%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO264+3 : TPTP v9.0.0. Released v4.0.0.
% 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 05:06:11 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : GEO264+3 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 14:43:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(left_apart_point_type, type, (
% 0.19/0.37 left_apart_point: ( $i * $i ) > $o)).
% 0.19/0.37 tff(reverse_line_type, type, (
% 0.19/0.37 reverse_line: $i > $i)).
% 0.19/0.37 tff(line_connecting_type, type, (
% 0.19/0.37 line_connecting: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_C_1_type, type, (
% 0.19/0.37 tptp_fun_C_1: $i)).
% 0.19/0.37 tff(tptp_fun_B_2_type, type, (
% 0.19/0.37 tptp_fun_B_2: $i)).
% 0.19/0.37 tff(tptp_fun_D_0_type, type, (
% 0.19/0.37 tptp_fun_D_0: $i)).
% 0.19/0.37 tff(right_apart_point_type, type, (
% 0.19/0.37 right_apart_point: ( $i * $i ) > $o)).
% 0.19/0.37 tff(tptp_fun_A_3_type, type, (
% 0.19/0.37 tptp_fun_A_3: $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[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))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(4,axiom,(![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a2_defns')).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.37 tff(6,plain,(
% 0.19/0.37 ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[5])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(D!0, line_connecting(B!2, C!1)) <=> left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (right_apart_point(D!0, line_connecting(B!2, C!1)) <=> left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 ((~(left_apart_point(D!0, line_connecting(A!3, B!2)) | (~(right_apart_point(D!0, line_connecting(B!2, C!1)) & right_apart_point(D!0, line_connecting(C!1, A!3)))) | (~left_apart_point(C!1, line_connecting(A!3, B!2))))) <=> (~(left_apart_point(D!0, line_connecting(A!3, B!2)) | (~(right_apart_point(D!0, line_connecting(B!2, C!1)) & right_apart_point(D!0, line_connecting(C!1, A!3)))) | (~left_apart_point(C!1, line_connecting(A!3, B!2)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(right_apart_point(D, line_connecting(B, C)) & right_apart_point(D, line_connecting(C, A)))) | (~left_apart_point(C, line_connecting(A, B))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(right_apart_point(D, line_connecting(B, C)) & right_apart_point(D, line_connecting(C, A)))) | (~left_apart_point(C, line_connecting(A, B)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(C, line_connecting(A, B)) => ((right_apart_point(D, line_connecting(B, C)) & right_apart_point(D, line_connecting(C, A))) => left_apart_point(D, line_connecting(A, B))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(right_apart_point(D, line_connecting(B, C)) & right_apart_point(D, line_connecting(C, A)))) | (~left_apart_point(C, line_connecting(A, B)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(13,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(C, line_connecting(A, B)) => ((right_apart_point(D, line_connecting(B, C)) & right_apart_point(D, line_connecting(C, A))) => left_apart_point(D, line_connecting(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(right_apart_point(D, line_connecting(B, C)) & right_apart_point(D, line_connecting(C, A)))) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(right_apart_point(D, line_connecting(B, C)) & right_apart_point(D, line_connecting(C, A)))) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(right_apart_point(D, line_connecting(B, C)) & right_apart_point(D, line_connecting(C, A)))) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(right_apart_point(D, line_connecting(B, C)) & right_apart_point(D, line_connecting(C, A)))) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.19/0.38 tff(18,plain,(
% 0.19/0.38 ~(left_apart_point(D!0, line_connecting(A!3, B!2)) | (~(right_apart_point(D!0, line_connecting(B!2, C!1)) & right_apart_point(D!0, line_connecting(C!1, A!3)))) | (~left_apart_point(C!1, line_connecting(A!3, B!2))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[17])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (~(left_apart_point(D!0, line_connecting(A!3, B!2)) | (~(right_apart_point(D!0, line_connecting(B!2, C!1)) & right_apart_point(D!0, line_connecting(C!1, A!3)))) | (~left_apart_point(C!1, line_connecting(A!3, B!2))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (right_apart_point(D!0, line_connecting(B!2, C!1)) & right_apart_point(D!0, line_connecting(C!1, A!3))),
% 0.19/0.38 inference(or_elim,[status(thm)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (right_apart_point(D!0, line_connecting(B!2, C!1))),
% 0.19/0.38 inference(and_elim,[status(thm)],[20])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 ((~(right_apart_point(D!0, line_connecting(B!2, C!1)) <=> left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1))))) | (~right_apart_point(D!0, line_connecting(B!2, C!1))) | left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 ((~(right_apart_point(D!0, line_connecting(B!2, C!1)) <=> left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1))))) | left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[23, 9])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 ((left_apart_point(D!0, line_connecting(B!2, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1)))) | (~left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (left_apart_point(D!0, line_connecting(B!2, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.19/0.38 tff(27,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(28,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)],[27])).
% 0.19/0.38 tff(29,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(30,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax10_basics')).
% 0.19/0.38 tff(31,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)],[30, 29])).
% 0.19/0.38 tff(32,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)],[31])).
% 0.19/0.38 tff(33,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)],[32, 28])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(D!0, line_connecting(B!2, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1)))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[34, 33, 26])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------