TSTP Solution File: GEO213+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO213+2 : TPTP v8.1.0. Released v3.3.0.
% 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 20:35:44 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO213+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:58:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 tff(convergent_lines_type, type, (
% 0.20/0.52 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.52 tff(tptp_fun_M_1_type, type, (
% 0.20/0.52 tptp_fun_M_1: $i)).
% 0.20/0.52 tff(tptp_fun_L_2_type, type, (
% 0.20/0.52 tptp_fun_L_2: $i)).
% 0.20/0.52 tff(unorthogonal_lines_type, type, (
% 0.20/0.52 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.52 tff(tptp_fun_N_0_type, type, (
% 0.20/0.52 tptp_fun_N_0: $i)).
% 0.20/0.52 tff(distinct_lines_type, type, (
% 0.20/0.52 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.52 tff(1,assumption,(convergent_lines(L!2, M!1)), introduced(assumption)).
% 0.20/0.52 tff(2,plain,
% 0.20/0.52 ((~(distinct_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))) <=> (~(distinct_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(3,plain,
% 0.20/0.52 ((~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))) <=> (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(4,plain,
% 0.20/0.52 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, M) => (distinct_lines(L, N) | unorthogonal_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(5,axiom,(~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, M) => (distinct_lines(L, N) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.52 tff(6,plain,
% 0.20/0.52 (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.52 tff(7,plain,
% 0.20/0.52 (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.20/0.52 tff(8,plain,
% 0.20/0.52 (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.52 tff(9,plain,
% 0.20/0.52 (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.20/0.52 tff(10,plain,
% 0.20/0.52 (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.20/0.52 tff(11,plain,
% 0.20/0.52 (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.52 tff(12,plain,
% 0.20/0.52 (~![L: $i, M: $i, N: $i] : (distinct_lines(L, N) | unorthogonal_lines(M, N) | (~unorthogonal_lines(L, M)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.20/0.52 tff(13,plain,(
% 0.20/0.52 ~(distinct_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[12])).
% 0.20/0.52 tff(14,plain,
% 0.20/0.52 (~(distinct_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | (~unorthogonal_lines(L!2, M!1)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.20/0.52 tff(15,plain,
% 0.20/0.52 (~distinct_lines(L!2, N!0)),
% 0.20/0.52 inference(or_elim,[status(thm)],[14])).
% 0.20/0.52 tff(16,plain,
% 0.20/0.52 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(17,plain,
% 0.20/0.52 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.52 tff(18,plain,
% 0.20/0.52 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(19,plain,
% 0.20/0.52 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(20,plain,
% 0.20/0.52 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.53 tff(21,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.20/0.53 tff(22,plain,
% 0.20/0.53 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.53 tff(23,plain,
% 0.20/0.53 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.53 tff(24,plain,(
% 0.20/0.53 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.53 inference(skolemize,[status(sab)],[23])).
% 0.20/0.53 tff(25,plain,
% 0.20/0.53 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.20/0.53 tff(26,plain,
% 0.20/0.53 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(L!2, N!0)) | distinct_lines(L!2, N!0))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(L!2, N!0)) | distinct_lines(L!2, N!0))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(27,plain,
% 0.20/0.53 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(L!2, N!0)) | distinct_lines(L!2, N!0))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(28,plain,
% 0.20/0.53 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(L!2, N!0)) | distinct_lines(L!2, N!0)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.53 tff(29,plain,
% 0.20/0.53 (~convergent_lines(L!2, N!0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[28, 25, 15])).
% 0.20/0.53 tff(30,plain,
% 0.20/0.53 (((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))) | convergent_lines(L!2, N!0)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(31,plain,
% 0.20/0.53 ((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.20/0.53 tff(32,plain,
% 0.20/0.53 (~unorthogonal_lines(M!1, N!0)),
% 0.20/0.53 inference(or_elim,[status(thm)],[14])).
% 0.20/0.53 tff(33,plain,
% 0.20/0.53 (((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))) | unorthogonal_lines(M!1, N!0)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(34,plain,
% 0.20/0.53 ((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.53 tff(35,plain,
% 0.20/0.53 (unorthogonal_lines(L!2, M!1)),
% 0.20/0.53 inference(or_elim,[status(thm)],[14])).
% 0.20/0.53 tff(36,plain,
% 0.20/0.53 (^[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))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(37,plain,
% 0.20/0.53 (![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)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.53 tff(38,plain,
% 0.20/0.53 (^[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)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(39,plain,
% 0.20/0.53 (![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)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.53 tff(40,plain,
% 0.20/0.53 (![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))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(41,plain,
% 0.20/0.53 (^[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))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(42,plain,
% 0.20/0.53 (![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))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.53 tff(43,axiom,(![L: $i, M: $i, N: $i] : ((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','oac1')).
% 0.20/0.53 tff(44,plain,
% 0.20/0.53 (![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))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.53 tff(45,plain,
% 0.20/0.53 (![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))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.53 tff(46,plain,(
% 0.20/0.53 ![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))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[45])).
% 0.20/0.53 tff(47,plain,
% 0.20/0.53 (![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)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.20/0.53 tff(48,plain,
% 0.20/0.53 (![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)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.20/0.53 tff(49,plain,
% 0.20/0.53 (((~![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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(50,plain,
% 0.20/0.53 (((~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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(51,plain,
% 0.20/0.53 (((~![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))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.53 tff(52,plain,
% 0.20/0.53 (((~![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)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[51, 49])).
% 0.20/0.53 tff(53,plain,
% 0.20/0.53 ((~![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)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(54,plain,
% 0.20/0.53 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(L!2, M!1)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(M!1, N!0)) | (~unorthogonal_lines(M!1, N!0)))) | (~convergent_lines(L!2, M!1))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.53 tff(55,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[54, 48, 35, 34, 31, 1])).
% 0.20/0.53 tff(56,plain,(~convergent_lines(L!2, M!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(57,assumption,(distinct_lines(M!1, M!1)), introduced(assumption)).
% 0.20/0.53 tff(58,plain,
% 0.20/0.53 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(59,plain,
% 0.20/0.53 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.53 tff(60,plain,
% 0.20/0.53 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(61,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.20/0.53 tff(62,plain,
% 0.20/0.53 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.53 tff(63,plain,(
% 0.20/0.53 ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.53 inference(skolemize,[status(sab)],[62])).
% 0.20/0.53 tff(64,plain,
% 0.20/0.53 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.53 tff(65,plain,
% 0.20/0.53 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(M!1, M!1))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(66,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[65, 64, 57])).
% 0.20/0.53 tff(67,plain,(~distinct_lines(M!1, M!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(68,plain,
% 0.20/0.53 (((~![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))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(69,plain,
% 0.20/0.53 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(M!1, M!1)) | distinct_lines(M!1, M!1))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(70,plain,
% 0.20/0.53 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(M!1, M!1)) | distinct_lines(M!1, M!1)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.53 tff(71,plain,
% 0.20/0.53 (~convergent_lines(M!1, M!1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[70, 25, 67])).
% 0.20/0.53 tff(72,assumption,(distinct_lines(N!0, N!0)), introduced(assumption)).
% 0.20/0.53 tff(73,plain,
% 0.20/0.53 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(N!0, N!0))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(74,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[73, 64, 72])).
% 0.20/0.53 tff(75,plain,(~distinct_lines(N!0, N!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(76,plain,
% 0.20/0.53 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(77,plain,
% 0.20/0.53 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.53 tff(78,plain,
% 0.20/0.53 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(79,plain,
% 0.20/0.53 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(80,plain,
% 0.20/0.53 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.53 tff(81,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart5')).
% 0.20/0.53 tff(82,plain,
% 0.20/0.53 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.53 tff(83,plain,
% 0.20/0.53 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.20/0.53 tff(84,plain,(
% 0.20/0.53 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[83])).
% 0.20/0.53 tff(85,plain,
% 0.20/0.53 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.20/0.53 tff(86,plain,
% 0.20/0.53 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(L!2, N!0) | distinct_lines(N!0, N!0) | (~distinct_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(L!2, N!0) | distinct_lines(N!0, N!0) | (~distinct_lines(N!0, L!2)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(87,plain,
% 0.20/0.53 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(L!2, N!0) | distinct_lines(N!0, N!0) | (~distinct_lines(N!0, L!2)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(88,plain,
% 0.20/0.53 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(L!2, N!0) | distinct_lines(N!0, N!0) | (~distinct_lines(N!0, L!2))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.53 tff(89,plain,
% 0.20/0.53 (distinct_lines(N!0, N!0) | (~distinct_lines(N!0, L!2))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[88, 85, 15])).
% 0.20/0.53 tff(90,plain,
% 0.20/0.53 (~distinct_lines(N!0, L!2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[89, 75])).
% 0.20/0.53 tff(91,plain,
% 0.20/0.53 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(N!0, L!2)) | distinct_lines(N!0, L!2))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(N!0, L!2)) | distinct_lines(N!0, L!2))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(92,plain,
% 0.20/0.53 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(N!0, L!2)) | distinct_lines(N!0, L!2))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(93,plain,
% 0.20/0.53 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(N!0, L!2)) | distinct_lines(N!0, L!2)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.53 tff(94,plain,
% 0.20/0.53 (~convergent_lines(N!0, L!2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[93, 25, 90])).
% 0.20/0.53 tff(95,plain,
% 0.20/0.53 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(96,plain,
% 0.20/0.53 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.53 tff(97,plain,
% 0.20/0.53 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(98,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.20/0.53 tff(99,plain,
% 0.20/0.53 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.53 tff(100,plain,(
% 0.20/0.53 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.53 inference(skolemize,[status(sab)],[99])).
% 0.20/0.53 tff(101,plain,
% 0.20/0.53 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.53 tff(102,plain,
% 0.20/0.53 (((~![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))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(103,plain,
% 0.20/0.53 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(104,plain,
% 0.20/0.53 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.53 tff(105,plain,
% 0.20/0.53 (convergent_lines(M!1, N!0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[104, 101, 32])).
% 0.20/0.53 tff(106,plain,
% 0.20/0.53 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(107,plain,
% 0.20/0.53 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.53 tff(108,plain,
% 0.20/0.53 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(109,plain,
% 0.20/0.53 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(110,plain,
% 0.20/0.53 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.53 tff(111,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.20/0.53 tff(112,plain,
% 0.20/0.53 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.53 tff(113,plain,
% 0.20/0.53 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.47/0.53 tff(114,plain,(
% 0.47/0.53 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.47/0.53 inference(skolemize,[status(sab)],[113])).
% 0.47/0.53 tff(115,plain,
% 0.47/0.53 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.47/0.53 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.47/0.53 tff(116,plain,
% 0.47/0.53 (((~![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))),
% 0.47/0.53 inference(rewrite,[status(thm)],[])).
% 0.47/0.53 tff(117,plain,
% 0.47/0.53 ((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))),
% 0.47/0.53 inference(rewrite,[status(thm)],[])).
% 0.47/0.53 tff(118,plain,
% 0.47/0.53 (((~![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)))),
% 0.47/0.53 inference(monotonicity,[status(thm)],[117])).
% 0.47/0.53 tff(119,plain,
% 0.47/0.53 (((~![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))),
% 0.47/0.53 inference(transitivity,[status(thm)],[118, 116])).
% 0.47/0.53 tff(120,plain,
% 0.47/0.53 ((~![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)))),
% 0.47/0.53 inference(quant_inst,[status(thm)],[])).
% 0.47/0.53 tff(121,plain,
% 0.47/0.53 ((~![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)),
% 0.47/0.53 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.47/0.53 tff(122,plain,
% 0.47/0.53 (convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2)),
% 0.47/0.53 inference(unit_resolution,[status(thm)],[121, 115, 105])).
% 0.47/0.53 tff(123,plain,
% 0.47/0.53 (convergent_lines(M!1, L!2)),
% 0.47/0.53 inference(unit_resolution,[status(thm)],[122, 94])).
% 0.47/0.53 tff(124,plain,
% 0.47/0.53 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)) | 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, M!1) | (~convergent_lines(M!1, L!2)) | convergent_lines(L!2, M!1))),
% 0.47/0.54 inference(rewrite,[status(thm)],[])).
% 0.47/0.54 tff(125,plain,
% 0.47/0.54 ((convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2))) <=> (convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)) | convergent_lines(L!2, M!1))),
% 0.47/0.54 inference(rewrite,[status(thm)],[])).
% 0.47/0.54 tff(126,plain,
% 0.47/0.54 (((~![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, M!1) | (~convergent_lines(M!1, L!2)) | convergent_lines(L!2, M!1)))),
% 0.47/0.54 inference(monotonicity,[status(thm)],[125])).
% 0.47/0.54 tff(127,plain,
% 0.47/0.54 (((~![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, M!1) | (~convergent_lines(M!1, L!2)) | convergent_lines(L!2, M!1))),
% 0.47/0.54 inference(transitivity,[status(thm)],[126, 124])).
% 0.47/0.54 tff(128,plain,
% 0.47/0.54 ((~![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)))),
% 0.47/0.54 inference(quant_inst,[status(thm)],[])).
% 0.47/0.54 tff(129,plain,
% 0.47/0.54 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)) | convergent_lines(L!2, M!1)),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.47/0.54 tff(130,plain,
% 0.47/0.54 ($false),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[129, 115, 123, 71, 56])).
% 0.47/0.54 % SZS output end Proof
%------------------------------------------------------------------------------