%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO225+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:06:02 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO225+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:42:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(distinct_points_type, type, (
% 0.11/0.37 distinct_points: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_B_0_type, type, (
% 0.11/0.37 tptp_fun_B_0: $i)).
% 0.11/0.37 tff(tptp_fun_A_1_type, type, (
% 0.11/0.37 tptp_fun_A_1: $i)).
% 0.11/0.37 tff(apart_point_and_line_type, type, (
% 0.11/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.11/0.37 tff(line_connecting_type, type, (
% 0.11/0.37 line_connecting: ( $i * $i ) > $i)).
% 0.11/0.37 tff(line_type, type, (
% 0.11/0.37 line: $i > $o)).
% 0.11/0.37 tff(point_type, type, (
% 0.11/0.37 point: $i > $o)).
% 0.11/0.37 tff(1,assumption,(distinct_points(A!1, A!1)), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (![X: $i] : (~distinct_points(X, X))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.37 tff(7,plain,(
% 0.11/0.37 ![X: $i] : (~distinct_points(X, X))),
% 0.11/0.37 inference(skolemize,[status(sab)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![X: $i] : (~distinct_points(X, X))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(A!1, A!1))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.37 tff(11,plain,(~distinct_points(A!1, A!1)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (((~distinct_points(A!1, A!1)) | (~distinct_points(A!1, B!0))) | distinct_points(A!1, A!1)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 ((~distinct_points(A!1, A!1)) | (~distinct_points(A!1, B!0))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.11/0.37 tff(14,assumption,(apart_point_and_line(A!1, line_connecting(A!1, B!0))), introduced(assumption)).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (((point(A!1) & point(B!0) & distinct_points(A!1, B!0)) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))) <=> (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 ((~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))) <=> (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 ((~![A: $i, B: $i] : (((point(A) & point(B)) & distinct_points(A, B)) => ?[X: $i] : (line(X) => ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))) <=> (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(18,axiom,(~![A: $i, B: $i] : (((point(A) & point(B)) & distinct_points(A, B)) => ?[X: $i] : (line(X) => ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (distinct_points(A!1, B!0)),
% 0.11/0.37 inference(and_elim,[status(thm)],[23])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (^[X: $i, Y: $i, Z: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(Z, X) & distinct_points(Z, Y)) <=> (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))), rewrite(((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))) <=> ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> (distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))))), rewrite((distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.11/0.37 tff(32,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.11/0.37 tff(35,plain,(
% 0.11/0.37 ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[34])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))) | (~((~distinct_points(A!1, A!1)) | (~distinct_points(A!1, B!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))) | (~((~distinct_points(A!1, A!1)) | (~distinct_points(A!1, B!0)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))) | (~((~distinct_points(A!1, A!1)) | (~distinct_points(A!1, B!0)))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))) | (~((~distinct_points(A!1, A!1)) | (~distinct_points(A!1, B!0))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[40, 37, 24, 14, 13])).
% 0.11/0.37 tff(42,plain,(~apart_point_and_line(A!1, line_connecting(A!1, B!0))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (^[X: $i] : refl((~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))) <=> (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))) <=> ![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (^[X: $i] : rewrite((~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X))))) <=> (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X))))) <=> ![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[45])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))),
% 0.11/0.38 inference(and_elim,[status(thm)],[23])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 (![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 (![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 ((~![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))) | (~((~line(line_connecting(A!1, B!0))) | (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (~((~line(line_connecting(A!1, B!0))) | (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0)))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (((~line(line_connecting(A!1, B!0))) | (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))))) | (apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 ((~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0)))) | apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 (apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[55, 42])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))) | (~((~distinct_points(B!0, A!1)) | (~distinct_points(B!0, B!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))) | (~((~distinct_points(B!0, A!1)) | (~distinct_points(B!0, B!0)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))) | (~((~distinct_points(B!0, A!1)) | (~distinct_points(B!0, B!0)))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))) | (~((~distinct_points(B!0, A!1)) | (~distinct_points(B!0, B!0))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (~((~distinct_points(B!0, A!1)) | (~distinct_points(B!0, B!0)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[59, 37, 24, 56])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 (((~distinct_points(B!0, A!1)) | (~distinct_points(B!0, B!0))) | distinct_points(B!0, B!0)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (distinct_points(B!0, B!0)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(B!0, B!0))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[63, 8, 62])).
% 0.11/0.38 % SZS output end Proof
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------