ($false),
% 10.34/10.50 inference(unit_resolution,[status(thm)],[55, 49, 28, 39, 25])).
% 10.34/10.50 tff(57,plain,(equidistant(v, x, v, x)), inference(lemma,lemma(discharge,[]))).
% 10.34/10.50 tff(58,assumption,(~equidistant(u, v, u, v)), introduced(assumption)).
% 10.34/10.50 tff(59,plain,
% 10.34/10.50 (^[V: $i, U: $i] : refl((reflection(U, V) = extension(U, V, U, V)) <=> (reflection(U, V) = extension(U, V, U, V)))),
% 10.34/10.50 inference(bind,[status(th)],[])).
% 10.34/10.50 tff(60,plain,
% 10.34/10.50 (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V)) <=> ![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 10.34/10.50 inference(quant_intro,[status(thm)],[59])).
% 10.34/10.50 tff(61,plain,
% 10.34/10.50 (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V)) <=> ![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 10.34/10.50 inference(rewrite,[status(thm)],[])).
% 10.34/10.50 tff(62,axiom,(![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-2.ax','reflection')).
% 10.34/10.50 tff(63,plain,
% 10.34/10.50 (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[62, 61])).
% 10.34/10.50 tff(64,plain,(
% 10.34/10.50 ![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 10.34/10.50 inference(skolemize,[status(sab)],[63])).
% 10.34/10.50 tff(65,plain,
% 10.34/10.50 (![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))),
% 10.34/10.50 inference(modus_ponens,[status(thm)],[64, 60])).
% 10.34/10.50 tff(66,plain,
% 10.34/10.50 ((~![V: $i, U: $i] : (reflection(U, V) = extension(U, V, U, V))) | (reflection(u, v) = extension(u, v, u, v))),
% 10.34/10.50 inference(quant_inst,[status(thm)],[])).
% 10.34/10.50 tff(67,plain,
% 10.34/10.50 (reflection(u, v) = extension(u, v, u, v)),
% 10.34/10.50 inference(unit_resolution,[status(thm)],[66, 65])).
% 10.34/10.51 tff(68,plain,
% 10.34/10.51 (extension(u, v, u, v) = reflection(u, v)),
% 10.34/10.51 inference(symmetry,[status(thm)],[67])).
% 10.34/10.51 tff(69,plain,
% 10.34/10.51 (equidistant(v, extension(u, v, u, v), u, v) <=> equidistant(v, reflection(u, v), u, v)),
% 10.34/10.51 inference(monotonicity,[status(thm)],[68])).
% 10.34/10.51 tff(70,plain,
% 10.34/10.51 (equidistant(v, reflection(u, v), u, v) <=> equidistant(v, extension(u, v, u, v), u, v)),
% 10.34/10.51 inference(symmetry,[status(thm)],[69])).
% 10.34/10.51 tff(71,plain,
% 10.34/10.51 (^[V: $i, U: $i] : refl(equidistant(V, reflection(U, V), U, V) <=> equidistant(V, reflection(U, V), U, V))),
% 10.34/10.51 inference(bind,[status(th)],[])).
% 10.34/10.51 tff(72,plain,
% 10.34/10.51 (![V: $i, U: $i] : equidistant(V, reflection(U, V), U, V) <=> ![V: $i, U: $i] : equidistant(V, reflection(U, V), U, V)),
% 10.34/10.51 inference(quant_intro,[status(thm)],[71])).
% 10.34/10.51 tff(73,plain,
% 10.34/10.51 (![V: $i, U: $i] : equidistant(V, reflection(U, V), U, V) <=> ![V: $i, U: $i] : equidistant(V, reflection(U, V), U, V)),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(74,axiom,(![V: $i, U: $i] : equidistant(V, reflection(U, V), U, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','r2_2')).
% 10.34/10.51 tff(75,plain,
% 10.34/10.51 (![V: $i, U: $i] : equidistant(V, reflection(U, V), U, V)),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[74, 73])).
% 10.34/10.51 tff(76,plain,(
% 10.34/10.51 ![V: $i, U: $i] : equidistant(V, reflection(U, V), U, V)),
% 10.34/10.51 inference(skolemize,[status(sab)],[75])).
% 10.34/10.51 tff(77,plain,
% 10.34/10.51 (![V: $i, U: $i] : equidistant(V, reflection(U, V), U, V)),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[76, 72])).
% 10.34/10.51 tff(78,plain,
% 10.34/10.51 ((~![V: $i, U: $i] : equidistant(V, reflection(U, V), U, V)) | equidistant(v, reflection(u, v), u, v)),
% 10.34/10.51 inference(quant_inst,[status(thm)],[])).
% 10.34/10.51 tff(79,plain,
% 10.34/10.51 (equidistant(v, reflection(u, v), u, v)),
% 10.34/10.51 inference(unit_resolution,[status(thm)],[78, 77])).
% 10.34/10.51 tff(80,plain,
% 10.34/10.51 (equidistant(v, extension(u, v, u, v), u, v)),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[79, 70])).
% 10.34/10.51 tff(81,plain,
% 10.34/10.51 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(v, extension(u, v, u, v), u, v)) | equidistant(u, v, v, extension(u, v, u, v)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(v, extension(u, v, u, v), u, v)) | equidistant(u, v, v, extension(u, v, u, v)))),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(82,plain,
% 10.34/10.51 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | ((~equidistant(v, extension(u, v, u, v), u, v)) | equidistant(u, v, v, extension(u, v, u, v)))),
% 10.34/10.51 inference(quant_inst,[status(thm)],[])).
% 10.34/10.51 tff(83,plain,
% 10.34/10.51 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(W, X, U, V))) | (~equidistant(v, extension(u, v, u, v), u, v)) | equidistant(u, v, v, extension(u, v, u, v))),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[82, 81])).
% 10.34/10.51 tff(84,plain,
% 10.34/10.51 ((~equidistant(v, extension(u, v, u, v), u, v)) | equidistant(u, v, v, extension(u, v, u, v))),
% 10.34/10.51 inference(unit_resolution,[status(thm)],[83, 35])).
% 10.34/10.51 tff(85,plain,
% 10.34/10.51 (equidistant(u, v, v, extension(u, v, u, v))),
% 10.34/10.51 inference(unit_resolution,[status(thm)],[84, 80])).
% 10.34/10.51 tff(86,plain,
% 10.34/10.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | ((~equidistant(v, extension(u, v, u, v), u, v)) | equidistant(u, v, u, v) | (~equidistant(u, v, v, extension(u, v, u, v))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(v, extension(u, v, u, v), u, v)) | equidistant(u, v, u, v) | (~equidistant(u, v, v, extension(u, v, u, v))))),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(87,plain,
% 10.34/10.51 ((equidistant(u, v, u, v) | (~equidistant(v, extension(u, v, u, v), u, v)) | (~equidistant(u, v, v, extension(u, v, u, v)))) <=> ((~equidistant(v, extension(u, v, u, v), u, v)) | equidistant(u, v, u, v) | (~equidistant(u, v, v, extension(u, v, u, v))))),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(88,plain,
% 10.34/10.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(u, v, u, v) | (~equidistant(v, extension(u, v, u, v), u, v)) | (~equidistant(u, v, v, extension(u, v, u, v))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | ((~equidistant(v, extension(u, v, u, v), u, v)) | equidistant(u, v, u, v) | (~equidistant(u, v, v, extension(u, v, u, v)))))),
% 10.34/10.51 inference(monotonicity,[status(thm)],[87])).
% 10.34/10.51 tff(89,plain,
% 10.34/10.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(u, v, u, v) | (~equidistant(v, extension(u, v, u, v), u, v)) | (~equidistant(u, v, v, extension(u, v, u, v))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(v, extension(u, v, u, v), u, v)) | equidistant(u, v, u, v) | (~equidistant(u, v, v, extension(u, v, u, v))))),
% 10.34/10.51 inference(transitivity,[status(thm)],[88, 86])).
% 10.34/10.51 tff(90,plain,
% 10.34/10.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(u, v, u, v) | (~equidistant(v, extension(u, v, u, v), u, v)) | (~equidistant(u, v, v, extension(u, v, u, v))))),
% 10.34/10.51 inference(quant_inst,[status(thm)],[])).
% 10.34/10.51 tff(91,plain,
% 10.34/10.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(v, extension(u, v, u, v), u, v)) | equidistant(u, v, u, v) | (~equidistant(u, v, v, extension(u, v, u, v)))),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[90, 89])).
% 10.34/10.51 tff(92,plain,
% 10.34/10.51 ($false),
% 10.34/10.51 inference(unit_resolution,[status(thm)],[91, 49, 80, 85, 58])).
% 10.34/10.51 tff(93,plain,(equidistant(u, v, u, v)), inference(lemma,lemma(discharge,[]))).
% 10.34/10.51 tff(94,plain,
% 10.34/10.51 ((~(u = v)) <=> (~(u = v))),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(95,axiom,(~(u = v)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','u_not_v')).
% 10.34/10.51 tff(96,plain,
% 10.34/10.51 (~(u = v)),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[95, 94])).
% 10.34/10.51 tff(97,plain,
% 10.34/10.51 (between(u, v, x) <=> between(u, v, x)),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(98,axiom,(between(u, v, x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','v_between_u_and_x')).
% 10.34/10.51 tff(99,plain,
% 10.34/10.51 (between(u, v, x)),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[98, 97])).
% 10.34/10.51 tff(100,plain,
% 10.34/10.51 (between(u, v, w) <=> between(u, v, w)),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(101,axiom,(between(u, v, w)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','v_between_u_and_w')).
% 10.34/10.51 tff(102,plain,
% 10.34/10.51 (between(u, v, w)),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[101, 100])).
% 10.34/10.51 tff(103,plain,
% 10.34/10.51 (^[V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : refl((equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) <=> (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))),
% 10.34/10.51 inference(bind,[status(th)],[])).
% 10.34/10.51 tff(104,plain,
% 10.34/10.51 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) <=> ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 10.34/10.51 inference(quant_intro,[status(thm)],[103])).
% 10.34/10.51 tff(105,plain,
% 10.34/10.51 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) <=> ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(106,plain,
% 10.34/10.51 (^[V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) <=> ((~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) <=> (((~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~equidistant(Y, V, Y1, V1))))), rewrite((((~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~equidistant(Y, V, Y1, V1))) <=> ((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) <=> ((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), ((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) <=> (((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X, Y, Z))))), rewrite((((~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X, Y, Z))) <=> ((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), ((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) <=> ((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), (((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) <=> (((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X1, Y1, Z1))))), rewrite((((~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (~between(X1, Y1, Z1))) <=> ((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) <=> ((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) <=> (((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (X = Y)))), rewrite((((~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | (X = Y)) <=> ((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) <=> ((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))))), (((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1)) <=> (((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | equidistant(Z, V, Z1, V1)))), rewrite((((X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1))) | equidistant(Z, V, Z1, V1)) <=> (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))), (((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1)) <=> (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))))),
% 10.34/10.51 inference(bind,[status(th)],[])).
% 10.34/10.51 tff(107,plain,
% 10.34/10.51 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1)) <=> ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 10.34/10.51 inference(quant_intro,[status(thm)],[106])).
% 10.34/10.51 tff(108,axiom,(![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : ((((((((~equidistant(X, Y, X1, Y1)) | (~equidistant(Y, Z, Y1, Z1))) | (~equidistant(X, V, X1, V1))) | (~equidistant(Y, V, Y1, V1))) | (~between(X, Y, Z))) | (~between(X1, Y1, Z1))) | (X = Y)) | equidistant(Z, V, Z1, V1))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','outer_five_segment')).
% 10.34/10.51 tff(109,plain,
% 10.34/10.51 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[108, 107])).
% 10.34/10.51 tff(110,plain,
% 10.34/10.51 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[109, 105])).
% 10.34/10.51 tff(111,plain,(
% 10.34/10.51 ![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 10.34/10.51 inference(skolemize,[status(sab)],[110])).
% 10.34/10.51 tff(112,plain,
% 10.34/10.51 (![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[111, 104])).
% 10.34/10.51 tff(113,plain,
% 10.34/10.51 (((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | ((u = v) | (~between(u, v, w)) | (~between(u, v, x)) | (~equidistant(v, x, v, w)) | (~equidistant(u, x, u, x)) | (~equidistant(v, x, v, x)) | equidistant(x, x, w, x) | (~equidistant(u, v, u, v)))) <=> ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (u = v) | (~between(u, v, w)) | (~between(u, v, x)) | (~equidistant(v, x, v, w)) | (~equidistant(u, x, u, x)) | (~equidistant(v, x, v, x)) | equidistant(x, x, w, x) | (~equidistant(u, v, u, v)))),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(114,plain,
% 10.34/10.51 ((equidistant(x, x, w, x) | (u = v) | (~between(u, v, w)) | (~between(u, v, x)) | (~equidistant(v, x, v, x)) | (~equidistant(u, x, u, x)) | (~equidistant(v, x, v, w)) | (~equidistant(u, v, u, v))) <=> ((u = v) | (~between(u, v, w)) | (~between(u, v, x)) | (~equidistant(v, x, v, w)) | (~equidistant(u, x, u, x)) | (~equidistant(v, x, v, x)) | equidistant(x, x, w, x) | (~equidistant(u, v, u, v)))),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(115,plain,
% 10.34/10.51 (((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (equidistant(x, x, w, x) | (u = v) | (~between(u, v, w)) | (~between(u, v, x)) | (~equidistant(v, x, v, x)) | (~equidistant(u, x, u, x)) | (~equidistant(v, x, v, w)) | (~equidistant(u, v, u, v)))) <=> ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | ((u = v) | (~between(u, v, w)) | (~between(u, v, x)) | (~equidistant(v, x, v, w)) | (~equidistant(u, x, u, x)) | (~equidistant(v, x, v, x)) | equidistant(x, x, w, x) | (~equidistant(u, v, u, v))))),
% 10.34/10.51 inference(monotonicity,[status(thm)],[114])).
% 10.34/10.51 tff(116,plain,
% 10.34/10.51 (((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (equidistant(x, x, w, x) | (u = v) | (~between(u, v, w)) | (~between(u, v, x)) | (~equidistant(v, x, v, x)) | (~equidistant(u, x, u, x)) | (~equidistant(v, x, v, w)) | (~equidistant(u, v, u, v)))) <=> ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (u = v) | (~between(u, v, w)) | (~between(u, v, x)) | (~equidistant(v, x, v, w)) | (~equidistant(u, x, u, x)) | (~equidistant(v, x, v, x)) | equidistant(x, x, w, x) | (~equidistant(u, v, u, v)))),
% 10.34/10.51 inference(transitivity,[status(thm)],[115, 113])).
% 10.34/10.51 tff(117,plain,
% 10.34/10.51 ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (equidistant(x, x, w, x) | (u = v) | (~between(u, v, w)) | (~between(u, v, x)) | (~equidistant(v, x, v, x)) | (~equidistant(u, x, u, x)) | (~equidistant(v, x, v, w)) | (~equidistant(u, v, u, v)))),
% 10.34/10.51 inference(quant_inst,[status(thm)],[])).
% 10.34/10.51 tff(118,plain,
% 10.34/10.51 ((~![V: $i, Z: $i, Y1: $i, Y: $i, Z1: $i, V1: $i, X: $i, X1: $i] : (equidistant(Z, V, Z1, V1) | (X = Y) | (~between(X1, Y1, Z1)) | (~between(X, Y, Z)) | (~equidistant(Y, V, Y1, V1)) | (~equidistant(X, V, X1, V1)) | (~equidistant(Y, Z, Y1, Z1)) | (~equidistant(X, Y, X1, Y1)))) | (u = v) | (~between(u, v, w)) | (~between(u, v, x)) | (~equidistant(v, x, v, w)) | (~equidistant(u, x, u, x)) | (~equidistant(v, x, v, x)) | equidistant(x, x, w, x) | (~equidistant(u, v, u, v))),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[117, 116])).
% 10.34/10.51 tff(119,plain,
% 10.34/10.51 ($false),
% 10.34/10.51 inference(unit_resolution,[status(thm)],[118, 112, 102, 99, 96, 39, 93, 57, 24, 2])).
% 10.34/10.51 tff(120,plain,(equidistant(x, x, w, x)), inference(lemma,lemma(discharge,[]))).
% 10.34/10.51 tff(121,assumption,(~equidistant(x, w, w, x)), introduced(assumption)).
% 10.34/10.51 tff(122,plain,
% 10.34/10.51 (^[Y: $i, X: $i] : refl(equidistant(X, Y, Y, X) <=> equidistant(X, Y, Y, X))),
% 10.34/10.51 inference(bind,[status(th)],[])).
% 10.34/10.51 tff(123,plain,
% 10.34/10.51 (![Y: $i, X: $i] : equidistant(X, Y, Y, X) <=> ![Y: $i, X: $i] : equidistant(X, Y, Y, X)),
% 10.34/10.51 inference(quant_intro,[status(thm)],[122])).
% 10.34/10.51 tff(124,plain,
% 10.34/10.51 (![Y: $i, X: $i] : equidistant(X, Y, Y, X) <=> ![Y: $i, X: $i] : equidistant(X, Y, Y, X)),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(125,axiom,(![Y: $i, X: $i] : equidistant(X, Y, Y, X)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','reflexivity_for_equidistance')).
% 10.34/10.51 tff(126,plain,
% 10.34/10.51 (![Y: $i, X: $i] : equidistant(X, Y, Y, X)),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[125, 124])).
% 10.34/10.51 tff(127,plain,(
% 10.34/10.51 ![Y: $i, X: $i] : equidistant(X, Y, Y, X)),
% 10.34/10.51 inference(skolemize,[status(sab)],[126])).
% 10.34/10.51 tff(128,plain,
% 10.34/10.51 (![Y: $i, X: $i] : equidistant(X, Y, Y, X)),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[127, 123])).
% 10.34/10.51 tff(129,plain,
% 10.34/10.51 ((~![Y: $i, X: $i] : equidistant(X, Y, Y, X)) | equidistant(x, w, w, x)),
% 10.34/10.51 inference(quant_inst,[status(thm)],[])).
% 10.34/10.51 tff(130,plain,
% 10.34/10.51 ($false),
% 10.34/10.51 inference(unit_resolution,[status(thm)],[129, 128, 121])).
% 10.34/10.51 tff(131,plain,(equidistant(x, w, w, x)), inference(lemma,lemma(discharge,[]))).
% 10.34/10.51 tff(132,plain,
% 10.34/10.51 (^[W: $i, V: $i, U: $i, X: $i] : refl(((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)) <=> ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)))),
% 10.34/10.51 inference(bind,[status(th)],[])).
% 10.34/10.51 tff(133,plain,
% 10.34/10.51 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 10.34/10.51 inference(quant_intro,[status(thm)],[132])).
% 10.34/10.51 tff(134,plain,
% 10.34/10.51 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W)) <=> ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(135,axiom,(![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_2')).
% 10.34/10.51 tff(136,plain,
% 10.34/10.51 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[135, 134])).
% 10.34/10.51 tff(137,plain,(
% 10.34/10.51 ![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 10.34/10.51 inference(skolemize,[status(sab)],[136])).
% 10.34/10.51 tff(138,plain,
% 10.34/10.51 (![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[137, 133])).
% 10.34/10.51 tff(139,plain,
% 10.34/10.51 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | ((~equidistant(x, w, w, x)) | equidistant(w, x, x, w))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | (~equidistant(x, w, w, x)) | equidistant(w, x, x, w))),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(140,plain,
% 10.34/10.51 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | ((~equidistant(x, w, w, x)) | equidistant(w, x, x, w))),
% 10.34/10.51 inference(quant_inst,[status(thm)],[])).
% 10.34/10.51 tff(141,plain,
% 10.34/10.51 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(V, U, X, W))) | (~equidistant(x, w, w, x)) | equidistant(w, x, x, w)),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[140, 139])).
% 10.34/10.51 tff(142,plain,
% 10.34/10.51 (equidistant(w, x, x, w)),
% 10.34/10.51 inference(unit_resolution,[status(thm)],[141, 138, 131])).
% 10.34/10.51 tff(143,plain,
% 10.34/10.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | ((~equidistant(w, x, x, w)) | equidistant(x, x, x, w) | (~equidistant(x, x, w, x)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(w, x, x, w)) | equidistant(x, x, x, w) | (~equidistant(x, x, w, x)))),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(144,plain,
% 10.34/10.51 ((equidistant(x, x, x, w) | (~equidistant(w, x, x, w)) | (~equidistant(x, x, w, x))) <=> ((~equidistant(w, x, x, w)) | equidistant(x, x, x, w) | (~equidistant(x, x, w, x)))),
% 10.34/10.51 inference(rewrite,[status(thm)],[])).
% 10.34/10.51 tff(145,plain,
% 10.34/10.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(x, x, x, w) | (~equidistant(w, x, x, w)) | (~equidistant(x, x, w, x)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | ((~equidistant(w, x, x, w)) | equidistant(x, x, x, w) | (~equidistant(x, x, w, x))))),
% 10.34/10.51 inference(monotonicity,[status(thm)],[144])).
% 10.34/10.51 tff(146,plain,
% 10.34/10.51 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(x, x, x, w) | (~equidistant(w, x, x, w)) | (~equidistant(x, x, w, x)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(w, x, x, w)) | equidistant(x, x, x, w) | (~equidistant(x, x, w, x)))),
% 10.34/10.51 inference(transitivity,[status(thm)],[145, 143])).
% 10.34/10.51 tff(147,plain,
% 10.34/10.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (equidistant(x, x, x, w) | (~equidistant(w, x, x, w)) | (~equidistant(x, x, w, x)))),
% 10.34/10.51 inference(quant_inst,[status(thm)],[])).
% 10.34/10.51 tff(148,plain,
% 10.34/10.51 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (equidistant(U, V, Y, Z) | (~equidistant(W, X, Y, Z)) | (~equidistant(U, V, W, X)))) | (~equidistant(w, x, x, w)) | equidistant(x, x, x, w) | (~equidistant(x, x, w, x))),
% 10.34/10.51 inference(modus_ponens,[status(thm)],[147, 146])).
% 10.34/10.51 tff(149,plain,
% 10.34/10.51 ($false),
% 10.34/10.52 inference(unit_resolution,[status(thm)],[148, 49, 142, 120, 1])).
% 10.34/10.52 tff(150,plain,(equidistant(x, x, x, w)), inference(lemma,lemma(discharge,[]))).
% 10.34/10.52 tff(151,plain,
% 10.34/10.52 (((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(x, x, x, w)) | equidistant(w, x, x, x))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(x, x, x, w)) | equidistant(w, x, x, x))),
% 10.34/10.52 inference(rewrite,[status(thm)],[])).
% 10.34/10.52 tff(152,plain,
% 10.34/10.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | ((~equidistant(x, x, x, w)) | equidistant(w, x, x, x))),
% 10.34/10.52 inference(quant_inst,[status(thm)],[])).
% 10.34/10.52 tff(153,plain,
% 10.34/10.52 ((~![W: $i, V: $i, U: $i, X: $i] : ((~equidistant(U, V, W, X)) | equidistant(X, W, V, U))) | (~equidistant(x, x, x, w)) | equidistant(w, x, x, x)),
% 10.34/10.52 inference(modus_ponens,[status(thm)],[152, 151])).
% 10.34/10.52 tff(154,plain,
% 10.34/10.52 (equidistant(w, x, x, x)),
% 10.34/10.52 inference(unit_resolution,[status(thm)],[153, 20, 150])).
% 10.34/10.52 tff(155,plain,
% 10.34/10.52 ((~(w = x)) <=> (~(w = x))),
% 10.34/10.52 inference(rewrite,[status(thm)],[])).
% 10.34/10.52 tff(156,axiom,(~(w = x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_w_is_x')).
% 10.34/10.52 tff(157,plain,
% 10.34/10.52 (~(w = x)),
% 10.34/10.52 inference(modus_ponens,[status(thm)],[156, 155])).
% 10.34/10.52 tff(158,plain,
% 10.34/10.52 (^[Z: $i, Y: $i, X: $i] : refl(((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ((~equidistant(X, Y, Z, Z)) | (X = Y)))),
% 10.34/10.52 inference(bind,[status(th)],[])).
% 10.34/10.52 tff(159,plain,
% 10.34/10.52 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 10.34/10.52 inference(quant_intro,[status(thm)],[158])).
% 10.34/10.52 tff(160,plain,
% 10.34/10.52 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 10.34/10.52 inference(rewrite,[status(thm)],[])).
% 10.34/10.52 tff(161,axiom,(![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','identity_for_equidistance')).
% 10.34/10.52 tff(162,plain,
% 10.34/10.52 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 10.34/10.52 inference(modus_ponens,[status(thm)],[161, 160])).
% 10.34/10.52 tff(163,plain,(
% 10.34/10.52 ![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 10.34/10.52 inference(skolemize,[status(sab)],[162])).
% 10.34/10.52 tff(164,plain,
% 10.34/10.52 (![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))),
% 10.34/10.52 inference(modus_ponens,[status(thm)],[163, 159])).
% 10.34/10.52 tff(165,plain,
% 10.34/10.52 (((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(w, x, x, x)) | (w = x))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(w, x, x, x)) | (w = x))),
% 10.34/10.52 inference(rewrite,[status(thm)],[])).
% 10.34/10.52 tff(166,plain,
% 10.34/10.52 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | ((~equidistant(w, x, x, x)) | (w = x))),
% 10.34/10.52 inference(quant_inst,[status(thm)],[])).
% 10.34/10.52 tff(167,plain,
% 10.34/10.52 ((~![Z: $i, Y: $i, X: $i] : ((~equidistant(X, Y, Z, Z)) | (X = Y))) | (~equidistant(w, x, x, x)) | (w = x)),
% 10.34/10.52 inference(modus_ponens,[status(thm)],[166, 165])).
% 10.34/10.52 tff(168,plain,
% 10.34/10.52 ($false),
% 10.34/10.52 inference(unit_resolution,[status(thm)],[167, 164, 157, 154])).
% 10.34/10.52 % SZS output end Proof
% 10.34/10.52 % E exiting
%------------------------------------------------------------------------------