TSTP Solution File: GEO183+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO183+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 20:35:22 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO183+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 06:11:36 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(apart_point_and_line_type, type, (
% 0.14/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_U_1_type, type, (
% 0.14/0.40 tptp_fun_U_1: $i)).
% 0.14/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.14/0.40 tptp_fun_Y_2: $i)).
% 0.14/0.40 tff(line_connecting_type, type, (
% 0.14/0.40 line_connecting: ( $i * $i ) > $i)).
% 0.14/0.40 tff(tptp_fun_X_3_type, type, (
% 0.14/0.40 tptp_fun_X_3: $i)).
% 0.14/0.40 tff(distinct_points_type, type, (
% 0.14/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.14/0.40 tff(distinct_lines_type, type, (
% 0.14/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.14/0.40 tff(convergent_lines_type, type, (
% 0.14/0.40 convergent_lines: ( $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_V_0_type, type, (
% 0.14/0.40 tptp_fun_V_0: $i)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (~distinct_lines(U, line_connecting(X, Y)))) => ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(3,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (~distinct_lines(U, line_connecting(X, Y)))) => ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_lines(U, line_connecting(X, Y))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(Y, U))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.14/0.40 tff(11,plain,(
% 0.14/0.40 ~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (~distinct_lines(U!1, line_connecting(X!3, Y!2))))) | ((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(Y!2, U!1))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[10])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (~distinct_lines(U!1, line_connecting(X!3, Y!2)))),
% 0.14/0.40 inference(or_elim,[status(thm)],[11])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (distinct_points(X!3, Y!2)),
% 0.14/0.40 inference(and_elim,[status(thm)],[12])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (^[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)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (![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))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (![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))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (^[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)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (![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))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.14/0.40 tff(19,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')).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.14/0.40 tff(22,plain,(
% 0.14/0.40 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[21])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (~distinct_lines(U!1, line_connecting(X!3, Y!2))),
% 0.14/0.40 inference(and_elim,[status(thm)],[12])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.14/0.40 tff(34,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.14/0.40 tff(37,plain,(
% 0.14/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[36])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 ((distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1))) <=> (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[40])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.14/0.40 inference(transitivity,[status(thm)],[41, 39])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 (~apart_point_and_line(Y!2, U!1)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[44, 38, 28, 27])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 (^[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)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 (![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))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 (![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))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 (^[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)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 (![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))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.14/0.40 tff(51,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')).
% 0.14/0.40 tff(52,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.14/0.40 tff(54,plain,(
% 0.14/0.40 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[53])).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.14/0.40 tff(56,plain,
% 0.14/0.40 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(57,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(58,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[58, 55, 13])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 ((distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1))) <=> (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[62, 60])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (~apart_point_and_line(X!3, U!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[65, 38, 28, 59])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 ((~(~(apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1)))) <=> (apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(Y!2, U!1))) <=> (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ((~((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(Y!2, U!1)))) <=> (~(~(apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[68])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 ((~((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(Y!2, U!1)))) <=> (apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1))),
% 0.21/0.41 inference(transitivity,[status(thm)],[69, 67])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (~((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(Y!2, U!1)))),
% 0.21/0.41 inference(or_elim,[status(thm)],[11])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (apart_point_and_line(X!3, U!1) | apart_point_and_line(Y!2, U!1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[72, 66, 45])).
% 0.21/0.41 % SZS output end Proof
%------------------------------------------------------------------------------