%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO238+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:06:05 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO238+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 14:43:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(left_apart_point_type, type, (
% 0.19/0.38 left_apart_point: ( $i * $i ) > $o)).
% 0.19/0.38 tff(reverse_line_type, type, (
% 0.19/0.38 reverse_line: $i > $i)).
% 0.19/0.38 tff(tptp_fun_L_0_type, type, (
% 0.19/0.38 tptp_fun_L_0: $i)).
% 0.19/0.38 tff(tptp_fun_B_2_type, type, (
% 0.19/0.38 tptp_fun_B_2: $i)).
% 0.19/0.38 tff(right_apart_point_type, type, (
% 0.19/0.38 right_apart_point: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_C_1_type, type, (
% 0.19/0.38 tptp_fun_C_1: $i)).
% 0.19/0.38 tff(divides_points_type, type, (
% 0.19/0.38 divides_points: ( $i * $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_A_3_type, type, (
% 0.19/0.38 tptp_fun_A_3: $i)).
% 0.19/0.38 tff(1,assumption,(left_apart_point(B!2, L!0) | left_apart_point(B!2, reverse_line(L!0))), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (^[A: $i, L: $i] : refl((~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(5,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax10_basics')).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.38 tff(7,plain,(
% 0.19/0.38 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[6])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(B!2, L!0) | left_apart_point(B!2, reverse_line(L!0))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.38 tff(11,plain,(~(left_apart_point(B!2, L!0) | left_apart_point(B!2, reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 ((left_apart_point(B!2, L!0) | left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(B!2, reverse_line(L!0)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (~left_apart_point(B!2, reverse_line(L!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 ((left_apart_point(B!2, L!0) | left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(B!2, L!0))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (~left_apart_point(B!2, L!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0))) | left_apart_point(B!2, L!0)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 ((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (^[A: $i, B: $i, L: $i] : refl((divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L)))))) <=> (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L)))))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (^[A: $i, B: $i, L: $i] : rewrite((divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L)))) <=> (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L)))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L)))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(23,axiom,(![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a8_defns')).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.38 tff(25,plain,(
% 0.19/0.38 ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[24])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0)))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C))))) <=> (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i, L: $i] : ((divides_points(L, A, B) & divides_points(L, A, C)) => (~divides_points(L, B, C)))) <=> (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(32,axiom,(~![A: $i, B: $i, C: $i, L: $i] : ((divides_points(L, A, B) & divides_points(L, A, C)) => (~divides_points(L, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.19/0.38 tff(37,plain,(
% 0.19/0.38 ~((~divides_points(L!0, B!2, C!1)) | (~(divides_points(L!0, A!3, B!2) & divides_points(L!0, A!3, C!1))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[36])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (divides_points(L!0, B!2, C!1)),
% 0.19/0.38 inference(or_elim,[status(thm)],[37])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 ((~(divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0))))))) | (~divides_points(L!0, B!2, C!1)) | ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0)))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 ((~(divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0))))))) | ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0)))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[40, 29])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 ((~((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0)))))) | (~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[43, 17])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0))) | right_apart_point(B!2, L!0)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (right_apart_point(B!2, L!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 ((~(right_apart_point(B!2, L!0) <=> left_apart_point(B!2, reverse_line(L!0)))) | (~right_apart_point(B!2, L!0)) | left_apart_point(B!2, reverse_line(L!0))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (~(right_apart_point(B!2, L!0) <=> left_apart_point(B!2, reverse_line(L!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[47, 46, 13])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : refl((right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(52,axiom,(![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a2_defns')).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.38 tff(54,plain,(
% 0.19/0.38 ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[53])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(B!2, L!0) <=> left_apart_point(B!2, reverse_line(L!0)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[56, 55, 48])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------