%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO111-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 : Sat Jun 21 05:05:36 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO111-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 14:26:48 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(inner_point_type, type, (
% 0.20/0.44 inner_point: ( $i * $i ) > $o)).
% 0.20/0.44 tff(ax1_sk1_type, type, (
% 0.20/0.44 ax1_sk1: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.44 tff(sk15_type, type, (
% 0.20/0.44 sk15: $i)).
% 0.20/0.44 tff(sk16_type, type, (
% 0.20/0.44 sk16: $i)).
% 0.20/0.44 tff(sk17_type, type, (
% 0.20/0.44 sk17: $i)).
% 0.20/0.44 tff(sk18_type, type, (
% 0.20/0.44 sk18: $i)).
% 0.20/0.44 tff(sum_type, type, (
% 0.20/0.44 sum: ( $i * $i ) > $i)).
% 0.20/0.44 tff(ax0_sk10_type, type, (
% 0.20/0.44 ax0_sk10: ( $i * $i ) > $i)).
% 0.20/0.44 tff(ax0_sk9_type, type, (
% 0.20/0.44 ax0_sk9: ( $i * $i ) > $i)).
% 0.20/0.44 tff(ax0_sk11_type, type, (
% 0.20/0.44 ax0_sk11: ( $i * $i ) > $i)).
% 0.20/0.44 tff(between_c_type, type, (
% 0.20/0.44 between_c: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.44 tff(end_point_type, type, (
% 0.20/0.44 end_point: ( $i * $i ) > $o)).
% 0.20/0.44 tff(incident_c_type, type, (
% 0.20/0.44 incident_c: ( $i * $i ) > $o)).
% 0.20/0.44 tff(part_of_type, type, (
% 0.20/0.44 part_of: ( $i * $i ) > $o)).
% 0.20/0.44 tff(1,plain,
% 0.20/0.44 (between_c(sk15, sk16, sk17, sk18) <=> between_c(sk15, sk16, sk17, sk18)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(2,axiom,(between_c(sk15, sk16, sk17, sk18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem_3_8_1_77')).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (between_c(sk15, sk16, sk17, sk18)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A))) <=> ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(7,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-1.ax','between_c_defn_5')).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.44 tff(9,plain,(
% 0.20/0.44 ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[8])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 (((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A)))) | ((~between_c(sk15, sk16, sk17, sk18)) | inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A)))) | (~between_c(sk15, sk16, sk17, sk18)) | inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A)))) | ((~between_c(sk15, sk16, sk17, sk18)) | inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | inner_point(C, ax1_sk1(D, C, B, A)))) | (~between_c(sk15, sk16, sk17, sk18)) | inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (^[B: $i, A: $i] : refl(((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B)))) <=> ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B)))) <=> ![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B)))) <=> ![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(18,axiom,(![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','c4_39')).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.44 tff(20,plain,(
% 0.20/0.44 ![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[19])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 (((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | ((~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))) | (ax1_sk1(sk18, sk17, sk16, sk15) = sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))) <=> ((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | (~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))) | (ax1_sk1(sk18, sk17, sk16, sk15) = sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 ((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | ((~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))) | (ax1_sk1(sk18, sk17, sk16, sk15) = sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 ((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | (~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))) | (ax1_sk1(sk18, sk17, sk16, sk15) = sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (ax1_sk1(sk18, sk17, sk16, sk15) = sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[24, 21, 14])).
% 0.20/0.44 tff(26,assumption,(sk16 = sk18), introduced(assumption)).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (sk18 = sk16),
% 0.20/0.44 inference(symmetry,[status(thm)],[26])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (between_c(sk15, sk18, sk17, sk18) <=> between_c(sk15, sk16, sk17, sk18)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (between_c(sk15, sk16, sk17, sk18) <=> between_c(sk15, sk18, sk17, sk18)),
% 0.20/0.44 inference(symmetry,[status(thm)],[28])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (between_c(sk15, sk18, sk17, sk18)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[3, 29])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (^[D: $i, A: $i, C: $i] : refl((~between_c(A, D, C, D)) <=> (~between_c(A, D, C, D)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D)) <=> ![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 (![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D)) <=> ![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 (![B: $i, D: $i, A: $i, C: $i] : (~between_c(A, D, C, D)) <=> ![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D))),
% 0.20/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (![B: $i, D: $i, A: $i, C: $i] : ((~(B = D)) | (~between_c(A, B, C, D))) <=> ![B: $i, D: $i, A: $i, C: $i] : (~between_c(A, D, C, D))),
% 0.20/0.44 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (![B: $i, D: $i, A: $i, C: $i] : ((~(B = D)) | (~between_c(A, B, C, D))) <=> ![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D))),
% 0.20/0.44 inference(transitivity,[status(thm)],[35, 34])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (^[B: $i, D: $i, A: $i, C: $i] : rewrite(((~between_c(A, B, C, D)) | (~(B = D))) <=> ((~(B = D)) | (~between_c(A, B, C, D))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | (~(B = D))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~(B = D)) | (~between_c(A, B, C, D)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | (~(B = D))) <=> ![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D))),
% 0.20/0.44 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.44 tff(40,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | (~(B = D)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-1.ax','between_c_defn_1')).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.20/0.44 tff(43,plain,(
% 0.20/0.44 ![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D))),
% 0.20/0.44 inference(skolemize,[status(sab)],[42])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[43, 32])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 ((~![D: $i, A: $i, C: $i] : (~between_c(A, D, C, D))) | (~between_c(sk15, sk18, sk17, sk18))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (~between_c(sk15, sk18, sk17, sk18)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[46, 30])).
% 0.20/0.44 tff(48,plain,(~(sk16 = sk18)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))) = ax1_sk1(sk18, sk17, sk16, sk15)),
% 0.20/0.44 inference(symmetry,[status(thm)],[25])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (ax0_sk11(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = ax0_sk11(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.44 inference(symmetry,[status(thm)],[50])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> end_point(ax0_sk11(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (end_point(ax0_sk11(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.44 inference(symmetry,[status(thm)],[52])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> end_point(sk16, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (end_point(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) <=> end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.44 inference(symmetry,[status(thm)],[54])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A))) <=> ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(59,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-1.ax','between_c_defn_3')).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.45 tff(61,plain,(
% 0.20/0.45 ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[60])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A)))) | ((~between_c(sk15, sk16, sk17, sk18)) | end_point(sk16, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A)))) | (~between_c(sk15, sk16, sk17, sk18)) | end_point(sk16, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A)))) | ((~between_c(sk15, sk16, sk17, sk18)) | end_point(sk16, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(B, ax1_sk1(D, C, B, A)))) | (~between_c(sk15, sk16, sk17, sk18)) | end_point(sk16, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (end_point(sk16, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[65, 62, 3])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[66, 55])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (^[B: $i, A: $i] : refl(((~end_point(A, B)) | end_point(ax0_sk11(A, B), B)) <=> ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B)) <=> ![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B)) <=> ![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(71,axiom,(![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','c6_41')).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.45 tff(73,plain,(
% 0.20/0.45 ![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))),
% 0.20/0.45 inference(skolemize,[status(sab)],[72])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (((~![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))) | ((~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | end_point(ax0_sk11(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))) <=> ((~![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | end_point(ax0_sk11(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 ((~![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))) | ((~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | end_point(ax0_sk11(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 ((~![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | end_point(ax0_sk11(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 ((~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | end_point(ax0_sk11(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[77, 74])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 (end_point(ax0_sk11(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[78, 67])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[79, 53])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) <=> end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.45 inference(symmetry,[status(thm)],[81])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A))) <=> ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(86,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-1.ax','between_c_defn_4')).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.45 tff(88,plain,(
% 0.20/0.45 ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[87])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 (((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A)))) | ((~between_c(sk15, sk16, sk17, sk18)) | end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A)))) | (~between_c(sk15, sk16, sk17, sk18)) | end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A)))) | ((~between_c(sk15, sk16, sk17, sk18)) | end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | end_point(D, ax1_sk1(D, C, B, A)))) | (~between_c(sk15, sk16, sk17, sk18)) | end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[92, 89, 3])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[93, 82])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (^[B: $i, A: $i] : refl(((~end_point(A, B)) | (~(A = ax0_sk11(A, B)))) <=> ((~end_point(A, B)) | (~(A = ax0_sk11(A, B)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 (![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B)))) <=> ![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 (![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B)))) <=> ![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(98,axiom,(![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','c6_42')).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.45 tff(100,plain,(
% 0.20/0.45 ![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[99])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 (![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (((~![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))) | ((~end_point(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (~(sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)))))) <=> ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))) | (~end_point(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (~(sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))) | ((~end_point(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (~(sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))) | (~end_point(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (~(sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (~(sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[104, 101, 66])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B))) <=> ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B))) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~end_point(A, B)) | (~end_point(C, B))) <=> ((~end_point(A, B)) | (~end_point(C, B)))), ((((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))) <=> (((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))))), rewrite((((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))) <=> ((~end_point(A, B)) | (~end_point(D, B)) | (~end_point(C, B)))), ((((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))) <=> ((~end_point(A, B)) | (~end_point(D, B)) | (~end_point(C, B))))), (((((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))) | (A = C)) <=> (((~end_point(A, B)) | (~end_point(D, B)) | (~end_point(C, B))) | (A = C)))), rewrite((((~end_point(A, B)) | (~end_point(D, B)) | (~end_point(C, B))) | (A = C)) <=> ((~end_point(A, B)) | (A = C) | (~end_point(D, B)) | (~end_point(C, B)))), (((((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))) | (A = C)) <=> ((~end_point(A, B)) | (A = C) | (~end_point(D, B)) | (~end_point(C, B))))), ((((((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))) | (A = C)) | (A = D)) <=> (((~end_point(A, B)) | (A = C) | (~end_point(D, B)) | (~end_point(C, B))) | (A = D)))), rewrite((((~end_point(A, B)) | (A = C) | (~end_point(D, B)) | (~end_point(C, B))) | (A = D)) <=> ((~end_point(A, B)) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))), ((((((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))) | (A = C)) | (A = D)) <=> ((~end_point(A, B)) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B))))), (((((((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))) | (A = C)) | (A = D)) | (C = D)) <=> (((~end_point(A, B)) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B))) | (C = D)))), rewrite((((~end_point(A, B)) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B))) | (C = D)) <=> ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))), (((((((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))) | (A = C)) | (A = D)) | (C = D)) <=> ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((((((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))) | (A = C)) | (A = D)) | (C = D)) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.45 tff(111,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((((((~end_point(A, B)) | (~end_point(C, B))) | (~end_point(D, B))) | (A = C)) | (A = D)) | (C = D))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','c5_40')).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.20/0.45 tff(114,plain,(
% 0.20/0.45 ![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[113])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | ((sk16 = sk18) | (sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | (sk16 = sk18) | (sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (((~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))) <=> ((sk16 = sk18) | (sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | ((~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | ((sk16 = sk18) | (sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 (((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | ((~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | (sk16 = sk18) | (sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18))),
% 0.20/0.46 inference(transitivity,[status(thm)],[118, 116])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 ((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | ((~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 ((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | (sk16 = sk18) | (sk16 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 ((sk16 = sk18) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[121, 115, 105, 94, 67])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 ((sk16 = sk18) | (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[122, 80])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[123, 48])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 (sk18 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.46 inference(symmetry,[status(thm)],[124])).
% 0.20/0.46 tff(126,assumption,(~(sk16 = sk18)), introduced(assumption)).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (ax0_sk11(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = ax0_sk11(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.47 inference(symmetry,[status(thm)],[127])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> end_point(ax0_sk11(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[128])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 (end_point(ax0_sk11(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.47 inference(symmetry,[status(thm)],[129])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (((~![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))) | ((~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | end_point(ax0_sk11(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))) <=> ((~![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | end_point(ax0_sk11(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 ((~![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))) | ((~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | end_point(ax0_sk11(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 ((~![B: $i, A: $i] : ((~end_point(A, B)) | end_point(ax0_sk11(A, B), B))) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | end_point(ax0_sk11(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 ((~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | end_point(ax0_sk11(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[133, 74])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 (end_point(ax0_sk11(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[134, 94])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[135, 130])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 ((ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) <=> (sk18 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.47 inference(commutativity,[status(thm)],[])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 ((sk18 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) <=> (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18)),
% 0.20/0.47 inference(symmetry,[status(thm)],[137])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 ((~(sk18 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> (~(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[138])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 (((~![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))) | ((~end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | (~(sk18 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))))) <=> ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))) | (~end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | (~(sk18 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))) | ((~end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | (~(sk18 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~(A = ax0_sk11(A, B))))) | (~end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | (~(sk18 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (~(sk18 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[142, 101, 93])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (~(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | ((sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | (sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (((~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | (sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))) <=> ((sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(147,plain,
% 0.20/0.48 (((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | ((~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | (sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | ((sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 (((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | ((~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | (sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | (sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[147, 145])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 ((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | ((~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | (sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 ((~![B: $i, D: $i, A: $i, C: $i] : ((~end_point(A, B)) | (C = D) | (A = C) | (A = D) | (~end_point(D, B)) | (~end_point(C, B)))) | (sk16 = sk18) | (~end_point(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(sk16, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 ((sk16 = sk18) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[150, 115, 94, 67])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 ((sk16 = sk18) | (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[151, 144, 136])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[152, 126])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15) <=> part_of(ax1_sk1(sk18, sk17, sk16, sk15), sk15)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 (part_of(ax1_sk1(sk18, sk17, sk16, sk15), sk15) <=> part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)),
% 0.20/0.48 inference(symmetry,[status(thm)],[154])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 (^[B: $i, D: $i, A: $i, C: $i] : refl(((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A)) <=> ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A)) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A)) <=> ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(159,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-1.ax','between_c_defn_2')).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.20/0.48 tff(161,plain,(
% 0.20/0.48 ![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A))),
% 0.20/0.48 inference(skolemize,[status(sab)],[160])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 (![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A))) | ((~between_c(sk15, sk16, sk17, sk18)) | part_of(ax1_sk1(sk18, sk17, sk16, sk15), sk15))) <=> ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A))) | (~between_c(sk15, sk16, sk17, sk18)) | part_of(ax1_sk1(sk18, sk17, sk16, sk15), sk15))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A))) | ((~between_c(sk15, sk16, sk17, sk18)) | part_of(ax1_sk1(sk18, sk17, sk16, sk15), sk15))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 ((~![B: $i, D: $i, A: $i, C: $i] : ((~between_c(A, B, C, D)) | part_of(ax1_sk1(D, C, B, A), A))) | (~between_c(sk15, sk16, sk17, sk18)) | part_of(ax1_sk1(sk18, sk17, sk16, sk15), sk15)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 (part_of(ax1_sk1(sk18, sk17, sk16, sk15), sk15)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[165, 162, 3])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 (part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[166, 155])).
% 0.20/0.48 tff(168,assumption,(~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)), introduced(assumption)).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.20/0.48 tff(170,plain,(part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (incident_c(sk17, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> incident_c(sk17, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 (incident_c(sk17, ax1_sk1(sk18, sk17, sk16, sk15)) <=> incident_c(sk17, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.48 inference(symmetry,[status(thm)],[171])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (^[B: $i, A: $i] : refl(((~inner_point(A, B)) | incident_c(A, B)) <=> ((~inner_point(A, B)) | incident_c(A, B)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B)) <=> ![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[173])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B)) <=> ![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(176,axiom,(![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','inner_point_defn_21')).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.48 tff(178,plain,(
% 0.20/0.48 ![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B))),
% 0.20/0.48 inference(skolemize,[status(sab)],[177])).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 (![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 (((~![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B))) | ((~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))) | incident_c(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> ((~![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B))) | (~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))) | incident_c(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(181,plain,
% 0.20/0.48 ((~![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B))) | ((~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))) | incident_c(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 ((~![B: $i, A: $i] : ((~inner_point(A, B)) | incident_c(A, B))) | (~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))) | incident_c(sk17, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (incident_c(sk17, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[182, 179, 14])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 (incident_c(sk17, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[183, 172])).
% 0.20/0.48 tff(185,assumption,(~incident_c(sk17, sk15)), introduced(assumption)).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 (^[B: $i, A: $i, C: $i] : refl((incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B))) <=> (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(187,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B))) <=> ![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[186])).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B))) <=> ![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(189,plain,
% 0.20/0.48 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite(((~part_of(A, B)) | (~incident_c(C, A))) <=> ((~incident_c(C, A)) | (~part_of(A, B)))), ((((~part_of(A, B)) | (~incident_c(C, A))) | incident_c(C, B)) <=> (((~incident_c(C, A)) | (~part_of(A, B))) | incident_c(C, B)))), rewrite((((~incident_c(C, A)) | (~part_of(A, B))) | incident_c(C, B)) <=> (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))), ((((~part_of(A, B)) | (~incident_c(C, A))) | incident_c(C, B)) <=> (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (((~part_of(A, B)) | (~incident_c(C, A))) | incident_c(C, B)) <=> ![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.48 tff(191,axiom,(![B: $i, A: $i, C: $i] : (((~part_of(A, B)) | (~incident_c(C, A))) | incident_c(C, B))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','part_of_defn_1')).
% 0.20/0.48 tff(192,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.20/0.48 tff(194,plain,(
% 0.20/0.48 ![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[193])).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(sk17, sk15) | (~incident_c(sk17, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | incident_c(sk17, sk15) | (~incident_c(sk17, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(sk17, sk15) | (~incident_c(sk17, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | incident_c(sk17, sk15) | (~incident_c(sk17, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[198, 195, 185, 184, 170])).
% 0.20/0.48 tff(200,plain,(incident_c(sk17, sk15)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(201,assumption,(~(sk17 = sk18)), introduced(assumption)).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 (incident_c(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> incident_c(sk18, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 (incident_c(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) <=> incident_c(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.49 inference(symmetry,[status(thm)],[202])).
% 0.20/0.49 tff(204,plain,
% 0.20/0.49 (^[B: $i, A: $i] : refl(((~end_point(A, B)) | incident_c(A, B)) <=> ((~end_point(A, B)) | incident_c(A, B)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(205,plain,
% 0.20/0.49 (![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B)) <=> ![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[204])).
% 0.20/0.49 tff(206,plain,
% 0.20/0.49 (![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B)) <=> ![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(207,axiom,(![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','end_point_defn_13')).
% 0.20/0.49 tff(208,plain,
% 0.20/0.49 (![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.20/0.49 tff(209,plain,(
% 0.20/0.49 ![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))),
% 0.20/0.49 inference(skolemize,[status(sab)],[208])).
% 0.20/0.49 tff(210,plain,
% 0.20/0.49 (![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.20/0.49 tff(211,plain,
% 0.20/0.49 (((~![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))) | ((~end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | incident_c(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> ((~![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))) | (~end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | incident_c(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(212,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))) | ((~end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | incident_c(sk18, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(213,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))) | (~end_point(sk18, ax1_sk1(sk18, sk17, sk16, sk15))) | incident_c(sk18, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.20/0.49 tff(214,plain,
% 0.20/0.49 (incident_c(sk18, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[213, 210, 93])).
% 0.20/0.49 tff(215,plain,
% 0.20/0.49 (incident_c(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[214, 203])).
% 0.20/0.49 tff(216,assumption,(~incident_c(sk18, sk15)), introduced(assumption)).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(sk18, sk15) | (~incident_c(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | incident_c(sk18, sk15) | (~incident_c(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(sk18, sk15) | (~incident_c(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | incident_c(sk18, sk15) | (~incident_c(sk18, sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.49 tff(220,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[219, 195, 216, 215, 170])).
% 0.20/0.49 tff(221,plain,(incident_c(sk18, sk15)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(222,assumption,(sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))), introduced(assumption)).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 (ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)) = sk16),
% 0.20/0.49 inference(symmetry,[status(thm)],[222])).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 (incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15) <=> incident_c(sk16, sk15)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[223])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 (incident_c(sk16, sk15) <=> incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15)),
% 0.20/0.49 inference(symmetry,[status(thm)],[224])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 ((~incident_c(sk16, sk15)) <=> (~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[225])).
% 0.20/0.49 tff(227,assumption,(~incident_c(sk16, sk15)), introduced(assumption)).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 (~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 (((~![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))) | ((~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))) <=> ((~![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))) | ((~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 ((~![B: $i, A: $i] : ((~end_point(A, B)) | incident_c(A, B))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 ((~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[231, 210])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 (incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[232, 136])).
% 0.20/0.49 tff(234,plain,
% 0.20/0.49 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | ((~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)) | incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)) | incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 ((incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15) | (~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15))) <=> ((~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)) | incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(236,plain,
% 0.20/0.49 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15) | (~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | ((~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)) | incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[235])).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15) | (~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)) | incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15))),
% 0.20/0.49 inference(transitivity,[status(thm)],[236, 234])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15) | (~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(239,plain,
% 0.20/0.49 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~part_of(sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))), sk15)) | incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 (incident_c(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sk15)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[239, 195, 233, 170])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[240, 228])).
% 0.20/0.49 tff(242,plain,(incident_c(sk16, sk15) | (~(sk16 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (incident_c(sk16, sk15)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[242, 153])).
% 0.20/0.49 tff(244,plain,
% 0.20/0.49 (((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (sk16 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17)) <=> ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (sk16 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(245,plain,
% 0.20/0.49 ((((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17)) | (sk16 = sk18)) <=> ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (sk16 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(246,plain,
% 0.20/0.49 ((((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (~incident_c(sk17, sk15)) | (sk16 = sk17)) | (sk17 = sk18)) <=> ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(247,plain,
% 0.20/0.49 ((((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (~incident_c(sk17, sk15))) | (sk16 = sk17)) <=> ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (~incident_c(sk17, sk15)) | (sk16 = sk17))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(248,plain,
% 0.20/0.49 ((((~incident_c(sk16, sk15)) | (~incident_c(sk17, sk15))) | (~incident_c(sk18, sk15))) <=> ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (~incident_c(sk17, sk15)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(249,plain,
% 0.20/0.49 (((((~incident_c(sk16, sk15)) | (~incident_c(sk17, sk15))) | (~incident_c(sk18, sk15))) | (sk16 = sk17)) <=> (((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (~incident_c(sk17, sk15))) | (sk16 = sk17))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.49 tff(250,plain,
% 0.20/0.49 (((((~incident_c(sk16, sk15)) | (~incident_c(sk17, sk15))) | (~incident_c(sk18, sk15))) | (sk16 = sk17)) <=> ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (~incident_c(sk17, sk15)) | (sk16 = sk17))),
% 0.20/0.49 inference(transitivity,[status(thm)],[249, 247])).
% 0.20/0.49 tff(251,plain,
% 0.20/0.49 ((((((~incident_c(sk16, sk15)) | (~incident_c(sk17, sk15))) | (~incident_c(sk18, sk15))) | (sk16 = sk17)) | (sk17 = sk18)) <=> (((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (~incident_c(sk17, sk15)) | (sk16 = sk17)) | (sk17 = sk18))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[250])).
% 0.20/0.49 tff(252,plain,
% 0.20/0.49 ((((((~incident_c(sk16, sk15)) | (~incident_c(sk17, sk15))) | (~incident_c(sk18, sk15))) | (sk16 = sk17)) | (sk17 = sk18)) <=> ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17))),
% 0.20/0.49 inference(transitivity,[status(thm)],[251, 246])).
% 0.20/0.49 tff(253,plain,
% 0.20/0.49 (((((((~incident_c(sk16, sk15)) | (~incident_c(sk17, sk15))) | (~incident_c(sk18, sk15))) | (sk16 = sk17)) | (sk17 = sk18)) | (sk16 = sk18)) <=> (((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17)) | (sk16 = sk18))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[252])).
% 0.20/0.49 tff(254,plain,
% 0.20/0.49 (((((((~incident_c(sk16, sk15)) | (~incident_c(sk17, sk15))) | (~incident_c(sk18, sk15))) | (sk16 = sk17)) | (sk17 = sk18)) | (sk16 = sk18)) <=> ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (sk16 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17))),
% 0.20/0.49 inference(transitivity,[status(thm)],[253, 245])).
% 0.20/0.49 tff(255,axiom,((((((~incident_c(sk16, sk15)) | (~incident_c(sk17, sk15))) | (~incident_c(sk18, sk15))) | (sk16 = sk17)) | (sk17 = sk18)) | (sk16 = sk18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem_3_8_1_78')).
% 0.20/0.49 tff(256,plain,
% 0.20/0.49 ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (sk16 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.20/0.49 tff(257,plain,
% 0.20/0.49 ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (sk16 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[256, 244])).
% 0.20/0.49 tff(258,plain,
% 0.20/0.49 ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (sk16 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[257, 244])).
% 0.20/0.49 tff(259,plain,
% 0.20/0.49 ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (sk16 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[258, 244])).
% 0.20/0.49 tff(260,plain,
% 0.20/0.49 ((~incident_c(sk16, sk15)) | (~incident_c(sk18, sk15)) | (sk17 = sk18) | (sk16 = sk18) | (~incident_c(sk17, sk15)) | (sk16 = sk17)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[259, 244])).
% 0.20/0.49 tff(261,plain,
% 0.20/0.49 (sk16 = sk17),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[260, 243, 221, 201, 200, 126])).
% 0.20/0.49 tff(262,plain,
% 0.20/0.49 (sk17 = sk16),
% 0.20/0.49 inference(symmetry,[status(thm)],[261])).
% 0.20/0.49 tff(263,plain,
% 0.20/0.49 (sk17 = ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.49 inference(transitivity,[status(thm)],[262, 153])).
% 0.20/0.49 tff(264,plain,
% 0.20/0.49 (inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15)) <=> inner_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[263, 25])).
% 0.20/0.49 tff(265,plain,
% 0.20/0.49 (inner_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.50 inference(symmetry,[status(thm)],[264])).
% 0.20/0.50 tff(266,plain,
% 0.20/0.50 ((~inner_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) <=> (~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[265])).
% 0.20/0.50 tff(267,plain,
% 0.20/0.50 (^[B: $i, A: $i] : refl(((~end_point(A, B)) | (~inner_point(A, B))) <=> ((~end_point(A, B)) | (~inner_point(A, B))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(268,plain,
% 0.20/0.50 (![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B))) <=> ![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[267])).
% 0.20/0.50 tff(269,plain,
% 0.20/0.50 (![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B))) <=> ![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(270,plain,
% 0.20/0.50 (^[B: $i, A: $i] : rewrite(((~inner_point(A, B)) | (~end_point(A, B))) <=> ((~end_point(A, B)) | (~inner_point(A, B))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(271,plain,
% 0.20/0.50 (![B: $i, A: $i] : ((~inner_point(A, B)) | (~end_point(A, B))) <=> ![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[270])).
% 0.20/0.50 tff(272,axiom,(![B: $i, A: $i] : ((~inner_point(A, B)) | (~end_point(A, B)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','inner_point_defn_22')).
% 0.20/0.50 tff(273,plain,
% 0.20/0.50 (![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.20/0.50 tff(274,plain,
% 0.20/0.50 (![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[273, 269])).
% 0.20/0.50 tff(275,plain,(
% 0.20/0.50 ![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[274])).
% 0.20/0.50 tff(276,plain,
% 0.20/0.50 (![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[275, 268])).
% 0.20/0.50 tff(277,plain,
% 0.20/0.50 (((~![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))) | ((~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~inner_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))) <=> ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~inner_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(278,plain,
% 0.20/0.50 ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))) | ((~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~inner_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(279,plain,
% 0.20/0.50 ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))) | (~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~inner_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.20/0.50 tff(280,plain,
% 0.20/0.50 ((~end_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~inner_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[279, 276])).
% 0.20/0.50 tff(281,plain,
% 0.20/0.50 (~inner_point(ax0_sk11(sk18, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[280, 136])).
% 0.20/0.50 tff(282,plain,
% 0.20/0.50 (~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[281, 266])).
% 0.20/0.50 tff(283,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[14, 282])).
% 0.20/0.50 tff(284,plain,((sk16 = sk18) | (sk17 = sk18)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(285,plain,
% 0.20/0.50 (sk17 = sk18),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[284, 48])).
% 0.20/0.50 tff(286,plain,
% 0.20/0.50 (sk17 = ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.50 inference(transitivity,[status(thm)],[285, 125])).
% 0.20/0.50 tff(287,plain,
% 0.20/0.50 (inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15)) <=> inner_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[286, 25])).
% 0.20/0.50 tff(288,plain,
% 0.20/0.50 (inner_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))) <=> inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.50 inference(symmetry,[status(thm)],[287])).
% 0.20/0.50 tff(289,plain,
% 0.20/0.50 ((~inner_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) <=> (~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[288])).
% 0.20/0.50 tff(290,plain,
% 0.20/0.50 (((~![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))) | ((~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~inner_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))) <=> ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~inner_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(291,plain,
% 0.20/0.50 ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))) | ((~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~inner_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(292,plain,
% 0.20/0.50 ((~![B: $i, A: $i] : ((~end_point(A, B)) | (~inner_point(A, B)))) | (~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~inner_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.20/0.50 tff(293,plain,
% 0.20/0.50 ((~end_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))) | (~inner_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[292, 276])).
% 0.20/0.50 tff(294,plain,
% 0.20/0.50 (~inner_point(ax0_sk11(sk16, ax1_sk1(sk18, sk17, sk16, sk15)), sum(ax0_sk9(sk17, ax1_sk1(sk18, sk17, sk16, sk15)), ax0_sk10(sk17, ax1_sk1(sk18, sk17, sk16, sk15))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[293, 80])).
% 0.20/0.50 tff(295,plain,
% 0.20/0.50 (~inner_point(sk17, ax1_sk1(sk18, sk17, sk16, sk15))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[294, 289])).
% 0.20/0.50 tff(296,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[14, 295])).
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------