TSTP Solution File: GEO231+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : GEO231+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n014.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 20:35:55 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO231+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n014.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 07:06:32 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.
% 0.19/0.43  % SZS status Theorem
% 0.19/0.43  % SZS output start Proof
% 0.19/0.43  tff(left_convergent_lines_type, type, (
% 0.19/0.43     left_convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.43  tff(tptp_fun_N_0_type, type, (
% 0.19/0.43     tptp_fun_N_0: $i)).
% 0.19/0.43  tff(tptp_fun_M_1_type, type, (
% 0.19/0.43     tptp_fun_M_1: $i)).
% 0.19/0.43  tff(reverse_line_type, type, (
% 0.19/0.43     reverse_line: $i > $i)).
% 0.19/0.43  tff(unequally_directed_lines_type, type, (
% 0.19/0.43     unequally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.43  tff(tptp_fun_L_2_type, type, (
% 0.19/0.43     tptp_fun_L_2: $i)).
% 0.19/0.43  tff(1,plain,
% 0.19/0.43      (^[L: $i, M: $i] : refl((~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))))),
% 0.19/0.43      inference(bind,[status(th)],[])).
% 0.19/0.43  tff(2,plain,
% 0.19/0.43      (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.43      inference(quant_intro,[status(thm)],[1])).
% 0.19/0.43  tff(3,plain,
% 0.19/0.43      (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.43      inference(rewrite,[status(thm)],[])).
% 0.19/0.43  tff(4,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag11')).
% 0.19/0.43  tff(5,plain,
% 0.19/0.43      (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.43      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.43  tff(6,plain,(
% 0.19/0.43      ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.43      inference(skolemize,[status(sab)],[5])).
% 0.19/0.43  tff(7,plain,
% 0.19/0.43      (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.43      inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.43  tff(8,plain,
% 0.19/0.43      ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(M!1, N!0) | left_convergent_lines(M!1, reverse_line(N!0))))),
% 0.19/0.43      inference(quant_inst,[status(thm)],[])).
% 0.19/0.43  tff(9,plain,
% 0.19/0.43      (~(left_convergent_lines(M!1, N!0) | left_convergent_lines(M!1, reverse_line(N!0)))),
% 0.19/0.43      inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.43  tff(10,plain,
% 0.19/0.43      ((left_convergent_lines(M!1, N!0) | left_convergent_lines(M!1, reverse_line(N!0))) | (~left_convergent_lines(M!1, N!0))),
% 0.19/0.43      inference(tautology,[status(thm)],[])).
% 0.19/0.43  tff(11,plain,
% 0.19/0.43      (~left_convergent_lines(M!1, N!0)),
% 0.19/0.43      inference(unit_resolution,[status(thm)],[10, 9])).
% 0.19/0.43  tff(12,plain,
% 0.19/0.43      ((left_convergent_lines(M!1, N!0) | left_convergent_lines(M!1, reverse_line(N!0))) | (~left_convergent_lines(M!1, reverse_line(N!0)))),
% 0.19/0.43      inference(tautology,[status(thm)],[])).
% 0.19/0.43  tff(13,plain,
% 0.19/0.43      (~left_convergent_lines(M!1, reverse_line(N!0))),
% 0.19/0.43      inference(unit_resolution,[status(thm)],[12, 9])).
% 0.19/0.43  tff(14,assumption,(~unequally_directed_lines(M!1, N!0)), introduced(assumption)).
% 0.19/0.43  tff(15,plain,
% 0.19/0.43      (^[L: $i, M: $i, N: $i] : refl((unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))))),
% 0.19/0.43      inference(bind,[status(th)],[])).
% 0.19/0.43  tff(16,plain,
% 0.19/0.43      (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.43      inference(quant_intro,[status(thm)],[15])).
% 0.19/0.43  tff(17,plain,
% 0.19/0.43      (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.43      inference(rewrite,[status(thm)],[])).
% 0.19/0.43  tff(18,plain,
% 0.19/0.43      (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(L, N) | unequally_directed_lines(M, N)) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))))), rewrite((unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))))),
% 0.19/0.44      inference(bind,[status(th)],[])).
% 0.19/0.44  tff(19,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.44      inference(quant_intro,[status(thm)],[18])).
% 0.19/0.44  tff(20,axiom,(![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag6')).
% 0.19/0.44  tff(21,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.44  tff(22,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.44  tff(23,plain,(
% 0.19/0.44      ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.44      inference(skolemize,[status(sab)],[22])).
% 0.19/0.44  tff(24,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.44  tff(25,plain,
% 0.19/0.44      (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, M!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, M!1)))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(26,plain,
% 0.19/0.44      ((unequally_directed_lines(M!1, N!0) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, M!1))) <=> (unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, M!1)))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(27,plain,
% 0.19/0.44      (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, N!0) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, M!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, M!1))))),
% 0.19/0.44      inference(monotonicity,[status(thm)],[26])).
% 0.19/0.44  tff(28,plain,
% 0.19/0.44      (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, N!0) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, M!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, M!1)))),
% 0.19/0.44      inference(transitivity,[status(thm)],[27, 25])).
% 0.19/0.44  tff(29,plain,
% 0.19/0.44      ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, N!0) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, M!1)))),
% 0.19/0.44      inference(quant_inst,[status(thm)],[])).
% 0.19/0.44  tff(30,plain,
% 0.19/0.44      ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, M!1))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.44  tff(31,plain,
% 0.19/0.44      (~unequally_directed_lines(M!1, M!1)),
% 0.19/0.44      inference(unit_resolution,[status(thm)],[30, 24, 14])).
% 0.19/0.44  tff(32,assumption,(~unequally_directed_lines(reverse_line(N!0), M!1)), introduced(assumption)).
% 0.19/0.44  tff(33,assumption,(~unequally_directed_lines(M!1, M!1)), introduced(assumption)).
% 0.19/0.44  tff(34,plain,
% 0.19/0.44      ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))) <=> (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N))))))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(35,plain,
% 0.19/0.44      ((~![L: $i, M: $i, N: $i] : (((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N))) => (~unequally_directed_lines(M, reverse_line(N))))) <=> (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N))))))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(36,axiom,(~![L: $i, M: $i, N: $i] : (((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N))) => (~unequally_directed_lines(M, reverse_line(N))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.44  tff(37,plain,
% 0.19/0.44      (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.44  tff(38,plain,
% 0.19/0.44      (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[37, 34])).
% 0.19/0.44  tff(39,plain,
% 0.19/0.44      (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.44  tff(40,plain,
% 0.19/0.44      (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[39, 34])).
% 0.19/0.44  tff(41,plain,
% 0.19/0.44      (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[40, 34])).
% 0.19/0.44  tff(42,plain,
% 0.19/0.44      (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.44  tff(43,plain,
% 0.19/0.44      (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[42, 34])).
% 0.19/0.44  tff(44,plain,(
% 0.19/0.44      ~((~unequally_directed_lines(M!1, reverse_line(N!0))) | (~((~unequally_directed_lines(L!2, reverse_line(M!1))) & (~unequally_directed_lines(L!2, N!0)))))),
% 0.19/0.44      inference(skolemize,[status(sab)],[43])).
% 0.19/0.44  tff(45,plain,
% 0.19/0.44      (unequally_directed_lines(M!1, reverse_line(N!0))),
% 0.19/0.44      inference(or_elim,[status(thm)],[44])).
% 0.19/0.44  tff(46,plain,
% 0.19/0.44      (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(47,plain,
% 0.19/0.44      ((unequally_directed_lines(reverse_line(N!0), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(N!0)))) <=> ((~unequally_directed_lines(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(48,plain,
% 0.19/0.44      (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(N!0), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1)))),
% 0.19/0.44      inference(monotonicity,[status(thm)],[47])).
% 0.19/0.44  tff(49,plain,
% 0.19/0.44      (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(N!0), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1))),
% 0.19/0.44      inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.44  tff(50,plain,
% 0.19/0.44      ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(N!0), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(N!0))))),
% 0.19/0.44      inference(quant_inst,[status(thm)],[])).
% 0.19/0.44  tff(51,plain,
% 0.19/0.44      ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1)),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.44  tff(52,plain,
% 0.19/0.44      ($false),
% 0.19/0.44      inference(unit_resolution,[status(thm)],[51, 24, 45, 33, 32])).
% 0.19/0.44  tff(53,plain,(unequally_directed_lines(reverse_line(N!0), M!1) | unequally_directed_lines(M!1, M!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44  tff(54,plain,
% 0.19/0.44      (unequally_directed_lines(reverse_line(N!0), M!1)),
% 0.19/0.44      inference(unit_resolution,[status(thm)],[53, 31])).
% 0.19/0.44  tff(55,plain,
% 0.19/0.44      (((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0)))) | unequally_directed_lines(M!1, N!0)),
% 0.19/0.44      inference(tautology,[status(thm)],[])).
% 0.19/0.44  tff(56,plain,
% 0.19/0.44      ((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0)))),
% 0.19/0.44      inference(unit_resolution,[status(thm)],[55, 14])).
% 0.19/0.44  tff(57,assumption,(unequally_directed_lines(reverse_line(N!0), M!1)), introduced(assumption)).
% 0.19/0.44  tff(58,assumption,(unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))), introduced(assumption)).
% 0.19/0.44  tff(59,plain,
% 0.19/0.44      (^[L: $i] : refl((~unequally_directed_lines(L, L)) <=> (~unequally_directed_lines(L, L)))),
% 0.19/0.44      inference(bind,[status(th)],[])).
% 0.19/0.44  tff(60,plain,
% 0.19/0.44      (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.19/0.44      inference(quant_intro,[status(thm)],[59])).
% 0.19/0.44  tff(61,plain,
% 0.19/0.44      (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(62,axiom,(![L: $i] : (~unequally_directed_lines(L, L))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag5')).
% 0.19/0.44  tff(63,plain,
% 0.19/0.44      (![L: $i] : (~unequally_directed_lines(L, L))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.44  tff(64,plain,(
% 0.19/0.44      ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.19/0.44      inference(skolemize,[status(sab)],[63])).
% 0.19/0.44  tff(65,plain,
% 0.19/0.44      (![L: $i] : (~unequally_directed_lines(L, L))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.44  tff(66,plain,
% 0.19/0.44      ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0)))),
% 0.19/0.44      inference(quant_inst,[status(thm)],[])).
% 0.19/0.44  tff(67,plain,
% 0.19/0.44      ($false),
% 0.19/0.44      inference(unit_resolution,[status(thm)],[66, 65, 58])).
% 0.19/0.44  tff(68,plain,(~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44  tff(69,plain,
% 0.19/0.44      (((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0)))) | unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))),
% 0.19/0.44      inference(tautology,[status(thm)],[])).
% 0.19/0.44  tff(70,plain,
% 0.19/0.44      ((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0)))),
% 0.19/0.44      inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.44  tff(71,assumption,(unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))), introduced(assumption)).
% 0.19/0.44  tff(72,assumption,((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0)))), introduced(assumption)).
% 0.19/0.44  tff(73,plain,
% 0.19/0.44      (^[L: $i, M: $i, N: $i] : refl(((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))) <=> ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))))),
% 0.19/0.44      inference(bind,[status(th)],[])).
% 0.19/0.44  tff(74,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))),
% 0.19/0.44      inference(quant_intro,[status(thm)],[73])).
% 0.19/0.44  tff(75,plain,
% 0.19/0.44      (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) <=> (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N)))))), rewrite((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) <=> (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))), trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite(((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))))),
% 0.19/0.44      inference(bind,[status(th)],[])).
% 0.19/0.44  tff(76,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))),
% 0.19/0.44      inference(quant_intro,[status(thm)],[75])).
% 0.19/0.44  tff(77,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(78,plain,
% 0.19/0.44      (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite(((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))))), rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))))),
% 0.19/0.44      inference(bind,[status(th)],[])).
% 0.19/0.44  tff(79,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.44      inference(quant_intro,[status(thm)],[78])).
% 0.19/0.44  tff(80,axiom,(![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag7')).
% 0.19/0.44  tff(81,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.44  tff(82,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.44  tff(83,plain,(
% 0.19/0.44      ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.44      inference(skolemize,[status(sab)],[82])).
% 0.19/0.44  tff(84,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[83, 76])).
% 0.19/0.44  tff(85,plain,
% 0.19/0.44      (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[84, 74])).
% 0.19/0.44  tff(86,plain,
% 0.19/0.44      (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | ((~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), M!1)))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), M!1)))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(87,plain,
% 0.19/0.44      (((~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~unequally_directed_lines(reverse_line(N!0), M!1)) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0)))))) <=> ((~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), M!1)))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(88,plain,
% 0.19/0.44      (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | ((~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~unequally_directed_lines(reverse_line(N!0), M!1)) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | ((~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), M!1))))),
% 0.19/0.44      inference(monotonicity,[status(thm)],[87])).
% 0.19/0.44  tff(89,plain,
% 0.19/0.44      (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | ((~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~unequally_directed_lines(reverse_line(N!0), M!1)) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), M!1)))),
% 0.19/0.44      inference(transitivity,[status(thm)],[88, 86])).
% 0.19/0.44  tff(90,plain,
% 0.19/0.44      ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | ((~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~unequally_directed_lines(reverse_line(N!0), M!1)) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))))))),
% 0.19/0.44      inference(quant_inst,[status(thm)],[])).
% 0.19/0.44  tff(91,plain,
% 0.19/0.44      ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~((~unequally_directed_lines(reverse_line(N!0), N!0)) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), M!1))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.44  tff(92,plain,
% 0.19/0.44      ($false),
% 0.19/0.44      inference(unit_resolution,[status(thm)],[91, 85, 72, 71, 70, 57])).
% 0.19/0.44  tff(93,plain,((~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(reverse_line(N!0), M!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44  tff(94,plain,
% 0.19/0.44      (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))),
% 0.19/0.44      inference(unit_resolution,[status(thm)],[93, 56, 54])).
% 0.19/0.44  tff(95,plain,
% 0.19/0.44      ((~unequally_directed_lines(L!2, reverse_line(M!1))) & (~unequally_directed_lines(L!2, N!0))),
% 0.19/0.44      inference(or_elim,[status(thm)],[44])).
% 0.19/0.44  tff(96,plain,
% 0.19/0.44      (~unequally_directed_lines(L!2, reverse_line(M!1))),
% 0.19/0.44      inference(and_elim,[status(thm)],[95])).
% 0.19/0.44  tff(97,plain,
% 0.19/0.44      (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, reverse_line(M!1)) | unequally_directed_lines(reverse_line(N!0), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(N!0), L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, reverse_line(M!1)) | unequally_directed_lines(reverse_line(N!0), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(N!0), L!2)))),
% 0.19/0.44      inference(rewrite,[status(thm)],[])).
% 0.19/0.44  tff(98,plain,
% 0.19/0.44      ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, reverse_line(M!1)) | unequally_directed_lines(reverse_line(N!0), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(N!0), L!2)))),
% 0.19/0.44      inference(quant_inst,[status(thm)],[])).
% 0.19/0.44  tff(99,plain,
% 0.19/0.44      ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, reverse_line(M!1)) | unequally_directed_lines(reverse_line(N!0), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(N!0), L!2))),
% 0.19/0.44      inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.44  tff(100,plain,
% 0.19/0.44      (~unequally_directed_lines(reverse_line(N!0), L!2)),
% 0.19/0.44      inference(unit_resolution,[status(thm)],[99, 24, 96, 94])).
% 0.19/0.44  tff(101,plain,
% 0.19/0.44      (~unequally_directed_lines(L!2, N!0)),
% 0.19/0.44      inference(and_elim,[status(thm)],[95])).
% 0.19/0.44  tff(102,plain,
% 0.19/0.44      (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, L!2)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, L!2)))),
% 0.19/0.45      inference(rewrite,[status(thm)],[])).
% 0.19/0.45  tff(103,plain,
% 0.19/0.45      ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, L!2)))),
% 0.19/0.45      inference(quant_inst,[status(thm)],[])).
% 0.19/0.45  tff(104,plain,
% 0.19/0.45      ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, L!2))),
% 0.19/0.45      inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.45  tff(105,plain,
% 0.19/0.45      (~unequally_directed_lines(M!1, L!2)),
% 0.19/0.45      inference(unit_resolution,[status(thm)],[104, 24, 101, 14])).
% 0.19/0.45  tff(106,plain,
% 0.19/0.45      (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, L!2) | (~unequally_directed_lines(reverse_line(N!0), M!1)) | unequally_directed_lines(reverse_line(N!0), L!2))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(M!1, L!2) | (~unequally_directed_lines(reverse_line(N!0), M!1)) | unequally_directed_lines(reverse_line(N!0), L!2))),
% 0.19/0.45      inference(rewrite,[status(thm)],[])).
% 0.19/0.45  tff(107,plain,
% 0.19/0.45      ((unequally_directed_lines(M!1, L!2) | unequally_directed_lines(reverse_line(N!0), L!2) | (~unequally_directed_lines(reverse_line(N!0), M!1))) <=> (unequally_directed_lines(M!1, L!2) | (~unequally_directed_lines(reverse_line(N!0), M!1)) | unequally_directed_lines(reverse_line(N!0), L!2))),
% 0.19/0.45      inference(rewrite,[status(thm)],[])).
% 0.19/0.45  tff(108,plain,
% 0.19/0.45      (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, L!2) | unequally_directed_lines(reverse_line(N!0), L!2) | (~unequally_directed_lines(reverse_line(N!0), M!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, L!2) | (~unequally_directed_lines(reverse_line(N!0), M!1)) | unequally_directed_lines(reverse_line(N!0), L!2)))),
% 0.19/0.45      inference(monotonicity,[status(thm)],[107])).
% 0.19/0.45  tff(109,plain,
% 0.19/0.45      (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, L!2) | unequally_directed_lines(reverse_line(N!0), L!2) | (~unequally_directed_lines(reverse_line(N!0), M!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(M!1, L!2) | (~unequally_directed_lines(reverse_line(N!0), M!1)) | unequally_directed_lines(reverse_line(N!0), L!2))),
% 0.19/0.45      inference(transitivity,[status(thm)],[108, 106])).
% 0.19/0.45  tff(110,plain,
% 0.19/0.45      ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, L!2) | unequally_directed_lines(reverse_line(N!0), L!2) | (~unequally_directed_lines(reverse_line(N!0), M!1)))),
% 0.19/0.45      inference(quant_inst,[status(thm)],[])).
% 0.19/0.45  tff(111,plain,
% 0.19/0.45      ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(M!1, L!2) | (~unequally_directed_lines(reverse_line(N!0), M!1)) | unequally_directed_lines(reverse_line(N!0), L!2)),
% 0.19/0.45      inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.45  tff(112,plain,
% 0.19/0.45      ($false),
% 0.19/0.45      inference(unit_resolution,[status(thm)],[111, 24, 105, 54, 100])).
% 0.19/0.45  tff(113,plain,(unequally_directed_lines(M!1, N!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45  tff(114,plain,
% 0.19/0.45      (^[L: $i, M: $i] : refl((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M))))),
% 0.19/0.45      inference(bind,[status(th)],[])).
% 0.19/0.45  tff(115,plain,
% 0.19/0.45      (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))),
% 0.19/0.45      inference(quant_intro,[status(thm)],[114])).
% 0.19/0.45  tff(116,plain,
% 0.19/0.45      (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))))),
% 0.19/0.45      inference(bind,[status(th)],[])).
% 0.19/0.45  tff(117,plain,
% 0.19/0.45      (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))),
% 0.19/0.45      inference(quant_intro,[status(thm)],[116])).
% 0.19/0.45  tff(118,plain,
% 0.19/0.45      (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.45      inference(rewrite,[status(thm)],[])).
% 0.19/0.45  tff(119,plain,
% 0.19/0.45      (^[L: $i, M: $i] : rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))))),
% 0.19/0.45      inference(bind,[status(th)],[])).
% 0.19/0.45  tff(120,plain,
% 0.19/0.45      (![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.45      inference(quant_intro,[status(thm)],[119])).
% 0.19/0.45  tff(121,axiom,(![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag9')).
% 0.19/0.45  tff(122,plain,
% 0.19/0.45      (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.45      inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.45  tff(123,plain,
% 0.19/0.45      (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.45      inference(modus_ponens,[status(thm)],[122, 118])).
% 0.19/0.45  tff(124,plain,(
% 0.19/0.45      ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.45      inference(skolemize,[status(sab)],[123])).
% 0.19/0.45  tff(125,plain,
% 0.19/0.45      (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))),
% 0.19/0.45      inference(modus_ponens,[status(thm)],[124, 117])).
% 0.19/0.45  tff(126,plain,
% 0.19/0.45      (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))),
% 0.19/0.45      inference(modus_ponens,[status(thm)],[125, 115])).
% 0.19/0.45  tff(127,plain,
% 0.19/0.45      (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0))),
% 0.19/0.45      inference(rewrite,[status(thm)],[])).
% 0.19/0.45  tff(128,plain,
% 0.19/0.45      ((left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0))) <=> ((~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0))),
% 0.19/0.45      inference(rewrite,[status(thm)],[])).
% 0.19/0.45  tff(129,plain,
% 0.19/0.45      (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0)))),
% 0.19/0.45      inference(monotonicity,[status(thm)],[128])).
% 0.19/0.45  tff(130,plain,
% 0.19/0.45      (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0))),
% 0.19/0.45      inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.45  tff(131,plain,
% 0.19/0.45      ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)))),
% 0.19/0.45      inference(quant_inst,[status(thm)],[])).
% 0.19/0.45  tff(132,plain,
% 0.19/0.45      ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0)),
% 0.19/0.45      inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.45  tff(133,plain,
% 0.19/0.45      ((~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0)),
% 0.19/0.45      inference(unit_resolution,[status(thm)],[132, 126, 45])).
% 0.19/0.45  tff(134,plain,
% 0.19/0.45      (left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0)),
% 0.19/0.45      inference(unit_resolution,[status(thm)],[133, 113])).
% 0.19/0.45  tff(135,plain,
% 0.19/0.45      ($false),
% 0.19/0.45      inference(unit_resolution,[status(thm)],[134, 13, 11])).
% 0.19/0.45  % SZS output end Proof
%------------------------------------------------------------------------------