TSTP Solution File: GEO212+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO212+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:35:43 EDT 2022
% Result : Theorem 0.16s 0.48s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GEO212+2 : TPTP v8.1.0. Released v3.3.0.
% 0.02/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n004.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 31 06:54:19 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.16/0.48 % SZS status Theorem
% 0.16/0.48 % SZS output start Proof
% 0.16/0.48 tff(convergent_lines_type, type, (
% 0.16/0.48 convergent_lines: ( $i * $i ) > $o)).
% 0.16/0.48 tff(tptp_fun_M_1_type, type, (
% 0.16/0.48 tptp_fun_M_1: $i)).
% 0.16/0.48 tff(tptp_fun_L_2_type, type, (
% 0.16/0.48 tptp_fun_L_2: $i)).
% 0.16/0.48 tff(distinct_lines_type, type, (
% 0.16/0.48 distinct_lines: ( $i * $i ) > $o)).
% 0.16/0.48 tff(tptp_fun_N_0_type, type, (
% 0.16/0.48 tptp_fun_N_0: $i)).
% 0.16/0.48 tff(unorthogonal_lines_type, type, (
% 0.16/0.48 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.16/0.48 tff(1,assumption,(distinct_lines(M!1, M!1)), introduced(assumption)).
% 0.16/0.48 tff(2,plain,
% 0.16/0.48 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.16/0.48 inference(bind,[status(th)],[])).
% 0.16/0.48 tff(3,plain,
% 0.16/0.48 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.16/0.48 inference(quant_intro,[status(thm)],[2])).
% 0.16/0.48 tff(4,plain,
% 0.16/0.48 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.16/0.48 inference(rewrite,[status(thm)],[])).
% 0.16/0.48 tff(5,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.16/0.48 tff(6,plain,
% 0.16/0.48 (![X: $i] : (~distinct_lines(X, X))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.16/0.48 tff(7,plain,(
% 0.16/0.48 ![X: $i] : (~distinct_lines(X, X))),
% 0.16/0.48 inference(skolemize,[status(sab)],[6])).
% 0.16/0.48 tff(8,plain,
% 0.16/0.48 (![X: $i] : (~distinct_lines(X, X))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.16/0.48 tff(9,plain,
% 0.16/0.48 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(M!1, M!1))),
% 0.16/0.48 inference(quant_inst,[status(thm)],[])).
% 0.16/0.48 tff(10,plain,
% 0.16/0.48 ($false),
% 0.16/0.48 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.16/0.48 tff(11,plain,(~distinct_lines(M!1, M!1)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.48 tff(12,plain,
% 0.16/0.48 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.16/0.48 inference(bind,[status(th)],[])).
% 0.16/0.48 tff(13,plain,
% 0.16/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.48 inference(quant_intro,[status(thm)],[12])).
% 0.16/0.48 tff(14,plain,
% 0.16/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.48 inference(rewrite,[status(thm)],[])).
% 0.16/0.48 tff(15,plain,
% 0.16/0.48 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.16/0.48 inference(bind,[status(th)],[])).
% 0.16/0.48 tff(16,plain,
% 0.16/0.48 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.48 inference(quant_intro,[status(thm)],[15])).
% 0.16/0.48 tff(17,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.16/0.48 tff(18,plain,
% 0.16/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.16/0.48 tff(19,plain,
% 0.16/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.16/0.48 tff(20,plain,(
% 0.16/0.48 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.48 inference(skolemize,[status(sab)],[19])).
% 0.16/0.48 tff(21,plain,
% 0.16/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.16/0.48 tff(22,plain,
% 0.16/0.48 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(M!1, M!1)) | distinct_lines(M!1, M!1))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(M!1, M!1)) | distinct_lines(M!1, M!1))),
% 0.16/0.48 inference(rewrite,[status(thm)],[])).
% 0.16/0.48 tff(23,plain,
% 0.16/0.48 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(M!1, M!1)) | distinct_lines(M!1, M!1))),
% 0.16/0.48 inference(quant_inst,[status(thm)],[])).
% 0.16/0.48 tff(24,plain,
% 0.16/0.48 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(M!1, M!1)) | distinct_lines(M!1, M!1)),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.16/0.48 tff(25,plain,
% 0.16/0.48 (~convergent_lines(M!1, M!1)),
% 0.16/0.48 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.16/0.48 tff(26,assumption,(convergent_lines(N!0, N!0)), introduced(assumption)).
% 0.16/0.48 tff(27,plain,
% 0.16/0.48 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.16/0.48 inference(bind,[status(th)],[])).
% 0.16/0.48 tff(28,plain,
% 0.16/0.48 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.16/0.48 inference(quant_intro,[status(thm)],[27])).
% 0.16/0.48 tff(29,plain,
% 0.16/0.48 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.16/0.48 inference(rewrite,[status(thm)],[])).
% 0.16/0.48 tff(30,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart3')).
% 0.16/0.48 tff(31,plain,
% 0.16/0.48 (![X: $i] : (~convergent_lines(X, X))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.16/0.48 tff(32,plain,(
% 0.16/0.48 ![X: $i] : (~convergent_lines(X, X))),
% 0.16/0.48 inference(skolemize,[status(sab)],[31])).
% 0.16/0.48 tff(33,plain,
% 0.16/0.48 (![X: $i] : (~convergent_lines(X, X))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.16/0.48 tff(34,plain,
% 0.16/0.48 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(N!0, N!0))),
% 0.16/0.48 inference(quant_inst,[status(thm)],[])).
% 0.16/0.48 tff(35,plain,
% 0.16/0.48 ($false),
% 0.16/0.48 inference(unit_resolution,[status(thm)],[34, 33, 26])).
% 0.16/0.48 tff(36,plain,(~convergent_lines(N!0, N!0)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.48 tff(37,plain,
% 0.16/0.48 ((~(convergent_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))) <=> (~(convergent_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1))))),
% 0.16/0.48 inference(rewrite,[status(thm)],[])).
% 0.16/0.48 tff(38,plain,
% 0.16/0.48 ((~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))) <=> (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M))))),
% 0.16/0.48 inference(rewrite,[status(thm)],[])).
% 0.16/0.48 tff(39,plain,
% 0.16/0.48 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, M) => (convergent_lines(L, N) | unorthogonal_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M))))),
% 0.16/0.48 inference(rewrite,[status(thm)],[])).
% 0.16/0.48 tff(40,axiom,(~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, M) => (convergent_lines(L, N) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.16/0.48 tff(41,plain,
% 0.16/0.48 (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.16/0.48 tff(42,plain,
% 0.16/0.48 (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.16/0.48 tff(43,plain,
% 0.16/0.48 (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.16/0.48 tff(44,plain,
% 0.16/0.48 (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.16/0.48 tff(45,plain,
% 0.16/0.48 (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[44, 38])).
% 0.16/0.48 tff(46,plain,
% 0.16/0.48 (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.16/0.48 tff(47,plain,
% 0.16/0.48 (~![L: $i, M: $i, N: $i] : (convergent_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[46, 38])).
% 0.16/0.48 tff(48,plain,(
% 0.16/0.48 ~(convergent_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))),
% 0.16/0.48 inference(skolemize,[status(sab)],[47])).
% 0.16/0.48 tff(49,plain,
% 0.16/0.48 (~(convergent_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))),
% 0.16/0.48 inference(modus_ponens,[status(thm)],[48, 37])).
% 0.16/0.48 tff(50,plain,
% 0.16/0.48 (~convergent_lines(L!2, N!0)),
% 0.16/0.48 inference(or_elim,[status(thm)],[49])).
% 0.16/0.49 tff(51,plain,
% 0.16/0.49 (^[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))))),
% 0.16/0.49 inference(bind,[status(th)],[])).
% 0.16/0.49 tff(52,plain,
% 0.16/0.49 (![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)))),
% 0.16/0.49 inference(quant_intro,[status(thm)],[51])).
% 0.16/0.49 tff(53,plain,
% 0.16/0.49 (![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)))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(54,plain,
% 0.16/0.49 (^[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)))))),
% 0.16/0.49 inference(bind,[status(th)],[])).
% 0.16/0.49 tff(55,plain,
% 0.16/0.49 (![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)))),
% 0.16/0.49 inference(quant_intro,[status(thm)],[54])).
% 0.16/0.49 tff(56,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.16/0.49 tff(57,plain,
% 0.16/0.49 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.16/0.49 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.16/0.49 tff(58,plain,
% 0.16/0.49 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.16/0.49 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.16/0.49 tff(59,plain,(
% 0.16/0.49 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.16/0.49 inference(skolemize,[status(sab)],[58])).
% 0.16/0.49 tff(60,plain,
% 0.16/0.49 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.16/0.49 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.16/0.49 tff(61,plain,
% 0.16/0.49 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(62,plain,
% 0.16/0.49 ((convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2))) <=> (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(63,plain,
% 0.16/0.49 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0)))),
% 0.16/0.49 inference(monotonicity,[status(thm)],[62])).
% 0.16/0.49 tff(64,plain,
% 0.16/0.49 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0))),
% 0.16/0.49 inference(transitivity,[status(thm)],[63, 61])).
% 0.16/0.49 tff(65,plain,
% 0.16/0.49 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))),
% 0.16/0.49 inference(quant_inst,[status(thm)],[])).
% 0.16/0.49 tff(66,plain,
% 0.16/0.49 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | (~convergent_lines(N!0, L!2)) | convergent_lines(N!0, N!0)),
% 0.16/0.49 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.16/0.49 tff(67,plain,
% 0.16/0.49 (~convergent_lines(N!0, L!2)),
% 0.16/0.49 inference(unit_resolution,[status(thm)],[66, 60, 50, 36])).
% 0.16/0.49 tff(68,plain,
% 0.16/0.49 (~unorthogonal_lines(M!1, N!0)),
% 0.16/0.49 inference(or_elim,[status(thm)],[49])).
% 0.16/0.49 tff(69,plain,
% 0.16/0.49 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.16/0.49 inference(bind,[status(th)],[])).
% 0.16/0.49 tff(70,plain,
% 0.16/0.49 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.16/0.49 inference(quant_intro,[status(thm)],[69])).
% 0.16/0.49 tff(71,plain,
% 0.16/0.49 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(72,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.16/0.49 tff(73,plain,
% 0.16/0.49 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.16/0.49 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.16/0.49 tff(74,plain,(
% 0.16/0.49 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.16/0.49 inference(skolemize,[status(sab)],[73])).
% 0.16/0.49 tff(75,plain,
% 0.16/0.49 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.16/0.49 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.16/0.49 tff(76,plain,
% 0.16/0.49 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(77,plain,
% 0.16/0.49 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))),
% 0.16/0.49 inference(quant_inst,[status(thm)],[])).
% 0.16/0.49 tff(78,plain,
% 0.16/0.49 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0)),
% 0.16/0.49 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.16/0.49 tff(79,plain,
% 0.16/0.49 (convergent_lines(M!1, N!0)),
% 0.16/0.49 inference(unit_resolution,[status(thm)],[78, 75, 68])).
% 0.16/0.49 tff(80,plain,
% 0.16/0.49 (((~![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(M!1, L!2) | convergent_lines(N!0, L!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(81,plain,
% 0.16/0.49 ((convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0))) <=> ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(82,plain,
% 0.16/0.49 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2)))),
% 0.16/0.49 inference(monotonicity,[status(thm)],[81])).
% 0.16/0.49 tff(83,plain,
% 0.16/0.49 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.16/0.49 inference(transitivity,[status(thm)],[82, 80])).
% 0.16/0.49 tff(84,plain,
% 0.16/0.49 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.16/0.49 inference(quant_inst,[status(thm)],[])).
% 0.16/0.49 tff(85,plain,
% 0.16/0.49 ((~![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(M!1, L!2) | convergent_lines(N!0, L!2)),
% 0.16/0.49 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.16/0.49 tff(86,plain,
% 0.16/0.49 (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2)),
% 0.16/0.49 inference(unit_resolution,[status(thm)],[85, 60, 79])).
% 0.16/0.49 tff(87,plain,
% 0.16/0.49 (convergent_lines(M!1, L!2)),
% 0.16/0.49 inference(unit_resolution,[status(thm)],[86, 67])).
% 0.16/0.49 tff(88,plain,
% 0.16/0.49 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, L!2)) | convergent_lines(M!1, M!1) | convergent_lines(L!2, M!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, L!2)) | convergent_lines(M!1, M!1) | convergent_lines(L!2, M!1))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(89,plain,
% 0.16/0.49 ((convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2))) <=> ((~convergent_lines(M!1, L!2)) | convergent_lines(M!1, M!1) | convergent_lines(L!2, M!1))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(90,plain,
% 0.16/0.49 (((~![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(M!1, M!1) | (~convergent_lines(M!1, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, L!2)) | convergent_lines(M!1, M!1) | convergent_lines(L!2, M!1)))),
% 0.16/0.49 inference(monotonicity,[status(thm)],[89])).
% 0.16/0.49 tff(91,plain,
% 0.16/0.49 (((~![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(M!1, M!1) | (~convergent_lines(M!1, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, L!2)) | convergent_lines(M!1, M!1) | convergent_lines(L!2, M!1))),
% 0.16/0.49 inference(transitivity,[status(thm)],[90, 88])).
% 0.16/0.49 tff(92,plain,
% 0.16/0.49 ((~![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(M!1, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.16/0.49 inference(quant_inst,[status(thm)],[])).
% 0.16/0.49 tff(93,plain,
% 0.16/0.49 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, L!2)) | convergent_lines(M!1, M!1) | convergent_lines(L!2, M!1)),
% 0.16/0.49 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.16/0.49 tff(94,plain,
% 0.16/0.49 (convergent_lines(L!2, M!1)),
% 0.16/0.49 inference(unit_resolution,[status(thm)],[93, 60, 87, 25])).
% 0.16/0.49 tff(95,plain,
% 0.16/0.49 (((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))) | unorthogonal_lines(M!1, N!0)),
% 0.16/0.49 inference(tautology,[status(thm)],[])).
% 0.16/0.49 tff(96,plain,
% 0.16/0.49 ((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))),
% 0.16/0.49 inference(unit_resolution,[status(thm)],[95, 68])).
% 0.16/0.49 tff(97,plain,
% 0.16/0.49 (((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))) | convergent_lines(L!2, N!0)),
% 0.16/0.49 inference(tautology,[status(thm)],[])).
% 0.16/0.49 tff(98,plain,
% 0.16/0.49 ((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.16/0.49 inference(unit_resolution,[status(thm)],[97, 50])).
% 0.16/0.49 tff(99,plain,
% 0.16/0.49 (unorthogonal_lines(L!2, M!1)),
% 0.16/0.49 inference(or_elim,[status(thm)],[49])).
% 0.16/0.49 tff(100,plain,
% 0.16/0.49 (^[L: $i, M: $i, N: $i] : refl(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.16/0.49 inference(bind,[status(th)],[])).
% 0.16/0.49 tff(101,plain,
% 0.16/0.49 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.16/0.49 inference(quant_intro,[status(thm)],[100])).
% 0.16/0.49 tff(102,plain,
% 0.16/0.49 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((convergent_lines(M, N) & unorthogonal_lines(M, N)) <=> (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N))))), rewrite((convergent_lines(L, N) & unorthogonal_lines(L, N)) <=> (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))), trans(monotonicity(rewrite((convergent_lines(L, M) & unorthogonal_lines(L, M)) <=> (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> (~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), rewrite((~(~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))), ((~(convergent_lines(L, M) & unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))), (((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M)))) <=> ((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), rewrite(((~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, 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(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))), (((convergent_lines(M, N) & unorthogonal_lines(M, 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(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.16/0.49 inference(bind,[status(th)],[])).
% 0.16/0.49 tff(103,plain,
% 0.16/0.49 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_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] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.16/0.49 inference(quant_intro,[status(thm)],[102])).
% 0.16/0.49 tff(104,plain,
% 0.16/0.49 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_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] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(105,plain,
% 0.16/0.50 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite(((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (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(M, N) & unorthogonal_lines(M, N)))) <=> ((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)))))), rewrite(((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, 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(M, N) & unorthogonal_lines(M, N)))) <=> ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))))),
% 0.16/0.50 inference(bind,[status(th)],[])).
% 0.16/0.50 tff(106,plain,
% 0.16/0.50 (![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] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.16/0.50 inference(quant_intro,[status(thm)],[105])).
% 0.16/0.50 tff(107,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/sandbox/benchmark/Axioms/GEO006+3.ax','oac1')).
% 0.16/0.50 tff(108,plain,
% 0.16/0.50 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.16/0.50 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.16/0.50 tff(109,plain,
% 0.16/0.50 (![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.16/0.50 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.16/0.50 tff(110,plain,(
% 0.16/0.50 ![L: $i, M: $i, N: $i] : ((convergent_lines(M, N) & unorthogonal_lines(M, N)) | (convergent_lines(L, N) & unorthogonal_lines(L, N)) | (~(convergent_lines(L, M) & unorthogonal_lines(L, M))))),
% 0.16/0.50 inference(skolemize,[status(sab)],[109])).
% 0.16/0.50 tff(111,plain,
% 0.16/0.50 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.16/0.50 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.16/0.50 tff(112,plain,
% 0.16/0.50 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.16/0.50 inference(modus_ponens,[status(thm)],[111, 101])).
% 0.16/0.50 tff(113,plain,
% 0.16/0.50 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(L!2, M!1)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(L!2, M!1)))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(114,plain,
% 0.16/0.50 (((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))))) <=> ((~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(L!2, M!1)))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(115,plain,
% 0.16/0.50 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(L!2, M!1))))),
% 0.16/0.50 inference(monotonicity,[status(thm)],[114])).
% 0.16/0.50 tff(116,plain,
% 0.16/0.50 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(L!2, M!1)))),
% 0.16/0.50 inference(transitivity,[status(thm)],[115, 113])).
% 0.16/0.50 tff(117,plain,
% 0.16/0.50 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.16/0.50 inference(quant_inst,[status(thm)],[])).
% 0.16/0.50 tff(118,plain,
% 0.16/0.50 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(L!2, M!1))),
% 0.16/0.50 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.16/0.50 tff(119,plain,
% 0.16/0.50 ($false),
% 0.16/0.50 inference(unit_resolution,[status(thm)],[118, 112, 99, 98, 96, 94])).
% 0.16/0.50 % SZS output end Proof
%------------------------------------------------------------------------------