%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO225+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:06:02 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO225+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 14:43:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(apart_point_and_line_type, type, (
% 0.12/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.37 tff(line_connecting_type, type, (
% 0.12/0.37 line_connecting: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_B_0_type, type, (
% 0.12/0.37 tptp_fun_B_0: $i)).
% 0.12/0.37 tff(tptp_fun_A_1_type, type, (
% 0.12/0.37 tptp_fun_A_1: $i)).
% 0.12/0.37 tff(line_type, type, (
% 0.12/0.37 line: $i > $o)).
% 0.12/0.37 tff(distinct_points_type, type, (
% 0.12/0.37 distinct_points: ( $i * $i ) > $o)).
% 0.12/0.37 tff(point_type, type, (
% 0.12/0.37 point: $i > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (((point(A!1) & point(B!0) & distinct_points(A!1, B!0)) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))) <=> (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))) <=> (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : (((point(A) & point(B)) & distinct_points(A, B)) => ?[X: $i] : (line(X) => ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))) <=> (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(~![A: $i, B: $i] : (((point(A) & point(B)) & distinct_points(A, B)) => ?[X: $i] : (line(X) => ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (distinct_points(A!1, B!0)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.37 tff(16,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.37 tff(19,plain,(
% 0.12/0.37 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[18])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (~apart_point_and_line(A!1, line_connecting(A!1, B!0))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.37 tff(30,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.12/0.37 tff(33,plain,(
% 0.12/0.37 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[32])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (~apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[37, 34, 10])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 ((~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0)))) | apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[39, 38, 24])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 (((~line(line_connecting(A!1, B!0))) | (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))))) | (apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 ((~line(line_connecting(A!1, B!0))) | (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (^[X: $i] : refl((~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))) <=> (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))) <=> ![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (^[X: $i] : rewrite((~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X))))) <=> (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 (![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X))))) <=> ![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[45])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 (![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 ((~![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))) | (~((~line(line_connecting(A!1, B!0))) | (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[50, 49, 42])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------