%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO188+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:05:50 AM UTC 2025
% Result : Theorem 0.16s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO188+1 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n003.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu Jun 19 14:40:39 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.16/0.37 % SZS status Theorem
% 0.16/0.37 % SZS output start Proof
% 0.16/0.37 tff(distinct_lines_type, type, (
% 0.16/0.37 distinct_lines: ( $i * $i ) > $o)).
% 0.16/0.37 tff(line_connecting_type, type, (
% 0.16/0.37 line_connecting: ( $i * $i ) > $i)).
% 0.16/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.16/0.37 tptp_fun_Y_1: $i)).
% 0.16/0.37 tff(tptp_fun_X_2_type, type, (
% 0.16/0.37 tptp_fun_X_2: $i)).
% 0.16/0.37 tff(tptp_fun_Z_0_type, type, (
% 0.16/0.37 tptp_fun_Z_0: $i)).
% 0.16/0.37 tff(apart_point_and_line_type, type, (
% 0.16/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.16/0.37 tff(distinct_points_type, type, (
% 0.16/0.37 distinct_points: ( $i * $i ) > $o)).
% 0.16/0.37 tff(1,assumption,(~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))), introduced(assumption)).
% 0.16/0.37 tff(2,plain,
% 0.16/0.37 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y)))))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(3,plain,
% 0.16/0.37 ((~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & (~apart_point_and_line(Z, line_connecting(X, Y)))) => (~apart_point_and_line(X, line_connecting(Z, Y))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y)))))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(4,axiom,(~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & (~apart_point_and_line(Z, line_connecting(X, Y)))) => (~apart_point_and_line(X, line_connecting(Z, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.16/0.37 tff(5,plain,
% 0.16/0.37 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.16/0.37 tff(6,plain,
% 0.16/0.37 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.16/0.37 tff(7,plain,
% 0.16/0.37 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.16/0.37 tff(8,plain,
% 0.16/0.37 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(X, line_connecting(Z, Y))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.16/0.37 tff(9,plain,(
% 0.16/0.37 ~((~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | (~(distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))))),
% 0.16/0.37 inference(skolemize,[status(sab)],[8])).
% 0.16/0.37 tff(10,plain,
% 0.16/0.37 (distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.16/0.37 inference(or_elim,[status(thm)],[9])).
% 0.16/0.37 tff(11,plain,
% 0.16/0.37 (distinct_points(X!2, Y!1)),
% 0.16/0.37 inference(and_elim,[status(thm)],[10])).
% 0.16/0.37 tff(12,plain,
% 0.16/0.37 (^[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)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(13,plain,
% 0.16/0.37 (![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))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.16/0.37 tff(14,plain,
% 0.16/0.37 (![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))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(15,plain,
% 0.16/0.37 (^[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)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(16,plain,
% 0.16/0.37 (![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))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.16/0.37 tff(17,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')).
% 0.16/0.37 tff(18,plain,
% 0.16/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.16/0.37 tff(19,plain,
% 0.16/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.16/0.37 tff(20,plain,(
% 0.16/0.37 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.16/0.37 inference(skolemize,[status(sab)],[19])).
% 0.16/0.37 tff(21,plain,
% 0.16/0.37 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.16/0.37 tff(22,plain,
% 0.16/0.37 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(23,plain,
% 0.16/0.37 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(24,plain,
% 0.16/0.37 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.16/0.37 tff(25,plain,
% 0.16/0.37 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.16/0.37 tff(26,plain,
% 0.16/0.37 (apart_point_and_line(X!2, line_connecting(Z!0, Y!1))),
% 0.16/0.37 inference(or_elim,[status(thm)],[9])).
% 0.16/0.37 tff(27,plain,
% 0.16/0.37 (^[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))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(28,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.16/0.37 tff(29,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(30,plain,
% 0.16/0.37 (^[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)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(31,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.16/0.37 tff(32,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')).
% 0.16/0.37 tff(33,plain,
% 0.16/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.16/0.37 tff(34,plain,
% 0.16/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.16/0.37 tff(35,plain,(
% 0.16/0.37 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.37 inference(skolemize,[status(sab)],[34])).
% 0.16/0.37 tff(36,plain,
% 0.16/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.16/0.37 tff(37,plain,
% 0.16/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(38,plain,
% 0.16/0.37 ((distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1)))) <=> ((~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(39,plain,
% 0.16/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))))),
% 0.16/0.37 inference(monotonicity,[status(thm)],[38])).
% 0.16/0.37 tff(40,plain,
% 0.16/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)))),
% 0.16/0.37 inference(transitivity,[status(thm)],[39, 37])).
% 0.16/0.37 tff(41,plain,
% 0.16/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(42,plain,
% 0.18/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(X!2, line_connecting(Z!0, Y!1))) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.37 tff(43,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[42, 36, 26, 25, 1])).
% 0.18/0.37 tff(44,plain,(distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(45,assumption,(distinct_points(Y!1, Y!1)), introduced(assumption)).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[46])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(49,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart1')).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 (![X: $i] : (~distinct_points(X, X))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.37 tff(51,plain,(
% 0.18/0.37 ![X: $i] : (~distinct_points(X, X))),
% 0.18/0.37 inference(skolemize,[status(sab)],[50])).
% 0.18/0.37 tff(52,plain,
% 0.18/0.37 (![X: $i] : (~distinct_points(X, X))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.18/0.37 tff(53,plain,
% 0.18/0.37 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!1, Y!1))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(54,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[53, 52, 45])).
% 0.18/0.37 tff(55,plain,(~distinct_points(Y!1, Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(56,assumption,(~distinct_points(Y!1, Y!1)), introduced(assumption)).
% 0.18/0.37 tff(57,assumption,(~distinct_points(Z!0, Y!1)), introduced(assumption)).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 (distinct_points(Y!1, Z!0)),
% 0.18/0.37 inference(and_elim,[status(thm)],[10])).
% 0.18/0.37 tff(59,plain,
% 0.18/0.37 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(62,plain,
% 0.18/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | distinct_points(Y, Z)) <=> (distinct_points(Y, Z) | distinct_points(X, Z))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))))), rewrite((distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(63,plain,
% 0.18/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.37 tff(64,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart4')).
% 0.18/0.38 tff(65,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.18/0.38 tff(66,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.18/0.38 tff(67,plain,(
% 0.18/0.38 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[66])).
% 0.18/0.38 tff(68,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.18/0.38 tff(69,plain,
% 0.18/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(70,plain,
% 0.18/0.38 ((distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0))) <=> ((~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(71,plain,
% 0.18/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1)))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[70])).
% 0.18/0.38 tff(72,plain,
% 0.18/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1))),
% 0.18/0.38 inference(transitivity,[status(thm)],[71, 69])).
% 0.18/0.38 tff(73,plain,
% 0.18/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1) | (~distinct_points(Y!1, Z!0)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(74,plain,
% 0.18/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(Y!1, Z!0)) | distinct_points(Z!0, Y!1) | distinct_points(Y!1, Y!1)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.38 tff(75,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[74, 68, 58, 57, 56])).
% 0.18/0.38 tff(76,plain,(distinct_points(Y!1, Y!1) | distinct_points(Z!0, Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(77,plain,
% 0.18/0.38 (distinct_points(Z!0, Y!1)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[76, 55])).
% 0.18/0.38 tff(78,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(79,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[78])).
% 0.18/0.38 tff(80,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(81,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(82,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[81])).
% 0.18/0.38 tff(83,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')).
% 0.18/0.38 tff(84,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.18/0.38 tff(85,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.18/0.38 tff(86,plain,(
% 0.18/0.38 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[85])).
% 0.18/0.38 tff(87,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.18/0.38 tff(88,plain,
% 0.18/0.38 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(89,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(90,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.18/0.38 tff(91,plain,
% 0.18/0.38 ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.18/0.38 tff(92,plain,
% 0.18/0.38 (~apart_point_and_line(Y!1, line_connecting(Z!0, Y!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[91, 77])).
% 0.18/0.38 tff(93,plain,
% 0.18/0.38 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(94,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(95,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.38 tff(96,plain,
% 0.18/0.38 ((~distinct_points(Z!0, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[95, 21])).
% 0.18/0.38 tff(97,plain,
% 0.18/0.38 (~apart_point_and_line(Z!0, line_connecting(Z!0, Y!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[96, 77])).
% 0.18/0.38 tff(98,plain,
% 0.18/0.38 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(99,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(100,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.18/0.38 tff(101,plain,
% 0.18/0.38 (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[100, 87, 11])).
% 0.18/0.38 tff(102,plain,
% 0.18/0.38 (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.18/0.38 inference(and_elim,[status(thm)],[10])).
% 0.18/0.38 tff(103,plain,
% 0.18/0.38 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(104,plain,
% 0.18/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[103])).
% 0.18/0.38 tff(105,plain,
% 0.18/0.38 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(106,plain,
% 0.18/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[105])).
% 0.18/0.38 tff(107,plain,
% 0.18/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(108,plain,
% 0.18/0.38 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(109,plain,
% 0.18/0.38 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[108])).
% 0.18/0.38 tff(110,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.18/0.38 tff(111,plain,
% 0.18/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.38 tff(112,plain,
% 0.18/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.18/0.38 tff(113,plain,(
% 0.18/0.38 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[112])).
% 0.18/0.38 tff(114,plain,
% 0.18/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.18/0.38 tff(115,plain,
% 0.18/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[114, 104])).
% 0.18/0.38 tff(116,plain,
% 0.18/0.38 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~distinct_points(Y!1, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~distinct_points(Y!1, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(117,plain,
% 0.18/0.38 ((apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)))) <=> (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~distinct_points(Y!1, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(118,plain,
% 0.18/0.38 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~distinct_points(Y!1, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[117])).
% 0.18/0.39 tff(119,plain,
% 0.18/0.39 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~distinct_points(Y!1, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[118, 116])).
% 0.18/0.39 tff(120,plain,
% 0.18/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_points(Y!1, Z!0)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(121,plain,
% 0.18/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~distinct_points(Y!1, Z!0)) | apart_point_and_line(Z!0, line_connecting(Z!0, Y!1)) | apart_point_and_line(Y!1, line_connecting(Z!0, Y!1)) | (~distinct_lines(line_connecting(Z!0, Y!1), line_connecting(X!2, Y!1)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.18/0.39 tff(122,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[121, 115, 58, 102, 101, 97, 92, 44])).
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------