TSTP Solution File: GEO208+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO208+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 20:35:41 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO208+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 : n029.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 07:05:42 EDT 2022
% 0.13/0.34 % 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.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(convergent_lines_type, type, (
% 0.21/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.21/0.39 tptp_fun_Z_0: $i)).
% 0.21/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.39 tptp_fun_Y_1: $i)).
% 0.21/0.39 tff(apart_point_and_line_type, type, (
% 0.21/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_X_2_type, type, (
% 0.21/0.39 tptp_fun_X_2: $i)).
% 0.21/0.39 tff(distinct_lines_type, type, (
% 0.21/0.39 distinct_lines: ( $i * $i ) > $o)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, Z)) | (~((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z)) & (~convergent_lines(Y, Z)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, Z)) | (~((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z)) & (~convergent_lines(Y, Z))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 ((~![X: $i, Y: $i, Z: $i] : ((((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z))) & (~convergent_lines(Y, Z))) => (~distinct_lines(Y, Z)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, Z)) | (~((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z)) & (~convergent_lines(Y, Z))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(3,axiom,(~![X: $i, Y: $i, Z: $i] : ((((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z))) & (~convergent_lines(Y, Z))) => (~distinct_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, Z)) | (~((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z)) & (~convergent_lines(Y, Z)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, Z)) | (~((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z)) & (~convergent_lines(Y, Z)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, Z)) | (~((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z)) & (~convergent_lines(Y, Z)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, Z)) | (~((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z)) & (~convergent_lines(Y, Z)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, Z)) | (~((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z)) & (~convergent_lines(Y, Z)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, Z)) | (~((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z)) & (~convergent_lines(Y, Z)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, Z)) | (~((~apart_point_and_line(X, Y)) & (~apart_point_and_line(X, Z)) & (~convergent_lines(Y, Z)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.39 tff(11,plain,(
% 0.21/0.39 ~((~distinct_lines(Y!1, Z!0)) | (~((~apart_point_and_line(X!2, Y!1)) & (~apart_point_and_line(X!2, Z!0)) & (~convergent_lines(Y!1, Z!0)))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 ((~apart_point_and_line(X!2, Y!1)) & (~apart_point_and_line(X!2, Z!0)) & (~convergent_lines(Y!1, Z!0))),
% 0.21/0.39 inference(or_elim,[status(thm)],[11])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (~convergent_lines(Y!1, Z!0)),
% 0.21/0.39 inference(and_elim,[status(thm)],[12])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (~apart_point_and_line(X!2, Z!0)),
% 0.21/0.39 inference(and_elim,[status(thm)],[12])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (~apart_point_and_line(X!2, Y!1)),
% 0.21/0.39 inference(and_elim,[status(thm)],[12])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (distinct_lines(Y!1, Z!0)),
% 0.21/0.39 inference(or_elim,[status(thm)],[11])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) <=> (apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> ((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)))), rewrite(((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))))), rewrite((distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.39 tff(22,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.21/0.39 tff(25,plain,(
% 0.21/0.39 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[24])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | ((~distinct_lines(Y!1, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(Y!1, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 ((convergent_lines(Y!1, Z!0) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, Z!0))) <=> ((~distinct_lines(Y!1, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, Z!0) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | ((~distinct_lines(Y!1, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[28])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, Z!0) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(Y!1, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0))),
% 0.21/0.40 inference(transitivity,[status(thm)],[29, 27])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, Z!0) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, Z!0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(Y!1, Z!0)) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, Z!0) | convergent_lines(Y!1, Z!0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[32, 26, 16, 15, 14, 13])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------