TSTP Solution File: GEO218+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO218+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 0.12s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % 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 07:22:03 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.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(convergent_lines_type, type, (
% 0.12/0.40 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_M_1_type, type, (
% 0.12/0.40 tptp_fun_M_1: $i)).
% 0.12/0.40 tff(tptp_fun_N_0_type, type, (
% 0.12/0.40 tptp_fun_N_0: $i)).
% 0.12/0.40 tff(unorthogonal_lines_type, type, (
% 0.12/0.40 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_L_2_type, type, (
% 0.12/0.40 tptp_fun_L_2: $i)).
% 0.12/0.40 tff(parallel_lines_type, type, (
% 0.12/0.40 parallel_lines: ( $i * $i ) > $o)).
% 0.12/0.40 tff(orthogonal_lines_type, type, (
% 0.12/0.40 orthogonal_lines: ( $i * $i ) > $o)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[X: $i, Y: $i] : refl((parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(4,axiom,(![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a3')).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.40 tff(6,plain,(
% 0.12/0.40 ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[5])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))) | (parallel_lines(L!2, M!1) <=> (~convergent_lines(L!2, M!1)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (parallel_lines(L!2, M!1) <=> (~convergent_lines(L!2, M!1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 ((~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & orthogonal_lines(L, N))) | orthogonal_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & orthogonal_lines(L, N))) | orthogonal_lines(M, N)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 ((~![L: $i, M: $i, N: $i] : ((parallel_lines(L, M) & orthogonal_lines(L, N)) => orthogonal_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & orthogonal_lines(L, N))) | orthogonal_lines(M, N)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(12,axiom,(~![L: $i, M: $i, N: $i] : ((parallel_lines(L, M) & orthogonal_lines(L, N)) => orthogonal_lines(M, N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & orthogonal_lines(L, N))) | orthogonal_lines(M, N))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & orthogonal_lines(L, N))) | orthogonal_lines(M, N))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & orthogonal_lines(L, N))) | orthogonal_lines(M, N))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & orthogonal_lines(L, N))) | orthogonal_lines(M, N))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & orthogonal_lines(L, N))) | orthogonal_lines(M, N))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & orthogonal_lines(L, N))) | orthogonal_lines(M, N))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (~![L: $i, M: $i, N: $i] : ((~(parallel_lines(L, M) & orthogonal_lines(L, N))) | orthogonal_lines(M, N))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.12/0.40 tff(20,plain,(
% 0.12/0.40 ~((~(parallel_lines(L!2, M!1) & orthogonal_lines(L!2, N!0))) | orthogonal_lines(M!1, N!0))),
% 0.12/0.40 inference(skolemize,[status(sab)],[19])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (parallel_lines(L!2, M!1) & orthogonal_lines(L!2, N!0)),
% 0.12/0.40 inference(or_elim,[status(thm)],[20])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (parallel_lines(L!2, M!1)),
% 0.12/0.40 inference(and_elim,[status(thm)],[21])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 ((~(parallel_lines(L!2, M!1) <=> (~convergent_lines(L!2, M!1)))) | (~parallel_lines(L!2, M!1)) | (~convergent_lines(L!2, M!1))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 ((~(parallel_lines(L!2, M!1) <=> (~convergent_lines(L!2, M!1)))) | (~convergent_lines(L!2, M!1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (~convergent_lines(L!2, M!1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[24, 9])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))) | convergent_lines(L!2, M!1)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 ((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (^[X: $i, Y: $i] : refl((orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(31,axiom,(![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a5')).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.40 tff(33,plain,(
% 0.12/0.40 ![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[32])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))) | (orthogonal_lines(L!2, N!0) <=> (~unorthogonal_lines(L!2, N!0)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (orthogonal_lines(L!2, N!0) <=> (~unorthogonal_lines(L!2, N!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (orthogonal_lines(L!2, N!0)),
% 0.12/0.40 inference(and_elim,[status(thm)],[21])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((~(orthogonal_lines(L!2, N!0) <=> (~unorthogonal_lines(L!2, N!0)))) | (~orthogonal_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 ((~(orthogonal_lines(L!2, N!0) <=> (~unorthogonal_lines(L!2, N!0)))) | (~unorthogonal_lines(L!2, N!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (~unorthogonal_lines(L!2, N!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))) | unorthogonal_lines(L!2, N!0)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 ((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))) | (orthogonal_lines(M!1, N!0) <=> (~unorthogonal_lines(M!1, N!0)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (orthogonal_lines(M!1, N!0) <=> (~unorthogonal_lines(M!1, N!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[43, 34])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (~orthogonal_lines(M!1, N!0)),
% 0.12/0.40 inference(or_elim,[status(thm)],[20])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 ((~(orthogonal_lines(M!1, N!0) <=> (~unorthogonal_lines(M!1, N!0)))) | orthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 ((~(orthogonal_lines(M!1, N!0) <=> (~unorthogonal_lines(M!1, N!0)))) | unorthogonal_lines(M!1, N!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (unorthogonal_lines(M!1, N!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (^[L: $i, M: $i, N: $i] : refl(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) <=> (~((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> (~(~((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))))), rewrite((~(~((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))) <=> ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))))), rewrite(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (^[L: $i, M: $i, N: $i] : rewrite(((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![L: $i, M: $i, N: $i] : ((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.12/0.40 tff(56,axiom,(![L: $i, M: $i, N: $i] : ((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax','cotno1')).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.12/0.40 tff(59,plain,(
% 0.12/0.40 ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[58])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (~convergent_lines(M!1, N!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[64, 61, 48, 42, 27])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (![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)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (^[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))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 (![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)))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.12/0.40 tff(73,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')).
% 0.12/0.41 tff(74,plain,
% 0.12/0.41 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.12/0.41 tff(75,plain,
% 0.12/0.41 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.12/0.41 tff(76,plain,(
% 0.12/0.41 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[75])).
% 0.12/0.41 tff(77,plain,
% 0.12/0.41 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.12/0.41 tff(78,plain,
% 0.12/0.41 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.12/0.41 tff(79,plain,
% 0.12/0.41 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(80,plain,
% 0.12/0.41 ((unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0))) <=> (unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(81,plain,
% 0.12/0.41 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[80])).
% 0.12/0.41 tff(82,plain,
% 0.12/0.41 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[81, 79])).
% 0.12/0.41 tff(83,plain,
% 0.12/0.41 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(84,plain,
% 0.12/0.41 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.12/0.41 tff(85,plain,
% 0.12/0.41 (~convergent_lines(N!0, N!0)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[84, 78, 40])).
% 0.12/0.41 tff(86,plain,
% 0.12/0.41 (^[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))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(87,plain,
% 0.12/0.41 (![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)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.12/0.41 tff(88,plain,
% 0.12/0.41 (![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)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(89,plain,
% 0.12/0.41 (^[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)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(90,plain,
% 0.12/0.41 (![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)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.12/0.41 tff(91,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')).
% 0.12/0.41 tff(92,plain,
% 0.12/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.12/0.41 tff(93,plain,
% 0.12/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.12/0.41 tff(94,plain,(
% 0.12/0.41 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[93])).
% 0.12/0.41 tff(95,plain,
% 0.12/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.12/0.41 tff(96,plain,
% 0.12/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(N!0, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(N!0, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(N!0, M!1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(97,plain,
% 0.12/0.41 ((convergent_lines(M!1, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, M!1))) <=> (convergent_lines(N!0, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(N!0, M!1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(98,plain,
% 0.12/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(N!0, M!1))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[97])).
% 0.12/0.41 tff(99,plain,
% 0.12/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(N!0, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(N!0, M!1)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[98, 96])).
% 0.12/0.41 tff(100,plain,
% 0.12/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, M!1)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(101,plain,
% 0.12/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(N!0, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(N!0, M!1))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.12/0.41 tff(102,plain,
% 0.12/0.41 (~convergent_lines(N!0, M!1)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[101, 95, 85, 65])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(106,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.41 tff(108,plain,(
% 0.20/0.41 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(skolemize,[status(sab)],[107])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (convergent_lines(L!2, N!0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[112, 109, 40])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, M!1) | convergent_lines(N!0, M!1) | (~convergent_lines(L!2, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, M!1) | convergent_lines(N!0, M!1) | (~convergent_lines(L!2, N!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((convergent_lines(N!0, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0))) <=> (convergent_lines(L!2, M!1) | convergent_lines(N!0, M!1) | (~convergent_lines(L!2, N!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, M!1) | convergent_lines(N!0, M!1) | (~convergent_lines(L!2, N!0))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, M!1) | convergent_lines(N!0, M!1) | (~convergent_lines(L!2, N!0)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, M!1) | convergent_lines(N!0, M!1) | (~convergent_lines(L!2, N!0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[119, 95, 25, 113, 102])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------