TSTP Solution File: GEO237+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 20:35:58 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.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 : Wed Aug 31 07:04:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(right_apart_point_type, type, (
% 0.12/0.39 right_apart_point: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_L_0_type, type, (
% 0.12/0.39 tptp_fun_L_0: $i)).
% 0.12/0.39 tff(tptp_fun_B_2_type, type, (
% 0.12/0.39 tptp_fun_B_2: $i)).
% 0.12/0.39 tff(left_apart_point_type, type, (
% 0.12/0.39 left_apart_point: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_A_3_type, type, (
% 0.12/0.39 tptp_fun_A_3: $i)).
% 0.12/0.39 tff(tptp_fun_C_1_type, type, (
% 0.12/0.39 tptp_fun_C_1: $i)).
% 0.12/0.39 tff(divides_points_type, type, (
% 0.12/0.39 divides_points: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(apart_point_and_line_type, type, (
% 0.12/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,assumption,(right_apart_point(C!1, L!0)), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[A: $i, B: $i, L: $i] : refl((divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L)))))) <=> (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L)))))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (^[A: $i, B: $i, L: $i] : rewrite((divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L)))) <=> (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L)))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L)))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(7,axiom,(![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a8_defns')).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.39 tff(9,plain,(
% 0.12/0.39 ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & right_apart_point(B, L)) | (right_apart_point(A, L) & left_apart_point(B, L))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[8])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 ((divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0)))))) <=> (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0)))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[14, 12])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~right_apart_point(B!2, L!0)) | (~left_apart_point(C!1, L!0))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~right_apart_point(B, L)))) | (~((~right_apart_point(A, L)) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[17, 11])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 ((~(divides_points(L!0, B!2, C!1) | divides_points(L!0, A!3, C!1) | (~divides_points(L!0, A!3, B!2)) | (~apart_point_and_line(C!1, L!0)))) <=> (~(divides_points(L!0, B!2, C!1) | divides_points(L!0, A!3, C!1) | (~divides_points(L!0, A!3, B!2)) | (~apart_point_and_line(C!1, L!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))) <=> (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i, L: $i] : (apart_point_and_line(C, L) => (divides_points(L, A, B) => (divides_points(L, A, C) | divides_points(L, B, C))))) <=> (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(22,axiom,(~![A: $i, B: $i, C: $i, L: $i] : (apart_point_and_line(C, L) => (divides_points(L, A, B) => (divides_points(L, A, C) | divides_points(L, B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.12/0.39 tff(30,plain,(
% 0.12/0.39 ~(divides_points(L!0, B!2, C!1) | divides_points(L!0, A!3, C!1) | (~divides_points(L!0, A!3, B!2)) | (~apart_point_and_line(C!1, L!0)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[29])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (~(divides_points(L!0, B!2, C!1) | divides_points(L!0, A!3, C!1) | (~divides_points(L!0, A!3, B!2)) | (~apart_point_and_line(C!1, L!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 19])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (~divides_points(L!0, B!2, C!1)),
% 0.12/0.39 inference(or_elim,[status(thm)],[31])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~(divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))))))) | divides_points(L!0, B!2, C!1) | (~((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ((~(divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))))))) | (~((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (~((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[34, 18])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))))) | ((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 ((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[36, 35])).
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% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(39,plain,
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% 0.12/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
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% 0.12/0.40 inference(unit_resolution,[status(thm)],[39, 1])).
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% 0.12/0.40 (((~left_apart_point(B!2, L!0)) | (~right_apart_point(A!3, L!0))) | left_apart_point(B!2, L!0)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 ((~left_apart_point(B!2, L!0)) | (~right_apart_point(A!3, L!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.40 tff(43,plain,
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% 0.12/0.40 inference(monotonicity,[status(thm)],[44])).
% 0.12/0.40 tff(46,plain,
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% 0.12/0.40 inference(transitivity,[status(thm)],[45, 43])).
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% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
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% 0.12/0.40 inference(unit_resolution,[status(thm)],[48, 11])).
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% 0.12/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
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% 0.12/0.40 inference(unit_resolution,[status(thm)],[52, 49])).
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% 0.12/0.40 inference(tautology,[status(thm)],[])).
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% 0.12/0.40 inference(unit_resolution,[status(thm)],[54, 53])).
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% 0.12/0.40 inference(tautology,[status(thm)],[])).
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% 0.12/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
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% 0.12/0.40 inference(unit_resolution,[status(thm)],[57, 1])).
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% 0.12/0.40 (((~left_apart_point(A!3, L!0)) | (~right_apart_point(B!2, L!0))) | left_apart_point(A!3, L!0)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
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% 0.12/0.40 inference(monotonicity,[status(thm)],[62])).
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% 0.18/0.41 tff(76,plain,
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% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(79,axiom,(![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a6_defns')).
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% 0.18/0.41 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.41 tff(81,plain,(
% 0.18/0.41 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[80])).
% 0.18/0.41 tff(82,plain,
% 0.18/0.41 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.18/0.41 tff(83,plain,
% 0.18/0.41 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(C!1, L!0) <=> (left_apart_point(C!1, L!0) | right_apart_point(C!1, L!0)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(84,plain,
% 0.18/0.41 (apart_point_and_line(C!1, L!0) <=> (left_apart_point(C!1, L!0) | right_apart_point(C!1, L!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 (apart_point_and_line(C!1, L!0)),
% 0.18/0.41 inference(or_elim,[status(thm)],[31])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 ((~(apart_point_and_line(C!1, L!0) <=> (left_apart_point(C!1, L!0) | right_apart_point(C!1, L!0)))) | (~apart_point_and_line(C!1, L!0)) | (left_apart_point(C!1, L!0) | right_apart_point(C!1, L!0))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 ((~(apart_point_and_line(C!1, L!0) <=> (left_apart_point(C!1, L!0) | right_apart_point(C!1, L!0)))) | (left_apart_point(C!1, L!0) | right_apart_point(C!1, L!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 (left_apart_point(C!1, L!0) | right_apart_point(C!1, L!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 ((~(left_apart_point(C!1, L!0) | right_apart_point(C!1, L!0))) | left_apart_point(C!1, L!0) | right_apart_point(C!1, L!0)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(90,plain,
% 0.18/0.41 (left_apart_point(C!1, L!0) | right_apart_point(C!1, L!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 (left_apart_point(C!1, L!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[90, 75])).
% 0.18/0.41 tff(92,plain,
% 0.18/0.41 (((~((~left_apart_point(B!2, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))))) | ((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(93,plain,
% 0.18/0.41 ((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[92, 35])).
% 0.18/0.41 tff(94,plain,
% 0.18/0.41 ((~((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0)))) | (~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(95,plain,
% 0.18/0.41 ((~left_apart_point(C!1, L!0)) | (~right_apart_point(B!2, L!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.18/0.41 tff(96,plain,
% 0.18/0.41 (~right_apart_point(B!2, L!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[95, 91])).
% 0.18/0.41 tff(97,plain,
% 0.18/0.41 (((~left_apart_point(A!3, L!0)) | (~right_apart_point(B!2, L!0))) | right_apart_point(B!2, L!0)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(98,plain,
% 0.18/0.41 ((~left_apart_point(A!3, L!0)) | (~right_apart_point(B!2, L!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 (((~((~left_apart_point(A!3, L!0)) | (~right_apart_point(C!1, L!0)))) | (~((~left_apart_point(C!1, L!0)) | (~right_apart_point(A!3, L!0))))) | ((~left_apart_point(C!1, L!0)) | (~right_apart_point(A!3, L!0)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 ((~left_apart_point(C!1, L!0)) | (~right_apart_point(A!3, L!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[99, 53])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 ((~((~left_apart_point(C!1, L!0)) | (~right_apart_point(A!3, L!0)))) | (~left_apart_point(C!1, L!0)) | (~right_apart_point(A!3, L!0))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 ((~left_apart_point(C!1, L!0)) | (~right_apart_point(A!3, L!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 (~right_apart_point(A!3, L!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[102, 91])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 (((~left_apart_point(B!2, L!0)) | (~right_apart_point(A!3, L!0))) | right_apart_point(A!3, L!0)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 ((~left_apart_point(B!2, L!0)) | (~right_apart_point(A!3, L!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[73, 105, 98])).
% 0.18/0.41 % SZS output end Proof
%------------------------------------------------------------------------------