%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO197+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:05:53 AM UTC 2025
% Result : Theorem 0.18s 0.46s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : GEO197+3 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 14:41:17 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 % SZS output start Proof
% 0.18/0.46 tff(distinct_lines_type, type, (
% 0.18/0.46 distinct_lines: ( $i * $i ) > $o)).
% 0.18/0.46 tff(parallel_through_point_type, type, (
% 0.18/0.46 parallel_through_point: ( $i * $i ) > $i)).
% 0.18/0.46 tff(intersection_point_type, type, (
% 0.18/0.46 intersection_point: ( $i * $i ) > $i)).
% 0.18/0.46 tff(tptp_fun_Y_1_type, type, (
% 0.18/0.46 tptp_fun_Y_1: $i)).
% 0.18/0.46 tff(tptp_fun_Z_0_type, type, (
% 0.18/0.46 tptp_fun_Z_0: $i)).
% 0.18/0.46 tff(tptp_fun_X_2_type, type, (
% 0.18/0.46 tptp_fun_X_2: $i)).
% 0.18/0.46 tff(apart_point_and_line_type, type, (
% 0.18/0.46 apart_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.46 tff(incident_point_and_line_type, type, (
% 0.18/0.46 incident_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.46 tff(convergent_lines_type, type, (
% 0.18/0.46 convergent_lines: ( $i * $i ) > $o)).
% 0.18/0.46 tff(1,assumption,(~distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1)))), introduced(assumption)).
% 0.18/0.46 tff(2,plain,
% 0.18/0.46 (^[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))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(3,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.46 tff(4,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(5,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.18/0.46 tff(6,plain,
% 0.18/0.46 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.46 tff(7,plain,(
% 0.18/0.46 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[6])).
% 0.18/0.46 tff(8,plain,
% 0.18/0.46 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.46 tff(9,plain,
% 0.18/0.46 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(10,plain,
% 0.18/0.46 (~apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.18/0.46 tff(11,plain,
% 0.18/0.46 (^[X: $i, Y: $i] : refl((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(12,plain,
% 0.18/0.46 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.46 tff(13,plain,
% 0.18/0.46 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(14,plain,
% 0.18/0.46 (^[X: $i, Y: $i] : trans(rewrite((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), rewrite((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), ((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(15,plain,
% 0.18/0.46 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[14])).
% 0.18/0.46 tff(16,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.18/0.46 tff(17,plain,
% 0.18/0.46 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.46 tff(18,plain,
% 0.18/0.46 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.18/0.46 tff(19,plain,(
% 0.18/0.46 ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[18])).
% 0.18/0.46 tff(20,plain,
% 0.18/0.46 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.18/0.46 tff(21,plain,
% 0.18/0.46 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) <=> incident_point_and_line(intersection_point(Z!0, Y!1), X!2)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(22,plain,
% 0.18/0.46 (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) <=> incident_point_and_line(intersection_point(Z!0, Y!1), X!2))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.18/0.46 tff(23,plain,
% 0.18/0.46 ((~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(24,plain,
% 0.18/0.46 ((~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & incident_point_and_line(intersection_point(X, Y), Z)) => incident_point_and_line(intersection_point(Z, Y), X))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(25,axiom,(~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & incident_point_and_line(intersection_point(X, Y), Z)) => incident_point_and_line(intersection_point(Z, Y), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.18/0.46 tff(26,plain,
% 0.18/0.46 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.18/0.46 tff(27,plain,
% 0.18/0.46 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.18/0.46 tff(28,plain,
% 0.18/0.46 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.18/0.46 tff(29,plain,
% 0.18/0.46 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.18/0.46 tff(30,plain,(
% 0.18/0.46 ~((~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & incident_point_and_line(intersection_point(X!2, Y!1), Z!0))) | incident_point_and_line(intersection_point(Z!0, Y!1), X!2))),
% 0.18/0.46 inference(skolemize,[status(sab)],[29])).
% 0.18/0.46 tff(31,plain,
% 0.18/0.46 (~incident_point_and_line(intersection_point(Z!0, Y!1), X!2)),
% 0.18/0.46 inference(or_elim,[status(thm)],[30])).
% 0.18/0.46 tff(32,plain,
% 0.18/0.46 ((apart_point_and_line(intersection_point(Z!0, Y!1), X!2) <=> incident_point_and_line(intersection_point(Z!0, Y!1), X!2)) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | incident_point_and_line(intersection_point(Z!0, Y!1), X!2)),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(33,plain,
% 0.18/0.46 ((apart_point_and_line(intersection_point(Z!0, Y!1), X!2) <=> incident_point_and_line(intersection_point(Z!0, Y!1), X!2)) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.18/0.46 tff(34,plain,
% 0.18/0.46 (apart_point_and_line(intersection_point(Z!0, Y!1), X!2)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[33, 22])).
% 0.18/0.46 tff(35,plain,
% 0.18/0.46 (^[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))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(36,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[35])).
% 0.18/0.46 tff(37,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(38,plain,
% 0.18/0.46 (^[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)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(39,plain,
% 0.18/0.46 (![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)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[38])).
% 0.18/0.46 tff(40,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')).
% 0.18/0.46 tff(41,plain,
% 0.18/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.46 tff(42,plain,
% 0.18/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.18/0.46 tff(43,plain,(
% 0.18/0.46 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[42])).
% 0.18/0.46 tff(44,plain,
% 0.18/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.18/0.46 tff(45,plain,
% 0.18/0.46 (((~![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(intersection_point(Z!0, Y!1), X!2)) | apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | distinct_lines(X!2, parallel_through_point(X!2, intersection_point(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(intersection_point(Z!0, Y!1), X!2)) | apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(46,plain,
% 0.18/0.46 ((distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2))) <=> ((~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)) | apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(47,plain,
% 0.18/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))) <=> ((~![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(intersection_point(Z!0, Y!1), X!2)) | apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1)))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[46])).
% 0.18/0.46 tff(48,plain,
% 0.18/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))) <=> ((~![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(intersection_point(Z!0, Y!1), X!2)) | apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[47, 45])).
% 0.18/0.46 tff(49,plain,
% 0.18/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(50,plain,
% 0.18/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)) | apart_point_and_line(intersection_point(Z!0, Y!1), parallel_through_point(X!2, intersection_point(Z!0, Y!1))) | distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.46 tff(51,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[50, 44, 34, 10, 1])).
% 0.18/0.46 tff(52,plain,(distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(53,plain,
% 0.18/0.46 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(54,plain,
% 0.18/0.46 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[53])).
% 0.18/0.46 tff(55,plain,
% 0.18/0.46 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(56,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.18/0.47 tff(57,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.47 tff(58,plain,(
% 0.18/0.47 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.18/0.47 inference(skolemize,[status(sab)],[57])).
% 0.18/0.47 tff(59,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.18/0.47 tff(60,plain,
% 0.18/0.47 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(61,plain,
% 0.18/0.47 (~convergent_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.18/0.47 tff(62,plain,
% 0.18/0.47 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(63,plain,
% 0.18/0.47 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.47 tff(64,plain,
% 0.18/0.47 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(65,plain,
% 0.18/0.47 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(66,plain,
% 0.18/0.47 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.47 tff(67,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.18/0.47 tff(68,plain,
% 0.18/0.47 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.47 tff(69,plain,
% 0.18/0.47 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.18/0.47 tff(70,plain,(
% 0.18/0.47 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.47 inference(skolemize,[status(sab)],[69])).
% 0.18/0.47 tff(71,plain,
% 0.18/0.47 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.18/0.47 tff(72,plain,
% 0.18/0.47 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2)) | convergent_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2)) | convergent_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(73,plain,
% 0.18/0.47 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2)) | convergent_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(74,plain,
% 0.18/0.47 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2)) | convergent_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.47 tff(75,plain,
% 0.18/0.47 (~distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[74, 71, 61])).
% 0.18/0.47 tff(76,assumption,(distinct_lines(X!2, X!2)), introduced(assumption)).
% 0.18/0.47 tff(77,plain,
% 0.18/0.47 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(78,plain,
% 0.18/0.47 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[77])).
% 0.18/0.47 tff(79,plain,
% 0.18/0.47 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(80,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart2')).
% 0.18/0.47 tff(81,plain,
% 0.18/0.47 (![X: $i] : (~distinct_lines(X, X))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.47 tff(82,plain,(
% 0.18/0.47 ![X: $i] : (~distinct_lines(X, X))),
% 0.18/0.47 inference(skolemize,[status(sab)],[81])).
% 0.18/0.47 tff(83,plain,
% 0.18/0.47 (![X: $i] : (~distinct_lines(X, X))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.18/0.47 tff(84,plain,
% 0.18/0.47 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(X!2, X!2))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(85,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[84, 83, 76])).
% 0.18/0.47 tff(86,plain,(~distinct_lines(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(87,plain,
% 0.18/0.47 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(88,plain,
% 0.18/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[87])).
% 0.18/0.47 tff(89,plain,
% 0.18/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(90,plain,
% 0.18/0.47 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(91,plain,
% 0.18/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.47 tff(92,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.18/0.47 tff(93,plain,
% 0.18/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.18/0.47 tff(94,plain,
% 0.18/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.18/0.47 tff(95,plain,(
% 0.18/0.47 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[94])).
% 0.18/0.47 tff(96,plain,
% 0.18/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.18/0.47 tff(97,plain,
% 0.18/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, X!2) | distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2) | (~distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, X!2) | distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2) | (~distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(98,plain,
% 0.18/0.47 ((distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2) | distinct_lines(X!2, X!2) | (~distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1))))) <=> (distinct_lines(X!2, X!2) | distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2) | (~distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(99,plain,
% 0.18/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2) | distinct_lines(X!2, X!2) | (~distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, X!2) | distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2) | (~distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1))))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[98])).
% 0.18/0.47 tff(100,plain,
% 0.18/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2) | distinct_lines(X!2, X!2) | (~distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, X!2) | distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2) | (~distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1)))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[99, 97])).
% 0.18/0.47 tff(101,plain,
% 0.18/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2) | distinct_lines(X!2, X!2) | (~distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(102,plain,
% 0.18/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, X!2) | distinct_lines(parallel_through_point(X!2, intersection_point(Z!0, Y!1)), X!2) | (~distinct_lines(X!2, parallel_through_point(X!2, intersection_point(Z!0, Y!1))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.18/0.47 tff(103,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[102, 96, 86, 75, 52])).
% 0.18/0.47 % SZS output end Proof
% 0.18/0.47 % E exiting
%------------------------------------------------------------------------------