%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO171+1 : 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 05:05:43 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO171+1 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.12 % 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 14:39:03 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(tptp_fun_X_1_type, type, (
% 0.12/0.37 tptp_fun_X_1: $i)).
% 0.12/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.37 tptp_fun_Y_0: $i)).
% 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] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,(
% 0.12/0.37 ![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.37 inference(skolemize,[status(sab)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![X: $i] : (~convergent_lines(X, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(Y!0, Y!0))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~convergent_lines(Y!0, Y!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] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) <=> (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))) <=> (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(12,axiom,(~![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 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] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 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] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 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] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.12/0.37 tff(17,plain,(
% 0.12/0.37 ~((~convergent_lines(X!1, Y!0)) | distinct_lines(X!1, Y!0))),
% 0.12/0.37 inference(skolemize,[status(sab)],[16])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (~distinct_lines(X!1, Y!0)),
% 0.12/0.37 inference(or_elim,[status(thm)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.37 tff(24,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.37 tff(27,plain,(
% 0.12/0.37 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[26])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!1, Y!0) | convergent_lines(Y!0, Y!0) | (~convergent_lines(Y!0, X!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(X!1, Y!0) | convergent_lines(Y!0, Y!0) | (~convergent_lines(Y!0, X!1)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!1, Y!0) | convergent_lines(Y!0, Y!0) | (~convergent_lines(Y!0, X!1)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(X!1, Y!0) | convergent_lines(Y!0, Y!0) | (~convergent_lines(Y!0, X!1))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (~convergent_lines(Y!0, X!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[31, 28, 18, 9])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!1, X!1))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (~convergent_lines(X!1, X!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[33, 7])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (convergent_lines(X!1, Y!0)),
% 0.12/0.37 inference(or_elim,[status(thm)],[17])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[36])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.12/0.38 tff(41,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.12/0.38 tff(44,plain,(
% 0.12/0.38 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[43])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | convergent_lines(X!1, X!1) | convergent_lines(Y!0, X!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(X!1, X!1) | convergent_lines(Y!0, X!1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ((convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0))) <=> ((~convergent_lines(X!1, Y!0)) | convergent_lines(X!1, X!1) | convergent_lines(Y!0, X!1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | convergent_lines(X!1, X!1) | convergent_lines(Y!0, X!1)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[47])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(X!1, X!1) | convergent_lines(Y!0, X!1))),
% 0.12/0.38 inference(transitivity,[status(thm)],[48, 46])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(X!1, X!1) | convergent_lines(Y!0, X!1)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[51, 45, 35, 34, 32])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------