TSTP Solution File: GEO246+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO246+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 20:36:02 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO246+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 06:55:31 EDT 2022
% 0.13/0.35 % 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.
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(left_apart_point_type, type, (
% 0.21/0.41 left_apart_point: ( $i * $i ) > $o)).
% 0.21/0.41 tff(reverse_line_type, type, (
% 0.21/0.41 reverse_line: $i > $i)).
% 0.21/0.41 tff(line_connecting_type, type, (
% 0.21/0.41 line_connecting: ( $i * $i ) > $i)).
% 0.21/0.41 tff(tptp_fun_B_1_type, type, (
% 0.21/0.41 tptp_fun_B_1: $i)).
% 0.21/0.41 tff(tptp_fun_A_2_type, type, (
% 0.21/0.41 tptp_fun_A_2: $i)).
% 0.21/0.41 tff(tptp_fun_C_0_type, type, (
% 0.21/0.41 tptp_fun_C_0: $i)).
% 0.21/0.41 tff(right_apart_point_type, type, (
% 0.21/0.41 right_apart_point: ( $i * $i ) > $o)).
% 0.21/0.41 tff(distinct_points_type, type, (
% 0.21/0.41 distinct_points: ( $i * $i ) > $o)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : refl((right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(4,axiom,(![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a2_defns')).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.41 tff(6,plain,(
% 0.21/0.41 ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[5])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(C!0, line_connecting(A!2, B!1)) <=> left_apart_point(C!0, reverse_line(line_connecting(A!2, B!1))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (right_apart_point(C!0, line_connecting(A!2, B!1)) <=> left_apart_point(C!0, reverse_line(line_connecting(A!2, B!1)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 ((~(left_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~right_apart_point(C!0, line_connecting(A!2, B!1))))) <=> (~(left_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~right_apart_point(C!0, line_connecting(A!2, B!1)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : (left_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~right_apart_point(C, line_connecting(A, B))))) <=> (~![A: $i, B: $i, C: $i] : (left_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~right_apart_point(C, line_connecting(A, B)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (right_apart_point(C, line_connecting(A, B)) => left_apart_point(B, line_connecting(A, C))))) <=> (~![A: $i, B: $i, C: $i] : (left_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~right_apart_point(C, line_connecting(A, B)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(13,axiom,(~![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (right_apart_point(C, line_connecting(A, B)) => left_apart_point(B, line_connecting(A, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (left_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~right_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (left_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~right_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (left_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~right_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (left_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~right_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (left_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~right_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (left_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~right_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (~![A: $i, B: $i, C: $i] : (left_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~right_apart_point(C, line_connecting(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.21/0.41 tff(21,plain,(
% 0.21/0.41 ~(left_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~right_apart_point(C!0, line_connecting(A!2, B!1))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[20])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (~(left_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~right_apart_point(C!0, line_connecting(A!2, B!1))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 10])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (right_apart_point(C!0, line_connecting(A!2, B!1))),
% 0.21/0.41 inference(or_elim,[status(thm)],[22])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 ((~(right_apart_point(C!0, line_connecting(A!2, B!1)) <=> left_apart_point(C!0, reverse_line(line_connecting(A!2, B!1))))) | (~right_apart_point(C!0, line_connecting(A!2, B!1))) | left_apart_point(C!0, reverse_line(line_connecting(A!2, B!1)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 ((~(right_apart_point(C!0, line_connecting(A!2, B!1)) <=> left_apart_point(C!0, reverse_line(line_connecting(A!2, B!1))))) | left_apart_point(C!0, reverse_line(line_connecting(A!2, B!1)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (left_apart_point(C!0, reverse_line(line_connecting(A!2, B!1)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[25, 9])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 ((left_apart_point(C!0, line_connecting(A!2, B!1)) | left_apart_point(C!0, reverse_line(line_connecting(A!2, B!1)))) | (~left_apart_point(C!0, reverse_line(line_connecting(A!2, B!1))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (left_apart_point(C!0, line_connecting(A!2, B!1)) | left_apart_point(C!0, reverse_line(line_connecting(A!2, B!1)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (^[A: $i, L: $i] : refl((~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(32,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax10_basics')).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.41 tff(34,plain,(
% 0.21/0.41 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[33])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(C!0, line_connecting(A!2, B!1)) | left_apart_point(C!0, reverse_line(line_connecting(A!2, B!1)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[36, 35, 28])).
% 0.21/0.41 % SZS output end Proof
%------------------------------------------------------------------------------