%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO225+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO225+3 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.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 14:46:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(incident_point_and_line_type, type, (
% 0.19/0.38 incident_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.38 tff(line_connecting_type, type, (
% 0.19/0.38 line_connecting: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_B_0_type, type, (
% 0.19/0.38 tptp_fun_B_0: $i)).
% 0.19/0.38 tff(tptp_fun_A_1_type, type, (
% 0.19/0.38 tptp_fun_A_1: $i)).
% 0.19/0.38 tff(line_type, type, (
% 0.19/0.38 line: $i > $o)).
% 0.19/0.38 tff(distinct_points_type, type, (
% 0.19/0.38 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.38 tff(point_type, type, (
% 0.19/0.38 point: $i > $o)).
% 0.19/0.38 tff(apart_point_and_line_type, type, (
% 0.19/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[X: $i] : refl((~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X)))))) <=> (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X)))))) <=> ![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (^[X: $i] : rewrite((~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X)))) <=> (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X)))) <=> ![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (((point(A!1) & point(B!0) & distinct_points(A!1, B!0)) & ![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X))))) <=> (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))) <=> (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : (((point(A) & point(B)) & distinct_points(A, B)) => ?[X: $i] : (line(X) => (incident_point_and_line(A, X) & incident_point_and_line(B, X))))) <=> (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(8,axiom,(~![A: $i, B: $i] : (((point(A) & point(B)) & distinct_points(A, B)) => ?[X: $i] : (line(X) => (incident_point_and_line(A, X) & incident_point_and_line(B, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X))))),
% 0.19/0.38 inference(and_elim,[status(thm)],[13])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 ((~![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X))))))) | (~((~line(line_connecting(A!1, B!0))) | (~((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0)))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (~((~line(line_connecting(A!1, B!0))) | (~((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (((~line(line_connecting(A!1, B!0))) | (~((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0)))))) | ((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 ((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : refl((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (^[X: $i, Y: $i] : trans(rewrite((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), rewrite((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), ((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.38 tff(26,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.38 tff(29,plain,(
% 0.19/0.38 ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[28])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(B!0, line_connecting(A!1, B!0)) <=> incident_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (~(apart_point_and_line(B!0, line_connecting(A!1, B!0)) <=> incident_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (distinct_points(A!1, B!0)),
% 0.19/0.38 inference(and_elim,[status(thm)],[13])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.38 tff(39,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')).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.38 tff(42,plain,(
% 0.19/0.38 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[41])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (((~![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 ((~![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))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 ((~![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)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (~apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[46, 43, 33])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 ((apart_point_and_line(B!0, line_connecting(A!1, B!0)) <=> incident_point_and_line(B!0, line_connecting(A!1, B!0))) | apart_point_and_line(B!0, line_connecting(A!1, B!0)) | incident_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 ((apart_point_and_line(B!0, line_connecting(A!1, B!0)) <=> incident_point_and_line(B!0, line_connecting(A!1, B!0))) | incident_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (incident_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[49, 32])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) <=> incident_point_and_line(A!1, line_connecting(A!1, B!0))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) <=> incident_point_and_line(A!1, line_connecting(A!1, B!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[51, 30])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.38 tff(58,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')).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.38 tff(61,plain,(
% 0.19/0.38 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[60])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 (((~![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 ((~![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))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (~apart_point_and_line(A!1, line_connecting(A!1, B!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[65, 62, 33])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 ((apart_point_and_line(A!1, line_connecting(A!1, B!0)) <=> incident_point_and_line(A!1, line_connecting(A!1, B!0))) | apart_point_and_line(A!1, line_connecting(A!1, B!0)) | incident_point_and_line(A!1, line_connecting(A!1, B!0))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 ((apart_point_and_line(A!1, line_connecting(A!1, B!0)) <=> incident_point_and_line(A!1, line_connecting(A!1, B!0))) | incident_point_and_line(A!1, line_connecting(A!1, B!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 (incident_point_and_line(A!1, line_connecting(A!1, B!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[68, 52])).
% 0.19/0.38 tff(70,plain,
% 0.19/0.38 ((~((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0))))) | (~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[70, 69, 50, 20])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------