TSTP Solution File: GEO224+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO224+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 20:35:52 EDT 2022
% Result : Theorem 0.14s 0.35s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GEO224+3 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n008.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Wed Aug 31 07:06:55 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.14/0.35 % SZS status Theorem
% 0.14/0.35 % SZS output start Proof
% 0.14/0.35 tff(apart_point_and_line_type, type, (
% 0.14/0.35 apart_point_and_line: ( $i * $i ) > $o)).
% 0.14/0.35 tff(tptp_fun_Y_0_type, type, (
% 0.14/0.35 tptp_fun_Y_0: $i)).
% 0.14/0.35 tff(intersection_point_type, type, (
% 0.14/0.35 intersection_point: ( $i * $i ) > $i)).
% 0.14/0.35 tff(orthogonal_through_point_type, type, (
% 0.14/0.35 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.14/0.35 tff(tptp_fun_X_1_type, type, (
% 0.14/0.35 tptp_fun_X_1: $i)).
% 0.14/0.35 tff(incident_point_and_line_type, type, (
% 0.14/0.35 incident_point_and_line: ( $i * $i ) > $o)).
% 0.14/0.35 tff(point_type, type, (
% 0.14/0.35 point: $i > $o)).
% 0.14/0.35 tff(convergent_lines_type, type, (
% 0.14/0.35 convergent_lines: ( $i * $i ) > $o)).
% 0.14/0.35 tff(unorthogonal_lines_type, type, (
% 0.14/0.35 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.14/0.35 tff(line_type, type, (
% 0.14/0.35 line: $i > $o)).
% 0.14/0.35 tff(1,plain,
% 0.14/0.35 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(2,plain,
% 0.14/0.35 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.35 tff(3,plain,
% 0.14/0.35 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(4,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.14/0.35 tff(5,plain,
% 0.14/0.35 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.35 tff(6,plain,(
% 0.14/0.35 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.14/0.35 inference(skolemize,[status(sab)],[5])).
% 0.14/0.35 tff(7,plain,
% 0.14/0.35 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.35 tff(8,plain,
% 0.14/0.35 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(Y!0, X!1), Y!0))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(9,plain,
% 0.14/0.35 (~unorthogonal_lines(orthogonal_through_point(Y!0, X!1), Y!0)),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.35 tff(10,plain,
% 0.14/0.35 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(11,plain,
% 0.14/0.35 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[10])).
% 0.14/0.35 tff(12,plain,
% 0.14/0.35 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(13,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','occu1')).
% 0.14/0.35 tff(14,plain,
% 0.14/0.35 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.14/0.35 tff(15,plain,(
% 0.14/0.35 ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.35 inference(skolemize,[status(sab)],[14])).
% 0.14/0.35 tff(16,plain,
% 0.14/0.35 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.14/0.35 tff(17,plain,
% 0.14/0.35 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0) | unorthogonal_lines(orthogonal_through_point(Y!0, X!1), Y!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0) | unorthogonal_lines(orthogonal_through_point(Y!0, X!1), Y!0))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(18,plain,
% 0.14/0.35 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0) | unorthogonal_lines(orthogonal_through_point(Y!0, X!1), Y!0))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(19,plain,
% 0.14/0.35 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0) | unorthogonal_lines(orthogonal_through_point(Y!0, X!1), Y!0)),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.14/0.35 tff(20,plain,
% 0.14/0.35 (convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.14/0.35 tff(21,plain,
% 0.14/0.35 (((point(X!1) & line(Y!0)) & ![Z: $i] : (~(point(Z) & incident_point_and_line(Z, Y!0)))) <=> (point(X!1) & line(Y!0) & ![Z: $i] : (~(point(Z) & incident_point_and_line(Z, Y!0))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(22,plain,
% 0.14/0.35 ((~(~(point(X!1) & line(Y!0)))) <=> (point(X!1) & line(Y!0))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(23,plain,
% 0.14/0.35 (((~(~(point(X!1) & line(Y!0)))) & ![Z: $i] : (~(point(Z) & incident_point_and_line(Z, Y!0)))) <=> ((point(X!1) & line(Y!0)) & ![Z: $i] : (~(point(Z) & incident_point_and_line(Z, Y!0))))),
% 0.14/0.35 inference(monotonicity,[status(thm)],[22])).
% 0.14/0.35 tff(24,plain,
% 0.14/0.35 (((~(~(point(X!1) & line(Y!0)))) & ![Z: $i] : (~(point(Z) & incident_point_and_line(Z, Y!0)))) <=> (point(X!1) & line(Y!0) & ![Z: $i] : (~(point(Z) & incident_point_and_line(Z, Y!0))))),
% 0.14/0.35 inference(transitivity,[status(thm)],[23, 21])).
% 0.14/0.35 tff(25,plain,
% 0.14/0.35 ((~![X: $i, Y: $i] : ((~(point(X) & line(Y))) | ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y)))) <=> (~![X: $i, Y: $i] : ((~(point(X) & line(Y))) | ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(26,plain,
% 0.14/0.35 ((~![X: $i, Y: $i] : ((point(X) & line(Y)) => ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y)))) <=> (~![X: $i, Y: $i] : ((~(point(X) & line(Y))) | ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(27,axiom,(~![X: $i, Y: $i] : ((point(X) & line(Y)) => ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.14/0.35 tff(28,plain,
% 0.14/0.35 (~![X: $i, Y: $i] : ((~(point(X) & line(Y))) | ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.14/0.35 tff(29,plain,
% 0.14/0.35 (~![X: $i, Y: $i] : ((~(point(X) & line(Y))) | ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.14/0.35 tff(30,plain,
% 0.14/0.35 (~![X: $i, Y: $i] : ((~(point(X) & line(Y))) | ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.14/0.35 tff(31,plain,
% 0.14/0.35 (~![X: $i, Y: $i] : ((~(point(X) & line(Y))) | ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.14/0.35 tff(32,plain,
% 0.14/0.35 (~![X: $i, Y: $i] : ((~(point(X) & line(Y))) | ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.14/0.35 tff(33,plain,
% 0.14/0.35 (~![X: $i, Y: $i] : ((~(point(X) & line(Y))) | ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.14/0.35 tff(34,plain,
% 0.14/0.35 (~![X: $i, Y: $i] : ((~(point(X) & line(Y))) | ?[Z: $i] : (point(Z) & incident_point_and_line(Z, Y)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.14/0.35 tff(35,plain,
% 0.14/0.35 (point(X!1) & line(Y!0) & ![Z: $i] : (~(point(Z) & incident_point_and_line(Z, Y!0)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.14/0.35 tff(36,plain,
% 0.14/0.35 (line(Y!0)),
% 0.14/0.35 inference(and_elim,[status(thm)],[35])).
% 0.14/0.35 tff(37,plain,
% 0.14/0.35 (point(X!1)),
% 0.14/0.35 inference(and_elim,[status(thm)],[35])).
% 0.14/0.35 tff(38,plain,
% 0.14/0.35 (^[L: $i, A: $i] : refl((line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L))) <=> (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(39,plain,
% 0.14/0.35 (![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L))) <=> ![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[38])).
% 0.14/0.35 tff(40,plain,
% 0.14/0.35 (^[L: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((line(L) & point(A)) <=> (~((~line(L)) | (~point(A))))), ((~(line(L) & point(A))) <=> (~(~((~line(L)) | (~point(A))))))), rewrite((~(~((~line(L)) | (~point(A))))) <=> ((~line(L)) | (~point(A)))), ((~(line(L) & point(A))) <=> ((~line(L)) | (~point(A))))), ((line(orthogonal_through_point(L, A)) | (~(line(L) & point(A)))) <=> (line(orthogonal_through_point(L, A)) | ((~line(L)) | (~point(A)))))), rewrite((line(orthogonal_through_point(L, A)) | ((~line(L)) | (~point(A)))) <=> (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))), ((line(orthogonal_through_point(L, A)) | (~(line(L) & point(A)))) <=> (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(41,plain,
% 0.14/0.35 (![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~(line(L) & point(A)))) <=> ![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[40])).
% 0.14/0.35 tff(42,plain,
% 0.14/0.35 (![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~(line(L) & point(A)))) <=> ![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~(line(L) & point(A))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(43,plain,
% 0.14/0.35 (^[L: $i, A: $i] : rewrite(((line(L) & point(A)) => line(orthogonal_through_point(L, A))) <=> (line(orthogonal_through_point(L, A)) | (~(line(L) & point(A)))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(44,plain,
% 0.14/0.35 (![L: $i, A: $i] : ((line(L) & point(A)) => line(orthogonal_through_point(L, A))) <=> ![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~(line(L) & point(A))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[43])).
% 0.14/0.35 tff(45,axiom,(![L: $i, A: $i] : ((line(L) & point(A)) => line(orthogonal_through_point(L, A)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax','orth1')).
% 0.14/0.35 tff(46,plain,
% 0.14/0.35 (![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~(line(L) & point(A))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.14/0.35 tff(47,plain,
% 0.14/0.35 (![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~(line(L) & point(A))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.14/0.35 tff(48,plain,(
% 0.14/0.35 ![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~(line(L) & point(A))))),
% 0.14/0.35 inference(skolemize,[status(sab)],[47])).
% 0.14/0.35 tff(49,plain,
% 0.14/0.35 (![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.14/0.35 tff(50,plain,
% 0.14/0.35 (![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.14/0.35 tff(51,plain,
% 0.14/0.35 (((~![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))) | ((~point(X!1)) | (~line(Y!0)) | line(orthogonal_through_point(Y!0, X!1)))) <=> ((~![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))) | (~point(X!1)) | (~line(Y!0)) | line(orthogonal_through_point(Y!0, X!1)))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(52,plain,
% 0.14/0.35 ((line(orthogonal_through_point(Y!0, X!1)) | (~point(X!1)) | (~line(Y!0))) <=> ((~point(X!1)) | (~line(Y!0)) | line(orthogonal_through_point(Y!0, X!1)))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(53,plain,
% 0.14/0.35 (((~![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))) | (line(orthogonal_through_point(Y!0, X!1)) | (~point(X!1)) | (~line(Y!0)))) <=> ((~![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))) | ((~point(X!1)) | (~line(Y!0)) | line(orthogonal_through_point(Y!0, X!1))))),
% 0.14/0.35 inference(monotonicity,[status(thm)],[52])).
% 0.14/0.35 tff(54,plain,
% 0.14/0.35 (((~![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))) | (line(orthogonal_through_point(Y!0, X!1)) | (~point(X!1)) | (~line(Y!0)))) <=> ((~![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))) | (~point(X!1)) | (~line(Y!0)) | line(orthogonal_through_point(Y!0, X!1)))),
% 0.14/0.35 inference(transitivity,[status(thm)],[53, 51])).
% 0.14/0.35 tff(55,plain,
% 0.14/0.35 ((~![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))) | (line(orthogonal_through_point(Y!0, X!1)) | (~point(X!1)) | (~line(Y!0)))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(56,plain,
% 0.14/0.35 ((~![L: $i, A: $i] : (line(orthogonal_through_point(L, A)) | (~point(A)) | (~line(L)))) | (~point(X!1)) | (~line(Y!0)) | line(orthogonal_through_point(Y!0, X!1))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.14/0.35 tff(57,plain,
% 0.14/0.35 (line(orthogonal_through_point(Y!0, X!1))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[56, 50, 37, 36])).
% 0.14/0.35 tff(58,plain,
% 0.14/0.35 (^[L: $i, M: $i] : refl(((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M))) <=> ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(59,plain,
% 0.14/0.35 (![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M))) <=> ![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[58])).
% 0.14/0.35 tff(60,plain,
% 0.14/0.35 (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((line(L) & line(M) & convergent_lines(L, M)) <=> (~((~convergent_lines(L, M)) | (~line(L)) | (~line(M))))), ((~(line(L) & line(M) & convergent_lines(L, M))) <=> (~(~((~convergent_lines(L, M)) | (~line(L)) | (~line(M))))))), rewrite((~(~((~convergent_lines(L, M)) | (~line(L)) | (~line(M))))) <=> ((~convergent_lines(L, M)) | (~line(L)) | (~line(M)))), ((~(line(L) & line(M) & convergent_lines(L, M))) <=> ((~convergent_lines(L, M)) | (~line(L)) | (~line(M))))), ((point(intersection_point(L, M)) | (~(line(L) & line(M) & convergent_lines(L, M)))) <=> (point(intersection_point(L, M)) | ((~convergent_lines(L, M)) | (~line(L)) | (~line(M)))))), rewrite((point(intersection_point(L, M)) | ((~convergent_lines(L, M)) | (~line(L)) | (~line(M)))) <=> ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))), ((point(intersection_point(L, M)) | (~(line(L) & line(M) & convergent_lines(L, M)))) <=> ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(61,plain,
% 0.14/0.35 (![L: $i, M: $i] : (point(intersection_point(L, M)) | (~(line(L) & line(M) & convergent_lines(L, M)))) <=> ![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[60])).
% 0.14/0.35 tff(62,plain,
% 0.14/0.35 (![L: $i, M: $i] : (point(intersection_point(L, M)) | (~(line(L) & line(M) & convergent_lines(L, M)))) <=> ![L: $i, M: $i] : (point(intersection_point(L, M)) | (~(line(L) & line(M) & convergent_lines(L, M))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(63,plain,
% 0.14/0.35 (^[L: $i, M: $i] : trans(monotonicity(rewrite(((line(L) & line(M)) & convergent_lines(L, M)) <=> (line(L) & line(M) & convergent_lines(L, M))), ((((line(L) & line(M)) & convergent_lines(L, M)) => point(intersection_point(L, M))) <=> ((line(L) & line(M) & convergent_lines(L, M)) => point(intersection_point(L, M))))), rewrite(((line(L) & line(M) & convergent_lines(L, M)) => point(intersection_point(L, M))) <=> (point(intersection_point(L, M)) | (~(line(L) & line(M) & convergent_lines(L, M))))), ((((line(L) & line(M)) & convergent_lines(L, M)) => point(intersection_point(L, M))) <=> (point(intersection_point(L, M)) | (~(line(L) & line(M) & convergent_lines(L, M))))))),
% 0.14/0.35 inference(bind,[status(th)],[])).
% 0.14/0.35 tff(64,plain,
% 0.14/0.35 (![L: $i, M: $i] : (((line(L) & line(M)) & convergent_lines(L, M)) => point(intersection_point(L, M))) <=> ![L: $i, M: $i] : (point(intersection_point(L, M)) | (~(line(L) & line(M) & convergent_lines(L, M))))),
% 0.14/0.35 inference(quant_intro,[status(thm)],[63])).
% 0.14/0.35 tff(65,axiom,(![L: $i, M: $i] : (((line(L) & line(M)) & convergent_lines(L, M)) => point(intersection_point(L, M)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax','int1')).
% 0.14/0.35 tff(66,plain,
% 0.14/0.36 (![L: $i, M: $i] : (point(intersection_point(L, M)) | (~(line(L) & line(M) & convergent_lines(L, M))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.14/0.36 tff(67,plain,
% 0.14/0.36 (![L: $i, M: $i] : (point(intersection_point(L, M)) | (~(line(L) & line(M) & convergent_lines(L, M))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.14/0.36 tff(68,plain,(
% 0.14/0.36 ![L: $i, M: $i] : (point(intersection_point(L, M)) | (~(line(L) & line(M) & convergent_lines(L, M))))),
% 0.14/0.36 inference(skolemize,[status(sab)],[67])).
% 0.14/0.36 tff(69,plain,
% 0.14/0.36 (![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.14/0.36 tff(70,plain,
% 0.14/0.36 (![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.14/0.36 tff(71,plain,
% 0.14/0.36 (((~![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))) | ((~line(Y!0)) | (~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0)) | (~line(orthogonal_through_point(Y!0, X!1))))) <=> ((~![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))) | (~line(Y!0)) | (~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0)) | (~line(orthogonal_through_point(Y!0, X!1))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(72,plain,
% 0.14/0.36 (((~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0)) | (~line(orthogonal_through_point(Y!0, X!1))) | (~line(Y!0))) <=> ((~line(Y!0)) | (~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0)) | (~line(orthogonal_through_point(Y!0, X!1))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(73,plain,
% 0.14/0.36 (((~![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))) | ((~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0)) | (~line(orthogonal_through_point(Y!0, X!1))) | (~line(Y!0)))) <=> ((~![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))) | ((~line(Y!0)) | (~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0)) | (~line(orthogonal_through_point(Y!0, X!1)))))),
% 0.14/0.36 inference(monotonicity,[status(thm)],[72])).
% 0.14/0.36 tff(74,plain,
% 0.14/0.36 (((~![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))) | ((~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0)) | (~line(orthogonal_through_point(Y!0, X!1))) | (~line(Y!0)))) <=> ((~![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))) | (~line(Y!0)) | (~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0)) | (~line(orthogonal_through_point(Y!0, X!1))))),
% 0.14/0.36 inference(transitivity,[status(thm)],[73, 71])).
% 0.14/0.36 tff(75,plain,
% 0.14/0.36 ((~![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))) | ((~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0)) | (~line(orthogonal_through_point(Y!0, X!1))) | (~line(Y!0)))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(76,plain,
% 0.14/0.36 ((~![L: $i, M: $i] : ((~convergent_lines(L, M)) | point(intersection_point(L, M)) | (~line(L)) | (~line(M)))) | (~line(Y!0)) | (~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0)) | (~line(orthogonal_through_point(Y!0, X!1)))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.14/0.36 tff(77,plain,
% 0.14/0.36 (point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[76, 70, 36, 57, 20])).
% 0.14/0.36 tff(78,plain,
% 0.14/0.36 (^[Z: $i] : refl(((~point(Z)) | (~incident_point_and_line(Z, Y!0))) <=> ((~point(Z)) | (~incident_point_and_line(Z, Y!0))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(79,plain,
% 0.14/0.36 (![Z: $i] : ((~point(Z)) | (~incident_point_and_line(Z, Y!0))) <=> ![Z: $i] : ((~point(Z)) | (~incident_point_and_line(Z, Y!0)))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[78])).
% 0.14/0.36 tff(80,plain,
% 0.14/0.36 (^[Z: $i] : trans(monotonicity(rewrite((point(Z) & incident_point_and_line(Z, Y!0)) <=> (~((~point(Z)) | (~incident_point_and_line(Z, Y!0))))), ((~(point(Z) & incident_point_and_line(Z, Y!0))) <=> (~(~((~point(Z)) | (~incident_point_and_line(Z, Y!0))))))), rewrite((~(~((~point(Z)) | (~incident_point_and_line(Z, Y!0))))) <=> ((~point(Z)) | (~incident_point_and_line(Z, Y!0)))), ((~(point(Z) & incident_point_and_line(Z, Y!0))) <=> ((~point(Z)) | (~incident_point_and_line(Z, Y!0)))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(81,plain,
% 0.14/0.36 (![Z: $i] : (~(point(Z) & incident_point_and_line(Z, Y!0))) <=> ![Z: $i] : ((~point(Z)) | (~incident_point_and_line(Z, Y!0)))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[80])).
% 0.14/0.36 tff(82,plain,
% 0.14/0.36 (![Z: $i] : (~(point(Z) & incident_point_and_line(Z, Y!0)))),
% 0.14/0.36 inference(and_elim,[status(thm)],[35])).
% 0.14/0.36 tff(83,plain,
% 0.14/0.36 (![Z: $i] : ((~point(Z)) | (~incident_point_and_line(Z, Y!0)))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.14/0.36 tff(84,plain,
% 0.14/0.36 (![Z: $i] : ((~point(Z)) | (~incident_point_and_line(Z, Y!0)))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.14/0.36 tff(85,plain,
% 0.14/0.36 (((~![Z: $i] : ((~point(Z)) | (~incident_point_and_line(Z, Y!0)))) | ((~point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0))) | (~incident_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)))) <=> ((~![Z: $i] : ((~point(Z)) | (~incident_point_and_line(Z, Y!0)))) | (~point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0))) | (~incident_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(86,plain,
% 0.14/0.36 ((~![Z: $i] : ((~point(Z)) | (~incident_point_and_line(Z, Y!0)))) | ((~point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0))) | (~incident_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(87,plain,
% 0.14/0.36 ((~![Z: $i] : ((~point(Z)) | (~incident_point_and_line(Z, Y!0)))) | (~point(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0))) | (~incident_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.14/0.36 tff(88,plain,
% 0.14/0.36 (~incident_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[87, 84, 77])).
% 0.14/0.36 tff(89,plain,
% 0.14/0.36 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(90,plain,
% 0.14/0.36 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[89])).
% 0.14/0.36 tff(91,plain,
% 0.14/0.36 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(92,plain,
% 0.14/0.36 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(93,plain,
% 0.14/0.36 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[92])).
% 0.14/0.36 tff(94,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.14/0.36 tff(95,plain,
% 0.14/0.36 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.14/0.36 tff(96,plain,
% 0.14/0.36 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.14/0.36 tff(97,plain,(
% 0.14/0.36 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.14/0.36 inference(skolemize,[status(sab)],[96])).
% 0.14/0.36 tff(98,plain,
% 0.14/0.36 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.14/0.36 tff(99,plain,
% 0.14/0.36 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(100,plain,
% 0.14/0.36 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(101,plain,
% 0.14/0.36 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(orthogonal_through_point(Y!0, X!1), Y!0)) | (~apart_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.14/0.36 tff(102,plain,
% 0.14/0.36 (~apart_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[101, 98, 20])).
% 0.14/0.36 tff(103,plain,
% 0.14/0.36 ((~(incident_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0) <=> (~apart_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)))) | incident_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0) | apart_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(104,plain,
% 0.14/0.36 (~(incident_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0) <=> (~apart_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[103, 102, 88])).
% 0.14/0.36 tff(105,plain,
% 0.14/0.36 (^[X: $i, Y: $i] : refl((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(106,plain,
% 0.14/0.36 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[105])).
% 0.14/0.36 tff(107,plain,
% 0.14/0.36 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(108,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.14/0.36 tff(109,plain,
% 0.14/0.36 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.14/0.36 tff(110,plain,(
% 0.14/0.36 ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.14/0.36 inference(skolemize,[status(sab)],[109])).
% 0.14/0.36 tff(111,plain,
% 0.14/0.36 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.14/0.36 tff(112,plain,
% 0.14/0.36 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0) <=> (~apart_point_and_line(intersection_point(orthogonal_through_point(Y!0, X!1), Y!0), Y!0)))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(113,plain,
% 0.14/0.36 ($false),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[112, 111, 104])).
% 0.14/0.36 % SZS output end Proof
%------------------------------------------------------------------------------