%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO036-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:24 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO036-3 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:07:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(between_type, type, (
% 0.20/0.38 between: ( $i * $i * $i ) > $o)).
% 0.20/0.38 tff(lower_dimension_point_3_type, type, (
% 0.20/0.38 lower_dimension_point_3: $i)).
% 0.20/0.38 tff(lower_dimension_point_2_type, type, (
% 0.20/0.38 lower_dimension_point_2: $i)).
% 0.20/0.38 tff(lower_dimension_point_1_type, type, (
% 0.20/0.38 lower_dimension_point_1: $i)).
% 0.20/0.38 tff(1,assumption,(lower_dimension_point_1 = lower_dimension_point_3), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (lower_dimension_point_3 = lower_dimension_point_1),
% 0.20/0.38 inference(symmetry,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (between(lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3) <=> between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_1)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[2, 2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_1) <=> between(lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.38 inference(symmetry,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 ((~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_1)) <=> (~between(lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[4])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (^[W: $i, V: $i, X: $i] : refl(((~between(X, W, X)) | between(V, W, X)) <=> ((~between(X, W, X)) | between(V, W, X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X)) <=> ![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X)) <=> ![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (![W: $i, V: $i, U: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X)) <=> ![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))),
% 0.20/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![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(X, W, X)) | between(V, W, X))),
% 0.20/0.38 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (![W: $i, V: $i, U: $i, X: $i] : (between(V, W, X) | (~(U = X)) | (~between(U, W, X))) <=> ![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))),
% 0.20/0.38 inference(transitivity,[status(thm)],[10, 9])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (^[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)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![W: $i, V: $i, U: $i, X: $i] : (((~between(U, W, X)) | (~(U = X))) | between(V, W, X)) <=> ![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))),
% 0.20/0.38 inference(transitivity,[status(thm)],[13, 11])).
% 0.20/0.38 tff(15,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((~between(U, W, X)) | (~(U = X))) | between(V, W, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','b1')).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 8])).
% 0.20/0.38 tff(18,plain,(
% 0.20/0.38 ![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))),
% 0.20/0.39 inference(skolemize,[status(sab)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 7])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 ((~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)) <=> (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(21,axiom,(~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','lower_dimension2')).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (~between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (((~![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))) | ((~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_1)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1))) <=> ((~![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_1)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ((~![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))) | ((~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_1)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ((~![W: $i, V: $i, X: $i] : ((~between(X, W, X)) | between(V, W, X))) | (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_1)) | between(lower_dimension_point_2, lower_dimension_point_3, lower_dimension_point_1)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[25, 22, 19])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (~between(lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 5])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (^[V: $i, U: $i] : refl(between(U, U, V) <=> between(U, U, V))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (![V: $i, U: $i] : between(U, U, V) <=> ![V: $i, U: $i] : between(U, U, V)),
% 0.20/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (![V: $i, U: $i] : between(U, U, V) <=> ![V: $i, U: $i] : between(U, U, V)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(31,axiom,(![V: $i, U: $i] : between(U, U, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2')).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (![V: $i, U: $i] : between(U, U, V)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.39 tff(33,plain,(
% 0.20/0.39 ![V: $i, U: $i] : between(U, U, V)),
% 0.20/0.39 inference(skolemize,[status(sab)],[32])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (![V: $i, U: $i] : between(U, U, V)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((~![V: $i, U: $i] : between(U, U, V)) | between(lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (between(lower_dimension_point_3, lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[36, 27])).
% 0.20/0.39 tff(38,plain,(~(lower_dimension_point_1 = lower_dimension_point_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(39,assumption,(lower_dimension_point_2 = lower_dimension_point_3), introduced(assumption)).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (lower_dimension_point_3 = lower_dimension_point_2),
% 0.20/0.39 inference(symmetry,[status(thm)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_3) <=> between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) <=> between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.39 inference(symmetry,[status(thm)],[41])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)) <=> (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_3))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ((~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)) <=> (~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(45,axiom,(~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax','lower_dimension1')).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (~between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (^[V: $i, U: $i] : refl(between(U, V, V) <=> between(U, V, V))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 0.20/0.39 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (![V: $i, U: $i] : between(U, V, V) <=> ![V: $i, U: $i] : between(U, V, V)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(51,axiom,(![V: $i, U: $i] : between(U, V, V)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3')).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (![V: $i, U: $i] : between(U, V, V)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.39 tff(53,plain,(
% 0.20/0.39 ![V: $i, U: $i] : between(U, V, V)),
% 0.20/0.39 inference(skolemize,[status(sab)],[52])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (![V: $i, U: $i] : between(U, V, V)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ((~![V: $i, U: $i] : between(U, V, V)) | between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (between(lower_dimension_point_1, lower_dimension_point_3, lower_dimension_point_3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[56, 47])).
% 0.20/0.39 tff(58,plain,(~(lower_dimension_point_2 = lower_dimension_point_3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (((lower_dimension_point_2 = lower_dimension_point_3) | (lower_dimension_point_1 = lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3)) <=> ((lower_dimension_point_2 = lower_dimension_point_3) | (lower_dimension_point_1 = lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((((lower_dimension_point_1 = lower_dimension_point_2) | (lower_dimension_point_2 = lower_dimension_point_3)) | (lower_dimension_point_1 = lower_dimension_point_3)) <=> ((lower_dimension_point_2 = lower_dimension_point_3) | (lower_dimension_point_1 = lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(61,axiom,(((lower_dimension_point_1 = lower_dimension_point_2) | (lower_dimension_point_2 = lower_dimension_point_3)) | (lower_dimension_point_1 = lower_dimension_point_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_axioms_points_are_distinct')).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((lower_dimension_point_2 = lower_dimension_point_3) | (lower_dimension_point_1 = lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 ((lower_dimension_point_2 = lower_dimension_point_3) | (lower_dimension_point_1 = lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 ((lower_dimension_point_2 = lower_dimension_point_3) | (lower_dimension_point_1 = lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((lower_dimension_point_2 = lower_dimension_point_3) | (lower_dimension_point_1 = lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[64, 59])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 ((lower_dimension_point_2 = lower_dimension_point_3) | (lower_dimension_point_1 = lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[65, 59])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ((lower_dimension_point_1 = lower_dimension_point_2) | (lower_dimension_point_1 = lower_dimension_point_3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[66, 58])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (lower_dimension_point_1 = lower_dimension_point_2),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[67, 38])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (lower_dimension_point_2 = lower_dimension_point_1),
% 0.20/0.39 inference(symmetry,[status(thm)],[68])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (between(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3) <=> between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3) <=> between(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3)),
% 0.20/0.39 inference(symmetry,[status(thm)],[70])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 ((~between(lower_dimension_point_1, lower_dimension_point_2, lower_dimension_point_3)) <=> (~between(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (~between(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[46, 72])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 ((~![V: $i, U: $i] : between(U, U, V)) | between(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (between(lower_dimension_point_2, lower_dimension_point_2, lower_dimension_point_3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[74, 34])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[75, 73])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------