%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO206+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:05:56 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO206+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 14:41:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(convergent_lines_type, type, (
% 0.12/0.37 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.37 tff(parallel_through_point_type, type, (
% 0.12/0.37 parallel_through_point: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_X_2_type, type, (
% 0.12/0.37 tptp_fun_X_2: $i)).
% 0.12/0.37 tff(tptp_fun_Z_0_type, type, (
% 0.12/0.37 tptp_fun_Z_0: $i)).
% 0.12/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.37 tptp_fun_Y_1: $i)).
% 0.12/0.37 tff(apart_point_and_line_type, type, (
% 0.12/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.37 tff(distinct_lines_type, type, (
% 0.12/0.37 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,(
% 0.12/0.37 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.12/0.37 inference(skolemize,[status(sab)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(Z!0, X!2), Z!0))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~convergent_lines(parallel_through_point(Z!0, X!2), Z!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : (((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z))) => (~distinct_lines(Y, parallel_through_point(Z, X))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(12,axiom,(~![X: $i, Y: $i, Z: $i] : (((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z))) => (~distinct_lines(Y, parallel_through_point(Z, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.12/0.37 tff(17,plain,(
% 0.12/0.37 ~((~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | (~((~apart_point_and_line(X!2, Y!1)) & (~convergent_lines(Y!1, Z!0)))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[16])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 ((~apart_point_and_line(X!2, Y!1)) & (~convergent_lines(Y!1, Z!0))),
% 0.20/0.37 inference(or_elim,[status(thm)],[17])).
% 0.20/0.37 tff(19,plain,
% 0.20/0.37 (~convergent_lines(Y!1, Z!0)),
% 0.20/0.37 inference(and_elim,[status(thm)],[18])).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.37 tff(25,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.20/0.37 tff(28,plain,(
% 0.20/0.37 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[27])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 ((convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))) <=> (convergent_lines(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[32, 30])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[35, 29, 19, 9])).
% 0.20/0.37 tff(37,plain,
% 0.20/0.37 (^[X: $i, Y: $i] : refl((~apart_point_and_line(X, parallel_through_point(Y, X))) <=> (~apart_point_and_line(X, parallel_through_point(Y, X))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.37 tff(39,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(40,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.20/0.37 tff(41,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.37 tff(42,plain,(
% 0.20/0.37 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[41])).
% 0.20/0.37 tff(43,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.37 tff(44,plain,
% 0.20/0.37 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(45,plain,
% 0.20/0.37 (~apart_point_and_line(X!2, parallel_through_point(Z!0, X!2))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.37 tff(46,plain,
% 0.20/0.37 (~apart_point_and_line(X!2, Y!1)),
% 0.20/0.37 inference(and_elim,[status(thm)],[18])).
% 0.20/0.37 tff(47,plain,
% 0.20/0.37 (distinct_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.20/0.37 inference(or_elim,[status(thm)],[17])).
% 0.20/0.37 tff(48,plain,
% 0.20/0.37 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(49,plain,
% 0.20/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) <=> (apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> ((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)))), rewrite(((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))))), rewrite((distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.38 tff(53,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.38 tff(56,plain,(
% 0.20/0.38 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[55])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | ((~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 ((convergent_lines(Y!1, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2)))) <=> ((~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | ((~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[60, 58])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[63, 57, 47, 46, 45, 36])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------