TSTP Solution File: GEO197+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO197+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 20:35:33 EDT 2022
% Result : Theorem 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO197+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 06:49:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55 % SZS output start Proof
% 0.20/0.55 tff(convergent_lines_type, type, (
% 0.20/0.55 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.55 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.55 tptp_fun_Z_0: $i)).
% 0.20/0.55 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.55 tptp_fun_Y_1: $i)).
% 0.20/0.55 tff(unorthogonal_lines_type, type, (
% 0.20/0.55 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.55 tff(orthogonal_through_point_type, type, (
% 0.20/0.55 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.20/0.55 tff(intersection_point_type, type, (
% 0.20/0.55 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.55 tff(distinct_lines_type, type, (
% 0.20/0.55 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.55 tff(distinct_points_type, type, (
% 0.20/0.55 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.55 tff(tptp_fun_X_2_type, type, (
% 0.20/0.55 tptp_fun_X_2: $i)).
% 0.20/0.55 tff(apart_point_and_line_type, type, (
% 0.20/0.55 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.55 tff(incident_point_and_line_type, type, (
% 0.20/0.55 incident_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.55 tff(1,plain,
% 0.20/0.55 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(2,plain,
% 0.20/0.55 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.55 tff(3,plain,
% 0.20/0.55 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 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')).
% 0.20/0.55 tff(5,plain,
% 0.20/0.55 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.55 tff(6,plain,(
% 0.20/0.55 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.55 inference(skolemize,[status(sab)],[5])).
% 0.20/0.55 tff(7,plain,
% 0.20/0.55 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.55 tff(8,plain,
% 0.20/0.55 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(9,plain,
% 0.20/0.55 (~unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.55 tff(10,plain,
% 0.20/0.55 (^[L: $i, M: $i, N: $i] : refl((unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(11,plain,
% 0.20/0.55 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.55 tff(12,plain,
% 0.20/0.55 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(13,plain,
% 0.20/0.55 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.55 tff(14,plain,
% 0.20/0.55 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(15,plain,
% 0.20/0.55 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(16,plain,
% 0.20/0.55 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.55 tff(17,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.20/0.55 tff(18,plain,
% 0.20/0.55 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.55 tff(19,plain,
% 0.20/0.55 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.55 tff(20,plain,(
% 0.20/0.55 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.20/0.55 inference(skolemize,[status(sab)],[19])).
% 0.20/0.55 tff(21,plain,
% 0.20/0.55 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.55 tff(22,plain,
% 0.20/0.55 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.20/0.55 tff(23,plain,
% 0.20/0.55 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | (~convergent_lines(Y!1, Y!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | (~convergent_lines(Y!1, Y!1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(24,plain,
% 0.20/0.55 ((unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | (~convergent_lines(Y!1, Y!1))) <=> (unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | (~convergent_lines(Y!1, Y!1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(25,plain,
% 0.20/0.55 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | (~convergent_lines(Y!1, Y!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | (~convergent_lines(Y!1, Y!1))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[24])).
% 0.20/0.55 tff(26,plain,
% 0.20/0.55 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | (~convergent_lines(Y!1, Y!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | (~convergent_lines(Y!1, Y!1)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.56 tff(27,plain,
% 0.20/0.56 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | (~convergent_lines(Y!1, Y!1)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(28,plain,
% 0.20/0.56 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(Y!1, intersection_point(Z!0, Y!1)), Y!1) | (~convergent_lines(Y!1, Y!1))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.56 tff(29,plain,
% 0.20/0.56 (~convergent_lines(Y!1, Y!1)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[28, 22, 9])).
% 0.20/0.56 tff(30,assumption,(~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))), introduced(assumption)).
% 0.20/0.56 tff(31,plain,
% 0.20/0.56 (^[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))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(32,plain,
% 0.20/0.56 (![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)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.56 tff(33,plain,
% 0.20/0.56 (![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)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(34,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')).
% 0.20/0.56 tff(35,plain,
% 0.20/0.56 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.56 tff(36,plain,(
% 0.20/0.56 ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.56 inference(skolemize,[status(sab)],[35])).
% 0.20/0.56 tff(37,plain,
% 0.20/0.56 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.56 tff(38,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(Z!0, Y!1), X!2) <=> (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(39,plain,
% 0.20/0.56 (incident_point_and_line(intersection_point(Z!0, Y!1), X!2) <=> (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.56 tff(40,plain,
% 0.20/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(41,plain,
% 0.20/0.56 ((~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & incident_point_and_line(intersection_point(X, Y), Z)) => incident_point_and_line(intersection_point(Z, Y), X))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(42,axiom,(~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & incident_point_and_line(intersection_point(X, Y), Z)) => incident_point_and_line(intersection_point(Z, Y), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.56 tff(43,plain,
% 0.20/0.56 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.56 tff(44,plain,
% 0.20/0.56 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.20/0.56 tff(45,plain,
% 0.20/0.56 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.56 tff(46,plain,
% 0.20/0.56 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.20/0.56 tff(47,plain,
% 0.20/0.56 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.20/0.56 tff(48,plain,
% 0.20/0.56 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.20/0.56 tff(49,plain,
% 0.20/0.56 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Z, Y), X))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[48, 40])).
% 0.20/0.56 tff(50,plain,(
% 0.20/0.56 ~((~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & incident_point_and_line(intersection_point(X!2, Y!1), Z!0))) | incident_point_and_line(intersection_point(Z!0, Y!1), X!2))),
% 0.20/0.56 inference(skolemize,[status(sab)],[49])).
% 0.20/0.56 tff(51,plain,
% 0.20/0.56 (~incident_point_and_line(intersection_point(Z!0, Y!1), X!2)),
% 0.20/0.56 inference(or_elim,[status(thm)],[50])).
% 0.20/0.56 tff(52,plain,
% 0.20/0.56 ((~(incident_point_and_line(intersection_point(Z!0, Y!1), X!2) <=> (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))) | incident_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2)),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(53,plain,
% 0.20/0.56 ((~(incident_point_and_line(intersection_point(Z!0, Y!1), X!2) <=> (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.56 tff(54,plain,
% 0.20/0.56 (apart_point_and_line(intersection_point(Z!0, Y!1), X!2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[53, 39])).
% 0.20/0.56 tff(55,plain,
% 0.20/0.56 (convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & incident_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.20/0.56 inference(or_elim,[status(thm)],[50])).
% 0.20/0.56 tff(56,plain,
% 0.20/0.56 (convergent_lines(X!2, Y!1)),
% 0.20/0.56 inference(and_elim,[status(thm)],[55])).
% 0.20/0.56 tff(57,plain,
% 0.20/0.56 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(58,plain,
% 0.20/0.56 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.56 tff(59,plain,
% 0.20/0.56 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(60,plain,
% 0.20/0.56 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(61,plain,
% 0.20/0.56 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.56 tff(62,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.20/0.56 tff(63,plain,
% 0.20/0.56 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.56 tff(64,plain,
% 0.20/0.56 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.56 tff(65,plain,(
% 0.20/0.56 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.56 inference(skolemize,[status(sab)],[64])).
% 0.20/0.56 tff(66,plain,
% 0.20/0.56 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.56 tff(67,plain,
% 0.20/0.56 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(68,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(69,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.56 tff(70,plain,
% 0.20/0.56 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[69, 66, 56])).
% 0.20/0.56 tff(71,plain,
% 0.20/0.56 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(72,plain,
% 0.20/0.56 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.56 tff(73,plain,
% 0.20/0.56 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(74,plain,
% 0.20/0.56 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | apart_point_and_line(Z, Y)) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))))), rewrite((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(75,plain,
% 0.20/0.56 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.56 tff(76,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.20/0.56 tff(77,plain,
% 0.20/0.56 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.56 tff(78,plain,
% 0.20/0.56 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.20/0.56 tff(79,plain,(
% 0.20/0.56 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.56 inference(skolemize,[status(sab)],[78])).
% 0.20/0.56 tff(80,plain,
% 0.20/0.56 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.20/0.56 tff(81,plain,
% 0.20/0.56 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(82,plain,
% 0.20/0.56 ((distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(83,plain,
% 0.20/0.56 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[82])).
% 0.20/0.56 tff(84,plain,
% 0.20/0.56 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[83, 81])).
% 0.20/0.56 tff(85,plain,
% 0.20/0.56 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(86,plain,
% 0.20/0.56 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.56 tff(87,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[86, 80, 70, 54, 30])).
% 0.20/0.56 tff(88,plain,(distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.56 tff(89,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(X!2, Y!1), Z!0) <=> (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(90,plain,
% 0.20/0.56 (incident_point_and_line(intersection_point(X!2, Y!1), Z!0) <=> (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[89, 37])).
% 0.20/0.56 tff(91,plain,
% 0.20/0.56 (incident_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.20/0.56 inference(and_elim,[status(thm)],[55])).
% 0.20/0.56 tff(92,plain,
% 0.20/0.56 ((~(incident_point_and_line(intersection_point(X!2, Y!1), Z!0) <=> (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) | (~incident_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(93,plain,
% 0.20/0.56 ((~(incident_point_and_line(intersection_point(X!2, Y!1), Z!0) <=> (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.20/0.56 tff(94,plain,
% 0.20/0.56 (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[93, 90])).
% 0.20/0.56 tff(95,plain,
% 0.20/0.56 (convergent_lines(Z!0, Y!1)),
% 0.20/0.56 inference(and_elim,[status(thm)],[55])).
% 0.20/0.56 tff(96,plain,
% 0.20/0.56 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(97,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(98,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.56 tff(99,plain,
% 0.20/0.56 (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[98, 66, 95])).
% 0.20/0.56 tff(100,plain,
% 0.20/0.56 (^[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))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(101,plain,
% 0.20/0.56 (![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)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.56 tff(102,plain,
% 0.20/0.56 (![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)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(103,plain,
% 0.20/0.56 (^[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))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(104,plain,
% 0.20/0.56 (![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)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.56 tff(105,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')).
% 0.20/0.56 tff(106,plain,
% 0.20/0.56 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.56 tff(107,plain,
% 0.20/0.56 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.56 tff(108,plain,(
% 0.20/0.56 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.56 inference(skolemize,[status(sab)],[107])).
% 0.20/0.56 tff(109,plain,
% 0.20/0.56 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.56 tff(110,plain,
% 0.20/0.56 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(111,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(112,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.56 tff(113,plain,
% 0.20/0.56 (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[112, 109, 95])).
% 0.20/0.56 tff(114,plain,
% 0.20/0.56 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(115,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(116,plain,
% 0.20/0.56 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.56 tff(117,plain,
% 0.20/0.56 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[116, 109, 56])).
% 0.20/0.56 tff(118,plain,
% 0.20/0.56 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(119,plain,
% 0.20/0.56 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[118])).
% 0.20/0.56 tff(120,plain,
% 0.20/0.56 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))))), rewrite((~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(121,plain,
% 0.20/0.56 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.56 tff(122,plain,
% 0.20/0.56 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(123,plain,
% 0.20/0.56 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(124,plain,
% 0.20/0.56 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[123])).
% 0.20/0.56 tff(125,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.20/0.56 tff(126,plain,
% 0.20/0.56 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.56 tff(127,plain,
% 0.20/0.56 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.20/0.56 tff(128,plain,(
% 0.20/0.56 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.20/0.56 inference(skolemize,[status(sab)],[127])).
% 0.20/0.56 tff(129,plain,
% 0.20/0.56 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.20/0.57 tff(130,plain,
% 0.20/0.57 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.20/0.57 tff(131,plain,
% 0.20/0.57 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(132,plain,
% 0.20/0.57 ((apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(133,plain,
% 0.20/0.57 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.57 tff(134,plain,
% 0.20/0.57 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 0.20/0.57 inference(transitivity,[status(thm)],[133, 131])).
% 0.20/0.57 tff(135,plain,
% 0.20/0.57 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(136,plain,
% 0.20/0.57 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~distinct_lines(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.57 tff(137,plain,
% 0.20/0.57 ((~distinct_lines(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[136, 130, 117, 113, 99, 94])).
% 0.20/0.57 tff(138,plain,
% 0.20/0.57 (~distinct_lines(Z!0, Y!1)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[137, 88])).
% 0.20/0.57 tff(139,plain,
% 0.20/0.57 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(140,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.57 tff(141,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(142,plain,
% 0.20/0.57 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(143,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[142])).
% 0.20/0.57 tff(144,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.20/0.57 tff(145,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.57 tff(146,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.20/0.57 tff(147,plain,(
% 0.20/0.57 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(skolemize,[status(sab)],[146])).
% 0.20/0.57 tff(148,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.20/0.57 tff(149,plain,
% 0.20/0.57 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Z!0, Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(Z!0, Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, Z!0)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(150,plain,
% 0.20/0.57 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Z!0, Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, Z!0)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(151,plain,
% 0.20/0.57 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(Z!0, Y!1) | convergent_lines(Y!1, Y!1) | (~convergent_lines(Y!1, Z!0))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.57 tff(152,plain,
% 0.20/0.57 (~convergent_lines(Y!1, Z!0)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[151, 148, 138, 29])).
% 0.20/0.57 tff(153,plain,
% 0.20/0.57 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(154,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[153])).
% 0.20/0.57 tff(155,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(156,plain,
% 0.20/0.57 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(157,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.57 tff(158,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.20/0.57 tff(159,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.57 tff(160,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.20/0.57 tff(161,plain,(
% 0.20/0.57 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(skolemize,[status(sab)],[160])).
% 0.20/0.57 tff(162,plain,
% 0.20/0.57 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.20/0.57 tff(163,plain,
% 0.20/0.57 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, Z!0) | convergent_lines(Z!0, Z!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, Z!0) | convergent_lines(Z!0, Z!0))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(164,plain,
% 0.20/0.57 ((convergent_lines(Y!1, Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, Y!1))) <=> ((~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, Z!0) | convergent_lines(Z!0, Z!0))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(165,plain,
% 0.20/0.57 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, Z!0) | convergent_lines(Z!0, Z!0)))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[164])).
% 0.20/0.57 tff(166,plain,
% 0.20/0.57 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, Z!0) | convergent_lines(Z!0, Z!0))),
% 0.20/0.57 inference(transitivity,[status(thm)],[165, 163])).
% 0.20/0.57 tff(167,plain,
% 0.20/0.57 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Z!0) | convergent_lines(Z!0, Z!0) | (~convergent_lines(Z!0, Y!1)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(168,plain,
% 0.20/0.57 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(Z!0, Y!1)) | convergent_lines(Y!1, Z!0) | convergent_lines(Z!0, Z!0)),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.57 tff(169,plain,
% 0.20/0.57 (convergent_lines(Z!0, Z!0)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[168, 162, 95, 152])).
% 0.20/0.57 tff(170,plain,
% 0.20/0.57 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(171,plain,
% 0.20/0.57 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.57 tff(172,plain,
% 0.20/0.57 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(173,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.20/0.57 tff(174,plain,
% 0.20/0.57 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.57 tff(175,plain,(
% 0.20/0.57 ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.57 inference(skolemize,[status(sab)],[174])).
% 0.20/0.57 tff(176,plain,
% 0.20/0.57 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.20/0.57 tff(177,plain,
% 0.20/0.57 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(Z!0, Z!0))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(178,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[177, 176, 169])).
% 0.20/0.57 % SZS output end Proof
%------------------------------------------------------------------------------