TSTP Solution File: GEO219+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO219+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 20:35:48 EDT 2022
% Result : Theorem 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GEO219+3 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 31 06:47:01 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 0.22/0.42 % SZS status Theorem
% 0.22/0.42 % SZS output start Proof
% 0.22/0.42 tff(convergent_lines_type, type, (
% 0.22/0.42 convergent_lines: ( $i * $i ) > $o)).
% 0.22/0.42 tff(tptp_fun_M_1_type, type, (
% 0.22/0.42 tptp_fun_M_1: $i)).
% 0.22/0.42 tff(tptp_fun_L_2_type, type, (
% 0.22/0.42 tptp_fun_L_2: $i)).
% 0.22/0.42 tff(unorthogonal_lines_type, type, (
% 0.22/0.42 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.22/0.42 tff(orthogonal_lines_type, type, (
% 0.22/0.42 orthogonal_lines: ( $i * $i ) > $o)).
% 0.22/0.42 tff(parallel_lines_type, type, (
% 0.22/0.42 parallel_lines: ( $i * $i ) > $o)).
% 0.22/0.42 tff(tptp_fun_N_0_type, type, (
% 0.22/0.42 tptp_fun_N_0: $i)).
% 0.22/0.42 tff(1,plain,
% 0.22/0.42 (^[X: $i, Y: $i] : refl((orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(2,plain,
% 0.22/0.42 (![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.42 tff(3,plain,
% 0.22/0.42 (![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y))) <=> ![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(4,axiom,(![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a5')).
% 0.22/0.42 tff(5,plain,
% 0.22/0.42 (![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.42 tff(6,plain,(
% 0.22/0.42 ![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[5])).
% 0.22/0.42 tff(7,plain,
% 0.22/0.42 (![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.42 tff(8,plain,
% 0.22/0.42 ((~![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))) | (orthogonal_lines(L!2, M!1) <=> (~unorthogonal_lines(L!2, M!1)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(9,plain,
% 0.22/0.42 (orthogonal_lines(L!2, M!1) <=> (~unorthogonal_lines(L!2, M!1))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.22/0.42 tff(10,plain,
% 0.22/0.42 ((~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & parallel_lines(L, N))) | orthogonal_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & parallel_lines(L, N))) | orthogonal_lines(M, N)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(11,plain,
% 0.22/0.42 ((~![L: $i, M: $i, N: $i] : ((orthogonal_lines(L, M) & parallel_lines(L, N)) => orthogonal_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & parallel_lines(L, N))) | orthogonal_lines(M, N)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(12,axiom,(~![L: $i, M: $i, N: $i] : ((orthogonal_lines(L, M) & parallel_lines(L, N)) => orthogonal_lines(M, N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.22/0.42 tff(13,plain,
% 0.22/0.42 (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & parallel_lines(L, N))) | orthogonal_lines(M, N))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.22/0.42 tff(14,plain,
% 0.22/0.42 (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & parallel_lines(L, N))) | orthogonal_lines(M, N))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.22/0.42 tff(15,plain,
% 0.22/0.42 (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & parallel_lines(L, N))) | orthogonal_lines(M, N))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.22/0.42 tff(16,plain,
% 0.22/0.42 (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & parallel_lines(L, N))) | orthogonal_lines(M, N))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.22/0.42 tff(17,plain,
% 0.22/0.42 (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & parallel_lines(L, N))) | orthogonal_lines(M, N))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.22/0.42 tff(18,plain,
% 0.22/0.42 (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & parallel_lines(L, N))) | orthogonal_lines(M, N))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.22/0.42 tff(19,plain,
% 0.22/0.42 (~![L: $i, M: $i, N: $i] : ((~(orthogonal_lines(L, M) & parallel_lines(L, N))) | orthogonal_lines(M, N))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.22/0.42 tff(20,plain,(
% 0.22/0.42 ~((~(orthogonal_lines(L!2, M!1) & parallel_lines(L!2, N!0))) | orthogonal_lines(M!1, N!0))),
% 0.22/0.42 inference(skolemize,[status(sab)],[19])).
% 0.22/0.42 tff(21,plain,
% 0.22/0.42 (orthogonal_lines(L!2, M!1) & parallel_lines(L!2, N!0)),
% 0.22/0.42 inference(or_elim,[status(thm)],[20])).
% 0.22/0.42 tff(22,plain,
% 0.22/0.42 (orthogonal_lines(L!2, M!1)),
% 0.22/0.42 inference(and_elim,[status(thm)],[21])).
% 0.22/0.42 tff(23,plain,
% 0.22/0.42 ((~(orthogonal_lines(L!2, M!1) <=> (~unorthogonal_lines(L!2, M!1)))) | (~orthogonal_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(24,plain,
% 0.22/0.42 ((~(orthogonal_lines(L!2, M!1) <=> (~unorthogonal_lines(L!2, M!1)))) | (~unorthogonal_lines(L!2, M!1))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.22/0.42 tff(25,plain,
% 0.22/0.42 (~unorthogonal_lines(L!2, M!1)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[24, 9])).
% 0.22/0.42 tff(26,plain,
% 0.22/0.42 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(27,plain,
% 0.22/0.42 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.42 tff(28,plain,
% 0.22/0.42 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(29,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.22/0.42 tff(31,plain,(
% 0.22/0.42 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.22/0.42 inference(skolemize,[status(sab)],[30])).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!2, M!1) | unorthogonal_lines(L!2, M!1)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 (convergent_lines(L!2, M!1)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[35, 32, 25])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))) | unorthogonal_lines(L!2, M!1)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 ((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[37, 25])).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 (^[X: $i, Y: $i] : refl((parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.22/0.42 tff(41,plain,
% 0.22/0.42 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(42,axiom,(![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax','a3')).
% 0.22/0.42 tff(43,plain,
% 0.22/0.42 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.22/0.43 tff(44,plain,(
% 0.22/0.43 ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[43])).
% 0.22/0.43 tff(45,plain,
% 0.22/0.43 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.22/0.43 tff(46,plain,
% 0.22/0.43 ((~![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))) | (parallel_lines(L!2, N!0) <=> (~convergent_lines(L!2, N!0)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(47,plain,
% 0.22/0.43 (parallel_lines(L!2, N!0) <=> (~convergent_lines(L!2, N!0))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.22/0.43 tff(48,plain,
% 0.22/0.43 (parallel_lines(L!2, N!0)),
% 0.22/0.43 inference(and_elim,[status(thm)],[21])).
% 0.22/0.43 tff(49,plain,
% 0.22/0.43 ((~(parallel_lines(L!2, N!0) <=> (~convergent_lines(L!2, N!0)))) | (~parallel_lines(L!2, N!0)) | (~convergent_lines(L!2, N!0))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(50,plain,
% 0.22/0.43 ((~(parallel_lines(L!2, N!0) <=> (~convergent_lines(L!2, N!0)))) | (~convergent_lines(L!2, N!0))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.22/0.43 tff(51,plain,
% 0.22/0.43 (~convergent_lines(L!2, N!0)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.22/0.43 tff(52,plain,
% 0.22/0.43 (((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))) | convergent_lines(L!2, N!0)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(53,plain,
% 0.22/0.43 ((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.22/0.43 tff(54,plain,
% 0.22/0.43 ((~![X: $i, Y: $i] : (orthogonal_lines(X, Y) <=> (~unorthogonal_lines(X, Y)))) | (orthogonal_lines(M!1, N!0) <=> (~unorthogonal_lines(M!1, N!0)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(55,plain,
% 0.22/0.43 (orthogonal_lines(M!1, N!0) <=> (~unorthogonal_lines(M!1, N!0))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[54, 7])).
% 0.22/0.43 tff(56,plain,
% 0.22/0.43 (~orthogonal_lines(M!1, N!0)),
% 0.22/0.43 inference(or_elim,[status(thm)],[20])).
% 0.22/0.43 tff(57,plain,
% 0.22/0.43 ((~(orthogonal_lines(M!1, N!0) <=> (~unorthogonal_lines(M!1, N!0)))) | orthogonal_lines(M!1, N!0) | unorthogonal_lines(M!1, N!0)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(58,plain,
% 0.22/0.43 ((~(orthogonal_lines(M!1, N!0) <=> (~unorthogonal_lines(M!1, N!0)))) | unorthogonal_lines(M!1, N!0)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.22/0.43 tff(59,plain,
% 0.22/0.43 (unorthogonal_lines(M!1, N!0)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.22/0.43 tff(60,plain,
% 0.22/0.43 (^[L: $i, M: $i, N: $i] : refl(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(61,plain,
% 0.22/0.43 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[60])).
% 0.22/0.43 tff(62,plain,
% 0.22/0.43 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) <=> (~((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> (~(~((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))))), rewrite((~(~((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))) <=> ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), ((~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N))))) <=> ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))))), rewrite(((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | ((~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))), (((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(63,plain,
% 0.22/0.43 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~(((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[62])).
% 0.22/0.43 tff(64,plain,
% 0.22/0.43 (![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))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(65,plain,
% 0.22/0.43 (^[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)))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(66,plain,
% 0.22/0.43 (![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))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[65])).
% 0.22/0.43 tff(67,axiom,(![L: $i, M: $i, N: $i] : ((((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M))) & ((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) => ((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax','cotno1')).
% 0.22/0.43 tff(68,plain,
% 0.22/0.43 (![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))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 (![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))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.22/0.43 tff(70,plain,(
% 0.22/0.43 ![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))))))),
% 0.22/0.43 inference(skolemize,[status(sab)],[69])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.22/0.43 tff(72,plain,
% 0.22/0.43 (![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 (((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(74,plain,
% 0.22/0.43 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | ((~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1)))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(75,plain,
% 0.22/0.43 ((~![L: $i, M: $i, N: $i] : ((~unorthogonal_lines(M, N)) | (~convergent_lines(M, N)) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~((~convergent_lines(L, M)) | (~unorthogonal_lines(L, M)))))) | (~unorthogonal_lines(M!1, N!0)) | (~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, N!0)) | (~unorthogonal_lines(L!2, N!0)))) | (~((~convergent_lines(L!2, M!1)) | (~unorthogonal_lines(L!2, M!1))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.22/0.43 tff(76,plain,
% 0.22/0.43 (~convergent_lines(M!1, N!0)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[75, 72, 59, 53, 38])).
% 0.22/0.43 tff(77,plain,
% 0.22/0.43 (^[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))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(78,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[77])).
% 0.22/0.43 tff(79,plain,
% 0.22/0.43 (![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)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(80,plain,
% 0.22/0.43 (^[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)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(81,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[80])).
% 0.22/0.44 tff(82,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.22/0.44 tff(83,plain,
% 0.22/0.44 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.22/0.44 tff(84,plain,
% 0.22/0.44 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.22/0.44 tff(85,plain,(
% 0.22/0.44 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[84])).
% 0.22/0.44 tff(86,plain,
% 0.22/0.44 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.22/0.44 tff(87,plain,
% 0.22/0.44 (((~![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(M!1, N!0) | (~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(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(88,plain,
% 0.22/0.44 ((convergent_lines(M!1, N!0) | convergent_lines(L!2, N!0) | (~convergent_lines(L!2, M!1))) <=> (convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(89,plain,
% 0.22/0.44 (((~![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(L!2, N!0) | (~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(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[88])).
% 0.22/0.44 tff(90,plain,
% 0.22/0.44 (((~![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(L!2, N!0) | (~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(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.22/0.44 inference(transitivity,[status(thm)],[89, 87])).
% 0.22/0.44 tff(91,plain,
% 0.22/0.44 ((~![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(L!2, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(92,plain,
% 0.22/0.44 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | convergent_lines(M!1, N!0) | (~convergent_lines(L!2, M!1))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.22/0.44 tff(93,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[92, 86, 51, 76, 36])).
% 0.22/0.44 % SZS output end Proof
%------------------------------------------------------------------------------