TSTP Solution File: GEO217+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO217+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 20:35:47 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO217+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n001.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 07:21:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.34 Usage: tptp [options] [-file:]file
% 0.20/0.34 -h, -? prints this message.
% 0.20/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.34 -m, -model generate model.
% 0.20/0.34 -p, -proof generate proof.
% 0.20/0.34 -c, -core generate unsat core of named formulas.
% 0.20/0.34 -st, -statistics display statistics.
% 0.20/0.34 -t:timeout set timeout (in second).
% 0.20/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.34 -<param>:<value> configuration parameter and value.
% 0.20/0.34 -o:<output-file> file to place output in.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(convergent_lines_type, type, (
% 0.20/0.45 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.45 tff(tptp_fun_N_0_type, type, (
% 0.20/0.45 tptp_fun_N_0: $i)).
% 0.20/0.45 tff(tptp_fun_L_2_type, type, (
% 0.20/0.45 tptp_fun_L_2: $i)).
% 0.20/0.45 tff(distinct_lines_type, type, (
% 0.20/0.45 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.45 tff(tptp_fun_M_1_type, type, (
% 0.20/0.45 tptp_fun_M_1: $i)).
% 0.20/0.45 tff(unorthogonal_lines_type, type, (
% 0.20/0.45 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.45 tff(orthogonal_through_point_type, type, (
% 0.20/0.45 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.20/0.45 tff(intersection_point_type, type, (
% 0.20/0.45 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.45 tff(parallel_lines_type, type, (
% 0.20/0.45 parallel_lines: ( $i * $i ) > $o)).
% 0.20/0.45 tff(1,plain,
% 0.20/0.45 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(4,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.45 tff(6,plain,(
% 0.20/0.45 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.45 inference(skolemize,[status(sab)],[5])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (~unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 (^[L: $i, M: $i, N: $i] : refl((unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(11,plain,
% 0.20/0.45 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.45 tff(14,plain,
% 0.20/0.45 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.45 tff(17,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.45 tff(20,plain,(
% 0.20/0.45 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[19])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | (~convergent_lines(M!1, M!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | (~convergent_lines(M!1, M!1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 ((unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | (~convergent_lines(M!1, M!1))) <=> (unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | (~convergent_lines(M!1, M!1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | (~convergent_lines(M!1, M!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | (~convergent_lines(M!1, M!1))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[24])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | (~convergent_lines(M!1, M!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | (~convergent_lines(M!1, M!1)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | (~convergent_lines(M!1, M!1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(M!1, intersection_point(M!1, N!0)), M!1) | (~convergent_lines(M!1, M!1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (~convergent_lines(M!1, M!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[28, 22, 9])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : refl((parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(33,axiom,(![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a3')).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.45 tff(35,plain,(
% 0.20/0.45 ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[34])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))) | (parallel_lines(L!2, M!1) <=> (~convergent_lines(L!2, M!1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (parallel_lines(L!2, M!1) <=> (~convergent_lines(L!2, M!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 ((~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 ((~![L: $i, M: $i, N: $i] : ((parallel_lines(L, M) & parallel_lines(L, N)) => parallel_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(41,axiom,(~![L: $i, M: $i, N: $i] : ((parallel_lines(L, M) & parallel_lines(L, N)) => parallel_lines(M, N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[42, 39])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[44, 39])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[45, 39])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & parallel_lines(L, N))) | parallel_lines(M, N))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[47, 39])).
% 0.20/0.45 tff(49,plain,(
% 0.20/0.45 ~((~(parallel_lines(L!2, M!1) & parallel_lines(L!2, N!0))) | parallel_lines(M!1, N!0))),
% 0.20/0.45 inference(skolemize,[status(sab)],[48])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (parallel_lines(L!2, M!1) & parallel_lines(L!2, N!0)),
% 0.20/0.45 inference(or_elim,[status(thm)],[49])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (parallel_lines(L!2, M!1)),
% 0.20/0.45 inference(and_elim,[status(thm)],[50])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 ((~(parallel_lines(L!2, M!1) <=> (~convergent_lines(L!2, M!1)))) | (~parallel_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 ((~(parallel_lines(L!2, M!1) <=> (~convergent_lines(L!2, M!1)))) | (~convergent_lines(L!2, M!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 (~convergent_lines(L!2, M!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[53, 38])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.45 tff(60,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.45 tff(63,plain,(
% 0.20/0.45 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.45 inference(skolemize,[status(sab)],[62])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(L!2, M!1)) | convergent_lines(L!2, M!1))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(L!2, M!1)) | convergent_lines(L!2, M!1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(L!2, M!1)) | convergent_lines(L!2, M!1))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(L!2, M!1)) | convergent_lines(L!2, M!1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (~distinct_lines(L!2, M!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[67, 64, 54])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.45 tff(74,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.45 tff(77,plain,(
% 0.20/0.45 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[76])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (~convergent_lines(M!1, L!2)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[81, 78, 68, 29])).
% 0.20/0.45 tff(83,assumption,(~distinct_lines(N!0, L!2)), introduced(assumption)).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))) | (parallel_lines(M!1, N!0) <=> (~convergent_lines(M!1, N!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (parallel_lines(M!1, N!0) <=> (~convergent_lines(M!1, N!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[84, 36])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (~parallel_lines(M!1, N!0)),
% 0.20/0.45 inference(or_elim,[status(thm)],[49])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 ((~(parallel_lines(M!1, N!0) <=> (~convergent_lines(M!1, N!0)))) | parallel_lines(M!1, N!0) | convergent_lines(M!1, N!0)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 ((~(parallel_lines(M!1, N!0) <=> (~convergent_lines(M!1, N!0)))) | convergent_lines(M!1, N!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (convergent_lines(M!1, N!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[88, 85])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 ((distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0))) <=> ((~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2))),
% 0.20/0.46 inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | distinct_lines(N!0, L!2) | convergent_lines(M!1, L!2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[95, 78, 89, 83, 82])).
% 0.20/0.46 tff(97,plain,(distinct_lines(N!0, L!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(N!0, L!2)) | convergent_lines(N!0, L!2))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(N!0, L!2)) | convergent_lines(N!0, L!2))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(N!0, L!2)) | convergent_lines(N!0, L!2))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(N!0, L!2)) | convergent_lines(N!0, L!2)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (convergent_lines(N!0, L!2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[100, 64, 97])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))) | (parallel_lines(L!2, N!0) <=> (~convergent_lines(L!2, N!0)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (parallel_lines(L!2, N!0) <=> (~convergent_lines(L!2, N!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[102, 36])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (parallel_lines(L!2, N!0)),
% 0.20/0.46 inference(and_elim,[status(thm)],[50])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 ((~(parallel_lines(L!2, N!0) <=> (~convergent_lines(L!2, N!0)))) | (~parallel_lines(L!2, N!0)) | (~convergent_lines(L!2, N!0))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 ((~(parallel_lines(L!2, N!0) <=> (~convergent_lines(L!2, N!0)))) | (~convergent_lines(L!2, N!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (~convergent_lines(L!2, N!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.46 tff(113,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')).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.46 tff(116,plain,(
% 0.20/0.46 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[115])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 ((convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2))) <=> (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[119])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.20/0.46 inference(transitivity,[status(thm)],[120, 118])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (convergent_lines(N!0, N!0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[123, 117, 107, 101])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(128,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.46 tff(130,plain,(
% 0.20/0.46 ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(skolemize,[status(sab)],[129])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(N!0, N!0))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[132, 131, 124])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------