TSTP Solution File: GEO225+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO225+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Fri Sep 16 20:35:53 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO225+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 07:12:45 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(incident_point_and_line_type, type, (
% 0.20/0.39 incident_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.39 tff(line_connecting_type, type, (
% 0.20/0.39 line_connecting: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_B_0_type, type, (
% 0.20/0.39 tptp_fun_B_0: $i)).
% 0.20/0.39 tff(tptp_fun_A_1_type, type, (
% 0.20/0.39 tptp_fun_A_1: $i)).
% 0.20/0.39 tff(line_type, type, (
% 0.20/0.39 line: $i > $o)).
% 0.20/0.39 tff(distinct_points_type, type, (
% 0.20/0.39 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.39 tff(point_type, type, (
% 0.20/0.39 point: $i > $o)).
% 0.20/0.39 tff(apart_point_and_line_type, type, (
% 0.20/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[X: $i] : refl((~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X)))))) <=> (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X)))))) <=> ![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (^[X: $i] : rewrite((~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X)))) <=> (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X)))) <=> ![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (((point(A!1) & point(B!0) & distinct_points(A!1, B!0)) & ![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X))))) <=> (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 ((~(~(point(A!1) & point(B!0) & distinct_points(A!1, B!0)))) <=> (point(A!1) & point(B!0) & distinct_points(A!1, B!0))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (((~(~(point(A!1) & point(B!0) & distinct_points(A!1, B!0)))) & ![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X))))) <=> ((point(A!1) & point(B!0) & distinct_points(A!1, B!0)) & ![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[6])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (((~(~(point(A!1) & point(B!0) & distinct_points(A!1, B!0)))) & ![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X))))) <=> (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[7, 5])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))) <=> (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (((point(A) & point(B)) & distinct_points(A, B)) => ?[X: $i] : (line(X) => (incident_point_and_line(A, X) & incident_point_and_line(B, X))))) <=> (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(11,axiom,(~![A: $i, B: $i] : (((point(A) & point(B)) & distinct_points(A, B)) => ?[X: $i] : (line(X) => (incident_point_and_line(A, X) & incident_point_and_line(B, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 9])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | (incident_point_and_line(A, X) & incident_point_and_line(B, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[17, 9])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![X: $i] : (~((~line(X)) | (incident_point_and_line(A!1, X) & incident_point_and_line(B!0, X))))),
% 0.20/0.39 inference(and_elim,[status(thm)],[19])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[20, 4])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ((~![X: $i] : (~((~line(X)) | (~((~incident_point_and_line(A!1, X)) | (~incident_point_and_line(B!0, X))))))) | (~((~line(line_connecting(A!1, B!0))) | (~((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0)))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (~((~line(line_connecting(A!1, B!0))) | (~((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (((~line(line_connecting(A!1, B!0))) | (~((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0)))))) | ((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : refl((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(30,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')).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.40 tff(32,plain,(
% 0.20/0.40 ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(B!0, line_connecting(A!1, B!0)) <=> (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (incident_point_and_line(B!0, line_connecting(A!1, B!0)) <=> (~apart_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (distinct_points(A!1, B!0)),
% 0.20/0.40 inference(and_elim,[status(thm)],[19])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.40 tff(42,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.40 tff(45,plain,(
% 0.20/0.40 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[44])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (~apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 ((~(incident_point_and_line(B!0, line_connecting(A!1, B!0)) <=> (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))) | incident_point_and_line(B!0, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 ((~(incident_point_and_line(B!0, line_connecting(A!1, B!0)) <=> (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))) | incident_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (incident_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[52, 35])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(A!1, line_connecting(A!1, B!0)) <=> (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (incident_point_and_line(A!1, line_connecting(A!1, B!0)) <=> (~apart_point_and_line(A!1, line_connecting(A!1, B!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[54, 33])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.40 tff(61,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.40 tff(64,plain,(
% 0.20/0.40 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[63])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (~apart_point_and_line(A!1, line_connecting(A!1, B!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[68, 65, 36])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 ((~(incident_point_and_line(A!1, line_connecting(A!1, B!0)) <=> (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))) | incident_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(A!1, line_connecting(A!1, B!0))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((~(incident_point_and_line(A!1, line_connecting(A!1, B!0)) <=> (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))) | incident_point_and_line(A!1, line_connecting(A!1, B!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (incident_point_and_line(A!1, line_connecting(A!1, B!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[71, 55])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 ((~((~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0))))) | (~incident_point_and_line(A!1, line_connecting(A!1, B!0))) | (~incident_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[73, 72, 53, 26])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------