%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO183+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:05:48 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : GEO183+1 : TPTP v9.0.0. Released v3.3.0.
% 0.01/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 14:40:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(apart_point_and_line_type, type, (
% 0.20/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_U_1_type, type, (
% 0.20/0.37 tptp_fun_U_1: $i)).
% 0.20/0.37 tff(tptp_fun_Y_2_type, type, (
% 0.20/0.37 tptp_fun_Y_2: $i)).
% 0.20/0.37 tff(line_connecting_type, type, (
% 0.20/0.37 line_connecting: ( $i * $i ) > $i)).
% 0.20/0.37 tff(tptp_fun_X_3_type, type, (
% 0.20/0.37 tptp_fun_X_3: $i)).
% 0.20/0.37 tff(distinct_points_type, type, (
% 0.20/0.37 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.37 tff(distinct_lines_type, type, (
% 0.20/0.37 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.37 tff(convergent_lines_type, type, (
% 0.20/0.37 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_V_0_type, type, (
% 0.20/0.37 tptp_fun_V_0: $i)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 ((~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (~distinct_lines(U, line_connecting(X, Y)))) => ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(3,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (~distinct_lines(U, line_connecting(X, Y)))) => ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.37 tff(8,plain,(
% 0.20/0.37 ~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (~distinct_lines(U!1, line_connecting(X!3, Y!2))))) | ((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(Y!2, U!1))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[7])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (~distinct_lines(U!1, line_connecting(X!3, Y!2)))),
% 0.20/0.37 inference(or_elim,[status(thm)],[8])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (distinct_points(X!3, Y!2)),
% 0.20/0.37 inference(and_elim,[status(thm)],[9])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (^[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)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (![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))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (![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))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (^[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)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (![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))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.37 tff(16,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.37 tff(19,plain,(
% 0.20/0.37 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[18])).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 (((~![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))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 ((~![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))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 ((~![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)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (~distinct_lines(U!1, line_connecting(X!3, Y!2))),
% 0.20/0.37 inference(and_elim,[status(thm)],[9])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 (^[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))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 (![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)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 (![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)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 (^[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)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 (![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)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.37 tff(31,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/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.37 tff(34,plain,(
% 0.20/0.37 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[33])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 (((~![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, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))) <=> ((~![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, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(37,plain,
% 0.20/0.37 ((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))) <=> (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (((~![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, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.37 tff(39,plain,
% 0.20/0.37 (((~![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, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.20/0.37 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 ((~![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)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(41,plain,
% 0.20/0.37 ((~![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, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.37 tff(42,plain,
% 0.20/0.37 (~apart_point_and_line(Y!2, U!1)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[41, 35, 25, 24])).
% 0.20/0.37 tff(43,plain,
% 0.20/0.37 (^[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)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(44,plain,
% 0.20/0.37 (![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))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.37 tff(45,plain,
% 0.20/0.37 (![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))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(46,plain,
% 0.20/0.37 (^[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)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(47,plain,
% 0.20/0.37 (![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))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.37 tff(48,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.20/0.37 tff(49,plain,
% 0.20/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.37 tff(50,plain,
% 0.20/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.20/0.37 tff(51,plain,(
% 0.20/0.37 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[50])).
% 0.20/0.37 tff(52,plain,
% 0.20/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.20/0.37 tff(53,plain,
% 0.20/0.37 (((~![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))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(54,plain,
% 0.20/0.37 ((~![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))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(55,plain,
% 0.20/0.37 ((~![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)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.37 tff(56,plain,
% 0.20/0.37 (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[55, 52, 10])).
% 0.20/0.37 tff(57,plain,
% 0.20/0.37 (((~![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, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))) <=> ((~![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, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(58,plain,
% 0.20/0.37 ((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))) <=> (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (((~![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, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[58])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (((~![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, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[59, 57])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 ((~![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)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 (~apart_point_and_line(X!3, U!1)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[62, 35, 25, 56])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 ((~(~(apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1)))) <=> (apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 (((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(Y!2, U!1))) <=> (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 ((~((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(Y!2, U!1)))) <=> (~(~(apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 ((~((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(Y!2, U!1)))) <=> (apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1))),
% 0.20/0.38 inference(transitivity,[status(thm)],[66, 64])).
% 0.20/0.38 tff(68,plain,
% 0.20/0.38 (~((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(Y!2, U!1)))),
% 0.20/0.38 inference(or_elim,[status(thm)],[8])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 (apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.38 tff(70,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[69, 63, 42])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------