TSTP Solution File: GEO225+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO225+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Fri Sep 16 20:35:52 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO225+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:56:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(distinct_points_type, type, (
% 0.20/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_B_0_type, type, (
% 0.20/0.40 tptp_fun_B_0: $i)).
% 0.20/0.40 tff(tptp_fun_A_1_type, type, (
% 0.20/0.40 tptp_fun_A_1: $i)).
% 0.20/0.40 tff(apart_point_and_line_type, type, (
% 0.20/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.40 tff(line_connecting_type, type, (
% 0.20/0.40 line_connecting: ( $i * $i ) > $i)).
% 0.20/0.40 tff(line_type, type, (
% 0.20/0.40 line: $i > $o)).
% 0.20/0.40 tff(point_type, type, (
% 0.20/0.40 point: $i > $o)).
% 0.20/0.40 tff(1,assumption,(distinct_points(A!1, A!1)), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.40 tff(7,plain,(
% 0.20/0.40 ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.40 inference(skolemize,[status(sab)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(A!1, A!1))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.40 tff(11,plain,(~distinct_points(A!1, A!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (((~distinct_points(A!1, A!1)) | (~distinct_points(A!1, B!0))) | distinct_points(A!1, A!1)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 ((~distinct_points(A!1, A!1)) | (~distinct_points(A!1, B!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.40 tff(14,assumption,(apart_point_and_line(A!1, line_connecting(A!1, B!0))), introduced(assumption)).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (((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))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 ((~(~(point(A!1) & point(B!0) & distinct_points(A!1, B!0)))) <=> (point(A!1) & point(B!0) & distinct_points(A!1, B!0))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (((~(~(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))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (((~(~(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))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[17, 15])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 ((~![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))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 ((~![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))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(21,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/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (~![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (~![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (~![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (~![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (~![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (~![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (~![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (distinct_points(A!1, B!0)),
% 0.20/0.40 inference(and_elim,[status(thm)],[29])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (^[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))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (^[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)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (^[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))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.40 tff(38,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/sandbox/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.40 tff(41,plain,(
% 0.20/0.40 ![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))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[40])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (((~![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)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 ((~![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)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))) | (~((~distinct_points(A!1, A!1)) | (~distinct_points(A!1, B!0))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[46, 43, 30, 14, 13])).
% 0.20/0.40 tff(48,plain,(~apart_point_and_line(A!1, line_connecting(A!1, B!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (^[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))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (^[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))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))),
% 0.20/0.40 inference(and_elim,[status(thm)],[29])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ((~![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))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (~((~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)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (((~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)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 ((~(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))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[61, 48])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (((~![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)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 ((~![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)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 ((~![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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (~((~distinct_points(B!0, A!1)) | (~distinct_points(B!0, B!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[65, 43, 30, 62])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (((~distinct_points(B!0, A!1)) | (~distinct_points(B!0, B!0))) | distinct_points(B!0, B!0)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (distinct_points(B!0, B!0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(B!0, B!0))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[69, 8, 68])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------