%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO178+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:05:46 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO178+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:39:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(distinct_points_type, type, (
% 0.11/0.36 distinct_points: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_X_2_type, type, (
% 0.11/0.36 tptp_fun_X_2: $i)).
% 0.11/0.36 tff(tptp_fun_Z_0_type, type, (
% 0.11/0.36 tptp_fun_Z_0: $i)).
% 0.11/0.36 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.36 tptp_fun_Y_1: $i)).
% 0.11/0.36 tff(apart_point_and_line_type, type, (
% 0.11/0.36 apart_point_and_line: ( $i * $i ) > $o)).
% 0.11/0.36 tff(line_connecting_type, type, (
% 0.11/0.36 line_connecting: ( $i * $i ) > $i)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 ((~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((~![X: $i, Y: $i, Z: $i] : ((distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y))) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,axiom,(~![X: $i, Y: $i, Z: $i] : ((distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y))) => (distinct_points(Z, X) & distinct_points(Z, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (~![X: $i, Y: $i, Z: $i] : ((~(distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y)))) | (distinct_points(Z, X) & distinct_points(Z, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.11/0.36 tff(8,plain,(
% 0.11/0.36 ~((~(distinct_points(X!2, Y!1) & apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) | (distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (distinct_points(X!2, Y!1) & apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.11/0.36 inference(or_elim,[status(thm)],[8])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.11/0.36 inference(and_elim,[status(thm)],[9])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (distinct_points(X!2, Y!1)),
% 0.11/0.36 inference(and_elim,[status(thm)],[9])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (^[X: $i, Y: $i, Z: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(Z, X) & distinct_points(Z, Y)) <=> (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))), rewrite(((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))) <=> ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> (distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))))), rewrite((distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[17])).
% 0.11/0.37 tff(19,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.11/0.37 tff(22,plain,(
% 0.11/0.37 ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[21])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[27, 24, 11, 10])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))) | distinct_points(Z!0, X!2)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (distinct_points(Z!0, X!2)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))) | distinct_points(Z!0, Y!1)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (distinct_points(Z!0, Y!1)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[31, 28])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 ((~(~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))))) <=> ((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 ((distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1)) <=> (~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 ((~(distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1))) <=> (~(~((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[34])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 ((~(distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1))) <=> ((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[35, 33])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (~(distinct_points(Z!0, X!2) & distinct_points(Z!0, Y!1))),
% 0.11/0.37 inference(or_elim,[status(thm)],[8])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 ((~distinct_points(Z!0, X!2)) | (~distinct_points(Z!0, Y!1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[38, 32, 30])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------