TSTP Solution File: GEO223+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO223+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 20:35:51 EDT 2022
% Result : Theorem 0.22s 0.46s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO223+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 31 07:04:45 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 0.22/0.46 % SZS status Theorem
% 0.22/0.46 % SZS output start Proof
% 0.22/0.46 tff(convergent_lines_type, type, (
% 0.22/0.46 convergent_lines: ( $i * $i ) > $o)).
% 0.22/0.46 tff(parallel_through_point_type, type, (
% 0.22/0.46 parallel_through_point: ( $i * $i ) > $i)).
% 0.22/0.46 tff(tptp_fun_A_1_type, type, (
% 0.22/0.46 tptp_fun_A_1: $i)).
% 0.22/0.46 tff(tptp_fun_L_0_type, type, (
% 0.22/0.46 tptp_fun_L_0: $i)).
% 0.22/0.46 tff(orthogonal_through_point_type, type, (
% 0.22/0.46 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.22/0.46 tff(unorthogonal_lines_type, type, (
% 0.22/0.46 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.22/0.46 tff(apart_point_and_line_type, type, (
% 0.22/0.46 apart_point_and_line: ( $i * $i ) > $o)).
% 0.22/0.46 tff(distinct_lines_type, type, (
% 0.22/0.46 distinct_lines: ( $i * $i ) > $o)).
% 0.22/0.46 tff(1,assumption,(convergent_lines(L!0, L!0)), introduced(assumption)).
% 0.22/0.46 tff(2,plain,
% 0.22/0.46 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(3,plain,
% 0.22/0.46 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[2])).
% 0.22/0.46 tff(4,plain,
% 0.22/0.46 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart3')).
% 0.22/0.46 tff(6,plain,
% 0.22/0.46 (![X: $i] : (~convergent_lines(X, X))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.22/0.46 tff(7,plain,(
% 0.22/0.46 ![X: $i] : (~convergent_lines(X, X))),
% 0.22/0.46 inference(skolemize,[status(sab)],[6])).
% 0.22/0.46 tff(8,plain,
% 0.22/0.46 (![X: $i] : (~convergent_lines(X, X))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.22/0.46 tff(9,plain,
% 0.22/0.46 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(L!0, L!0))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(10,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.22/0.46 tff(11,plain,(~convergent_lines(L!0, L!0)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(12,plain,
% 0.22/0.46 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(13,plain,
% 0.22/0.46 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[12])).
% 0.22/0.46 tff(14,plain,
% 0.22/0.46 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(15,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.22/0.46 tff(16,plain,
% 0.22/0.46 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.22/0.46 tff(17,plain,(
% 0.22/0.46 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.22/0.46 inference(skolemize,[status(sab)],[16])).
% 0.22/0.46 tff(18,plain,
% 0.22/0.46 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.22/0.46 tff(19,plain,
% 0.22/0.46 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(L!0, A!1), L!0))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(20,plain,
% 0.22/0.46 (~convergent_lines(parallel_through_point(L!0, A!1), L!0)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.46 tff(21,plain,
% 0.22/0.46 (^[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))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(22,plain,
% 0.22/0.46 (![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)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[21])).
% 0.22/0.46 tff(23,plain,
% 0.22/0.46 (![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)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(24,plain,
% 0.22/0.46 (^[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)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(25,plain,
% 0.22/0.46 (![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)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[24])).
% 0.22/0.46 tff(26,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.22/0.46 tff(27,plain,
% 0.22/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.22/0.46 tff(28,plain,
% 0.22/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.22/0.46 tff(29,plain,(
% 0.22/0.46 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.46 inference(skolemize,[status(sab)],[28])).
% 0.22/0.46 tff(30,plain,
% 0.22/0.46 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.22/0.46 tff(31,plain,
% 0.22/0.46 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(parallel_through_point(L!0, A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(32,plain,
% 0.22/0.46 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(33,plain,
% 0.22/0.46 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(parallel_through_point(L!0, A!1), L!0) | convergent_lines(L!0, L!0) | (~convergent_lines(L!0, parallel_through_point(L!0, A!1)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.22/0.46 tff(34,plain,
% 0.22/0.46 (~convergent_lines(L!0, parallel_through_point(L!0, A!1))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[33, 30, 20, 11])).
% 0.22/0.46 tff(35,plain,
% 0.22/0.46 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(36,plain,
% 0.22/0.46 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[35])).
% 0.22/0.46 tff(37,plain,
% 0.22/0.46 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(38,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.22/0.46 tff(39,plain,
% 0.22/0.46 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.22/0.46 tff(40,plain,(
% 0.22/0.46 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.22/0.46 inference(skolemize,[status(sab)],[39])).
% 0.22/0.46 tff(41,plain,
% 0.22/0.46 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.22/0.46 tff(42,plain,
% 0.22/0.46 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(43,plain,
% 0.22/0.46 (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.22/0.46 tff(44,plain,
% 0.22/0.46 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(45,plain,
% 0.22/0.46 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[44])).
% 0.22/0.46 tff(46,plain,
% 0.22/0.46 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(47,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.22/0.46 tff(48,plain,
% 0.22/0.46 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.22/0.46 tff(49,plain,(
% 0.22/0.46 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.22/0.46 inference(skolemize,[status(sab)],[48])).
% 0.22/0.46 tff(50,plain,
% 0.22/0.46 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.22/0.46 tff(51,plain,
% 0.22/0.46 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(52,plain,
% 0.22/0.46 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(53,plain,
% 0.22/0.46 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.22/0.46 tff(54,plain,
% 0.22/0.46 (convergent_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[53, 50, 43])).
% 0.22/0.46 tff(55,plain,
% 0.22/0.46 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(56,plain,
% 0.22/0.46 ((convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0))) <=> ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(57,plain,
% 0.22/0.46 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[56])).
% 0.22/0.46 tff(58,plain,
% 0.22/0.46 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))),
% 0.22/0.46 inference(transitivity,[status(thm)],[57, 55])).
% 0.22/0.46 tff(59,plain,
% 0.22/0.46 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(60,plain,
% 0.22/0.46 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | convergent_lines(L!0, parallel_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.22/0.46 tff(61,plain,
% 0.22/0.46 (convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[60, 30, 54, 34])).
% 0.22/0.46 tff(62,plain,
% 0.22/0.46 (((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0))) | convergent_lines(parallel_through_point(L!0, A!1), L!0)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(63,plain,
% 0.22/0.46 ((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[62, 20])).
% 0.22/0.46 tff(64,plain,
% 0.22/0.46 (^[A: $i, L: $i] : refl((~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> (~apart_point_and_line(A, orthogonal_through_point(L, A))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(65,plain,
% 0.22/0.46 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[64])).
% 0.22/0.46 tff(66,plain,
% 0.22/0.46 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A))) <=> ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(67,axiom,(![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc2')).
% 0.22/0.46 tff(68,plain,
% 0.22/0.46 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.22/0.46 tff(69,plain,(
% 0.22/0.46 ![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.22/0.46 inference(skolemize,[status(sab)],[68])).
% 0.22/0.46 tff(70,plain,
% 0.22/0.46 (![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.22/0.46 tff(71,plain,
% 0.22/0.46 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(72,plain,
% 0.22/0.46 (~apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.22/0.46 tff(73,plain,
% 0.22/0.46 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(74,plain,
% 0.22/0.46 (~unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[73, 41])).
% 0.22/0.46 tff(75,plain,
% 0.22/0.46 (^[X: $i, Y: $i] : refl((~apart_point_and_line(X, parallel_through_point(Y, X))) <=> (~apart_point_and_line(X, parallel_through_point(Y, X))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(76,plain,
% 0.22/0.46 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[75])).
% 0.22/0.46 tff(77,plain,
% 0.22/0.46 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(78,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.22/0.46 tff(79,plain,
% 0.22/0.46 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.22/0.46 tff(80,plain,(
% 0.22/0.46 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.22/0.46 inference(skolemize,[status(sab)],[79])).
% 0.22/0.46 tff(81,plain,
% 0.22/0.46 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.22/0.46 tff(82,plain,
% 0.22/0.46 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(A!1, parallel_through_point(L!0, A!1)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(83,plain,
% 0.22/0.46 (~apart_point_and_line(A!1, parallel_through_point(L!0, A!1))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.22/0.46 tff(84,plain,
% 0.22/0.46 ((~(~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(85,plain,
% 0.22/0.46 ((~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))) <=> (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(86,axiom,(~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.22/0.46 tff(87,plain,
% 0.22/0.46 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.22/0.46 tff(88,plain,
% 0.22/0.46 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[87, 85])).
% 0.22/0.46 tff(89,plain,
% 0.22/0.46 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.22/0.46 tff(90,plain,
% 0.22/0.46 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.22/0.46 tff(91,plain,
% 0.22/0.46 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[90, 85])).
% 0.22/0.46 tff(92,plain,
% 0.22/0.46 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[91, 85])).
% 0.22/0.46 tff(93,plain,
% 0.22/0.46 (~![A: $i, L: $i] : (~distinct_lines(parallel_through_point(L, A), orthogonal_through_point(orthogonal_through_point(L, A), A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.22/0.46 tff(94,plain,(
% 0.22/0.46 ~(~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))),
% 0.22/0.46 inference(skolemize,[status(sab)],[93])).
% 0.22/0.46 tff(95,plain,
% 0.22/0.46 (distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.22/0.46 tff(96,plain,
% 0.22/0.46 (^[A: $i, L: $i, M: $i, N: $i] : refl((apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(97,plain,
% 0.22/0.46 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[96])).
% 0.22/0.46 tff(98,plain,
% 0.22/0.46 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(99,plain,
% 0.22/0.46 (^[A: $i, L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(A, L) | apart_point_and_line(A, M)) <=> (apart_point_and_line(A, M) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> ((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)))), rewrite(((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> ((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)))), rewrite(((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))))), rewrite((distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(100,plain,
% 0.22/0.46 (![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[99])).
% 0.22/0.46 tff(101,axiom,(![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ouo1')).
% 0.22/0.46 tff(102,plain,
% 0.22/0.46 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.22/0.46 tff(103,plain,
% 0.22/0.46 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.22/0.46 tff(104,plain,(
% 0.22/0.46 ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.22/0.47 inference(skolemize,[status(sab)],[103])).
% 0.22/0.47 tff(105,plain,
% 0.22/0.47 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.22/0.47 tff(106,plain,
% 0.22/0.47 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | ((~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(107,plain,
% 0.22/0.47 ((apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)))) <=> ((~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(108,plain,
% 0.22/0.47 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | ((~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[107])).
% 0.22/0.47 tff(109,plain,
% 0.22/0.47 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.22/0.47 inference(transitivity,[status(thm)],[108, 106])).
% 0.22/0.47 tff(110,plain,
% 0.22/0.47 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(111,plain,
% 0.22/0.47 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (~distinct_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1))) | apart_point_and_line(A!1, parallel_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1), orthogonal_through_point(L!0, A!1)) | apart_point_and_line(A!1, orthogonal_through_point(orthogonal_through_point(L!0, A!1), A!1)) | unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.22/0.47 tff(112,plain,
% 0.22/0.47 (unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[111, 105, 95, 83, 74, 72])).
% 0.22/0.47 tff(113,assumption,(convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))), introduced(assumption)).
% 0.22/0.47 tff(114,plain,
% 0.22/0.47 (((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(115,plain,
% 0.22/0.47 ((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[114, 43])).
% 0.22/0.47 tff(116,plain,
% 0.22/0.47 (^[L: $i, M: $i, N: $i] : refl(((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(117,plain,
% 0.22/0.47 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[116])).
% 0.22/0.47 tff(118,plain,
% 0.22/0.47 (^[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)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~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(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(119,plain,
% 0.22/0.47 (![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)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[118])).
% 0.22/0.47 tff(120,plain,
% 0.22/0.47 (![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))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(121,plain,
% 0.22/0.47 (^[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))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(122,plain,
% 0.22/0.47 (![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))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[121])).
% 0.22/0.47 tff(123,axiom,(![L: $i, M: $i, N: $i] : ((convergent_lines(L, M) & unorthogonal_lines(L, M)) => ((convergent_lines(L, N) & unorthogonal_lines(L, N)) | (convergent_lines(M, N) & unorthogonal_lines(M, N))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','oac1')).
% 0.22/0.47 tff(124,plain,
% 0.22/0.47 (![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))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.22/0.47 tff(125,plain,
% 0.22/0.47 (![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))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.22/0.47 tff(126,plain,(
% 0.22/0.47 ![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))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[125])).
% 0.22/0.47 tff(127,plain,
% 0.22/0.47 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.22/0.47 tff(128,plain,
% 0.22/0.47 (![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[127, 117])).
% 0.22/0.47 tff(129,plain,
% 0.22/0.47 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(130,plain,
% 0.22/0.47 (((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(131,plain,
% 0.22/0.47 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[130])).
% 0.22/0.47 tff(132,plain,
% 0.22/0.47 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[131, 129])).
% 0.22/0.47 tff(133,plain,
% 0.22/0.47 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | ((~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0)))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(134,plain,
% 0.22/0.47 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(L, M)) | (~((~convergent_lines(M, N)) | (~unorthogonal_lines(M, N)))) | (~((~convergent_lines(L, N)) | (~unorthogonal_lines(L, N)))) | (~unorthogonal_lines(L, M)))) | (~((~convergent_lines(orthogonal_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0)))) | (~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | (~((~convergent_lines(parallel_through_point(L!0, A!1), L!0)) | (~unorthogonal_lines(parallel_through_point(L!0, A!1), L!0))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.22/0.47 tff(135,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[134, 128, 115, 113, 112, 63])).
% 0.22/0.47 tff(136,plain,(~convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(137,plain,
% 0.22/0.47 ((~![A: $i, L: $i] : (~apart_point_and_line(A, orthogonal_through_point(L, A)))) | (~apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(138,plain,
% 0.22/0.47 (~apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[137, 70])).
% 0.22/0.47 tff(139,plain,
% 0.22/0.47 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(140,plain,
% 0.22/0.47 ((apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(141,plain,
% 0.22/0.47 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[140])).
% 0.22/0.47 tff(142,plain,
% 0.22/0.47 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[141, 139])).
% 0.22/0.47 tff(143,plain,
% 0.22/0.47 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(144,plain,
% 0.22/0.47 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(orthogonal_through_point(L!0, A!1), L!0) | apart_point_and_line(A!1, orthogonal_through_point(L!0, A!1)) | (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.22/0.47 tff(145,plain,
% 0.22/0.47 (~distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[144, 105, 43, 138])).
% 0.22/0.47 tff(146,plain,
% 0.22/0.47 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(147,plain,
% 0.22/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[146])).
% 0.22/0.47 tff(148,plain,
% 0.22/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(149,plain,
% 0.22/0.47 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(150,plain,
% 0.22/0.47 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[149])).
% 0.22/0.47 tff(151,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.22/0.47 tff(152,plain,
% 0.22/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.22/0.47 tff(153,plain,
% 0.22/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.22/0.47 tff(154,plain,(
% 0.22/0.47 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.22/0.47 inference(skolemize,[status(sab)],[153])).
% 0.22/0.47 tff(155,plain,
% 0.22/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.22/0.47 tff(156,plain,
% 0.22/0.47 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(157,plain,
% 0.22/0.47 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(158,plain,
% 0.22/0.47 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))) | distinct_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.22/0.47 tff(159,plain,
% 0.22/0.47 (~convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[158, 155, 145])).
% 0.22/0.47 tff(160,plain,
% 0.22/0.47 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(161,plain,
% 0.22/0.48 ((convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))) <=> (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(162,plain,
% 0.22/0.48 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[161])).
% 0.22/0.48 tff(163,plain,
% 0.22/0.48 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[162, 160])).
% 0.22/0.48 tff(164,plain,
% 0.22/0.48 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(165,plain,
% 0.22/0.48 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(orthogonal_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | convergent_lines(parallel_through_point(L!0, A!1), orthogonal_through_point(L!0, A!1)) | (~convergent_lines(orthogonal_through_point(L!0, A!1), parallel_through_point(L!0, A!1)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.22/0.48 tff(166,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[165, 30, 159, 136, 61])).
% 0.22/0.48 % SZS output end Proof
%------------------------------------------------------------------------------