TSTP Solution File: GEO209+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO209+1 : TPTP v8.1.0. Released v3.3.0.
% 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 20:35:41 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO209+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 06:53:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -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(convergent_lines_type, type, (
% 0.12/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_N_0_type, type, (
% 0.12/0.39 tptp_fun_N_0: $i)).
% 0.12/0.39 tff(tptp_fun_M_1_type, type, (
% 0.12/0.39 tptp_fun_M_1: $i)).
% 0.12/0.39 tff(tptp_fun_L_2_type, type, (
% 0.12/0.39 tptp_fun_L_2: $i)).
% 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(tptp_fun_A_3_type, type, (
% 0.12/0.39 tptp_fun_A_3: $i)).
% 0.12/0.39 tff(distinct_lines_type, type, (
% 0.12/0.39 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 ((~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))) <=> (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 ((~![A: $i, L: $i, M: $i, N: $i] : (((((apart_point_and_line(A, L) & (~apart_point_and_line(A, M))) & (~apart_point_and_line(A, N))) & (~convergent_lines(M, L))) & (~convergent_lines(N, L))) => (~distinct_lines(M, N)))) <=> (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,axiom,(~![A: $i, L: $i, M: $i, N: $i] : (((((apart_point_and_line(A, L) & (~apart_point_and_line(A, M))) & (~apart_point_and_line(A, N))) & (~convergent_lines(M, L))) & (~convergent_lines(N, L))) => (~distinct_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~![A: $i, L: $i, M: $i, N: $i] : ((~distinct_lines(M, N)) | (~(apart_point_and_line(A, L) & (~apart_point_and_line(A, M)) & (~apart_point_and_line(A, N)) & (~convergent_lines(M, L)) & (~convergent_lines(N, L)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.39 tff(11,plain,(
% 0.12/0.39 ~((~distinct_lines(M!1, N!0)) | (~(apart_point_and_line(A!3, L!2) & (~apart_point_and_line(A!3, M!1)) & (~apart_point_and_line(A!3, N!0)) & (~convergent_lines(M!1, L!2)) & (~convergent_lines(N!0, L!2)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (apart_point_and_line(A!3, L!2) & (~apart_point_and_line(A!3, M!1)) & (~apart_point_and_line(A!3, N!0)) & (~convergent_lines(M!1, L!2)) & (~convergent_lines(N!0, L!2))),
% 0.12/0.39 inference(or_elim,[status(thm)],[11])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (~convergent_lines(N!0, L!2)),
% 0.12/0.39 inference(and_elim,[status(thm)],[12])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (~convergent_lines(M!1, L!2)),
% 0.12/0.39 inference(and_elim,[status(thm)],[12])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.39 tff(20,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.12/0.39 tff(23,plain,(
% 0.12/0.39 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 ((convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0))) <=> (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[26])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[27, 25])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2) | (~convergent_lines(M!1, N!0))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (~convergent_lines(M!1, N!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[30, 24, 14, 13])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (~apart_point_and_line(A!3, N!0)),
% 0.12/0.39 inference(and_elim,[status(thm)],[12])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (~apart_point_and_line(A!3, M!1)),
% 0.12/0.39 inference(and_elim,[status(thm)],[12])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (distinct_lines(M!1, N!0)),
% 0.12/0.39 inference(or_elim,[status(thm)],[11])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.40 tff(40,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/sandbox2/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.12/0.40 tff(43,plain,(
% 0.12/0.40 ![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)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[42])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (((~![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(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, N!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(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, N!0))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 ((convergent_lines(M!1, N!0) | apart_point_and_line(A!3, N!0) | apart_point_and_line(A!3, M!1) | (~distinct_lines(M!1, N!0))) <=> ((~distinct_lines(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, N!0))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (((~![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(M!1, N!0) | apart_point_and_line(A!3, N!0) | apart_point_and_line(A!3, M!1) | (~distinct_lines(M!1, N!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(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, N!0)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[46])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (((~![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(M!1, N!0) | apart_point_and_line(A!3, N!0) | apart_point_and_line(A!3, M!1) | (~distinct_lines(M!1, N!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(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, N!0))),
% 0.12/0.40 inference(transitivity,[status(thm)],[47, 45])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 ((~![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(M!1, N!0) | apart_point_and_line(A!3, N!0) | apart_point_and_line(A!3, M!1) | (~distinct_lines(M!1, N!0)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(M!1, N!0)) | apart_point_and_line(A!3, M!1) | apart_point_and_line(A!3, N!0) | convergent_lines(M!1, N!0)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[50, 44, 34, 33, 32, 31])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------