%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO174+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:05:45 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO174+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.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 14:41:16 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(apart_point_and_line_type, type, (
% 0.11/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_U_1_type, type, (
% 0.11/0.37 tptp_fun_U_1: $i)).
% 0.11/0.37 tff(tptp_fun_Y_2_type, type, (
% 0.11/0.37 tptp_fun_Y_2: $i)).
% 0.11/0.37 tff(line_connecting_type, type, (
% 0.11/0.37 line_connecting: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_X_3_type, type, (
% 0.11/0.37 tptp_fun_X_3: $i)).
% 0.11/0.37 tff(distinct_points_type, type, (
% 0.11/0.37 distinct_points: ( $i * $i ) > $o)).
% 0.11/0.37 tff(convergent_lines_type, type, (
% 0.11/0.37 convergent_lines: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_V_0_type, type, (
% 0.11/0.37 tptp_fun_V_0: $i)).
% 0.11/0.37 tff(distinct_lines_type, type, (
% 0.11/0.37 distinct_lines: ( $i * $i ) > $o)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 ((distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1))) <=> (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 ((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) <=> (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2))) <=> ((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 ((~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))) <=> (~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[3])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(X, U) | apart_point_and_line(Y, U))) => distinct_lines(U, line_connecting(X, Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(7,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(X, U) | apart_point_and_line(Y, U))) => distinct_lines(U, line_connecting(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.11/0.37 tff(12,plain,(
% 0.11/0.37 ~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[11])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1))),
% 0.11/0.37 inference(or_elim,[status(thm)],[13])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (distinct_points(X!3, Y!2)),
% 0.11/0.37 inference(and_elim,[status(thm)],[14])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (^[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)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![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))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (![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))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (^[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)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (![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))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.38 tff(21,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')).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.11/0.38 tff(24,plain,(
% 0.11/0.38 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[23])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[28, 25, 15])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (~distinct_lines(U!1, line_connecting(X!3, Y!2))),
% 0.19/0.38 inference(or_elim,[status(thm)],[13])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(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, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.38 tff(36,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.38 tff(39,plain,(
% 0.19/0.38 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[38])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (~apart_point_and_line(Y!2, U!1)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[43, 40, 30, 29])).
% 0.19/0.38 tff(45,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(46,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)],[45])).
% 0.19/0.38 tff(47,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(48,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(49,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)],[48])).
% 0.19/0.38 tff(50,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(51,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)],[50, 49])).
% 0.19/0.38 tff(52,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)],[51, 47])).
% 0.19/0.38 tff(53,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)],[52])).
% 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))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[53, 46])).
% 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))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 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))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[57, 54, 15])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (~apart_point_and_line(X!3, U!1)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[61, 40, 30, 58])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)),
% 0.19/0.38 inference(and_elim,[status(thm)],[14])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[63, 62, 44])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------