%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO208+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:05:57 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO208+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.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 14:43:11 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(convergent_lines_type, type, (
% 0.11/0.36 convergent_lines: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_Z_0_type, type, (
% 0.11/0.36 tptp_fun_Z_0: $i)).
% 0.11/0.36 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.36 tptp_fun_Y_1: $i)).
% 0.11/0.36 tff(apart_point_and_line_type, type, (
% 0.11/0.36 apart_point_and_line: ( $i * $i ) > $o)).
% 0.11/0.36 tff(tptp_fun_X_2_type, type, (
% 0.11/0.36 tptp_fun_X_2: $i)).
% 0.11/0.36 tff(distinct_lines_type, type, (
% 0.11/0.36 distinct_lines: ( $i * $i ) > $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 ((~![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] : ((~distinct_lines(Y, Z)) | (~((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z)) & (~convergent_lines(Y, Z))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((~![X: $i, Y: $i, Z: $i] : ((((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z))) & (~convergent_lines(Y, Z))) => (~distinct_lines(Y, Z)))) <=> (~![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))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,axiom,(~![X: $i, Y: $i, Z: $i] : ((((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z))) & (~convergent_lines(Y, Z))) => (~distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (~![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)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (~![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)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~![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)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (~![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)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.11/0.36 tff(8,plain,(
% 0.11/0.36 ~((~distinct_lines(Y!1, Z!0)) | (~((~apart_point_and_line(X!2, Y!1)) & (~apart_point_and_line(X!2, Z!0)) & (~convergent_lines(Y!1, Z!0)))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 ((~apart_point_and_line(X!2, Y!1)) & (~apart_point_and_line(X!2, Z!0)) & (~convergent_lines(Y!1, Z!0))),
% 0.11/0.36 inference(or_elim,[status(thm)],[8])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (~convergent_lines(Y!1, Z!0)),
% 0.11/0.36 inference(and_elim,[status(thm)],[9])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (~apart_point_and_line(X!2, Z!0)),
% 0.11/0.36 inference(and_elim,[status(thm)],[9])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (~apart_point_and_line(X!2, Y!1)),
% 0.11/0.36 inference(and_elim,[status(thm)],[9])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (distinct_lines(Y!1, Z!0)),
% 0.11/0.36 inference(or_elim,[status(thm)],[8])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (^[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))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (^[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)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[17])).
% 0.11/0.36 tff(19,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')).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.11/0.36 tff(22,plain,(
% 0.11/0.36 ![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)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[21])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (![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)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (((~![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, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0))) <=> ((~![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, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 ((convergent_lines(Y!1, Z!0) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, Z!0))) <=> ((~distinct_lines(Y!1, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (((~![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, Z!0) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, Z!0)))) <=> ((~![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, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[25])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (((~![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)))) | (convergent_lines(Y!1, Z!0) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, Z!0)))) <=> ((~![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, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0))),
% 0.11/0.37 inference(transitivity,[status(thm)],[26, 24])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 ((~![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)))) | (convergent_lines(Y!1, Z!0) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, Z!0)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(Y!1, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[29, 23, 13, 12, 11, 10])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------