TSTP Solution File: GEO218+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO218+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:35:47 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO218+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 07:01:40 EDT 2022
% 0.13/0.33 % 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.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(convergent_lines_type, type, (
% 0.19/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_N_0_type, type, (
% 0.19/0.39 tptp_fun_N_0: $i)).
% 0.19/0.39 tff(tptp_fun_M_1_type, type, (
% 0.19/0.39 tptp_fun_M_1: $i)).
% 0.19/0.39 tff(tptp_fun_L_2_type, type, (
% 0.19/0.39 tptp_fun_L_2: $i)).
% 0.19/0.39 tff(unorthogonal_lines_type, type, (
% 0.19/0.39 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.19/0.39 tff(1,assumption,(~convergent_lines(N!0, N!0)), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N)))))) <=> (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 ((~![L: $i, M: $i, N: $i] : (((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~unorthogonal_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(~![L: $i, M: $i, N: $i] : (((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.19/0.39 tff(12,plain,(
% 0.19/0.39 ~((~unorthogonal_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) & (~unorthogonal_lines(L!2, N!0)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[11])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 ((~convergent_lines(L!2, M!1)) & (~unorthogonal_lines(L!2, N!0))),
% 0.19/0.39 inference(or_elim,[status(thm)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (~unorthogonal_lines(L!2, N!0)),
% 0.19/0.39 inference(and_elim,[status(thm)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (^[L: $i, M: $i] : 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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(20,axiom,(![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','coipo1')).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.39 tff(22,plain,(
% 0.19/0.39 ![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[21])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (convergent_lines(L!2, N!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (~convergent_lines(L!2, M!1)),
% 0.19/0.39 inference(and_elim,[status(thm)],[13])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.40 tff(35,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/GEO006+0.ax','ax6')).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.40 tff(38,plain,(
% 0.19/0.40 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[37])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (((~![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(L!2, N!0)) | convergent_lines(N!0, M!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0)) | convergent_lines(N!0, M!1))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((convergent_lines(N!0, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0))) <=> (convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0)) | convergent_lines(N!0, M!1))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0)) | convergent_lines(N!0, M!1)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0)) | convergent_lines(N!0, M!1))),
% 0.19/0.40 inference(transitivity,[status(thm)],[42, 40])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, M!1) | convergent_lines(L!2, M!1) | (~convergent_lines(L!2, N!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 ((~![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(L!2, N!0)) | convergent_lines(N!0, M!1)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (convergent_lines(N!0, M!1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[45, 39, 29, 28])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))) | unorthogonal_lines(L!2, N!0)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 ((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[47, 14])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))) | convergent_lines(L!2, M!1)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 ((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[49, 29])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (unorthogonal_lines(M!1, N!0)),
% 0.19/0.40 inference(or_elim,[status(thm)],[12])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (^[L: $i, M: $i, N: $i] : refl(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) <=> (~((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> (~(~((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))))), rewrite((~(~((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))) <=> ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))), rewrite(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (^[L: $i, M: $i, N: $i] : rewrite(((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.40 tff(59,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+4.ax','cotno1')).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.40 tff(62,plain,(
% 0.19/0.40 ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[61])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) | (~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (~convergent_lines(M!1, N!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 64, 51, 50, 48])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, M!1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(M!1, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, M!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(M!1, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, M!1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[71, 39, 68, 46, 1])).
% 0.19/0.40 tff(73,plain,(convergent_lines(N!0, N!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (^[L: $i, M: $i, N: $i] : refl(((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.41 tff(81,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.41 tff(84,plain,(
% 0.19/0.41 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[83])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (((~convergent_lines(N!0, N!0)) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0)) <=> (unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(N!0, N!0)) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(N!0, N!0)) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[89, 87])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(N!0, N!0)) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(L!2, N!0))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(N!0, N!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[92, 86, 14, 73])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------