%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO169+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:05:43 AM UTC 2025
% Result : Theorem 1.37s 1.60s
% Output : Proof 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO169+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:38:54 EDT 2025
% 0.18/0.33 % CPUTime :
% 1.37/1.60 % SZS status Theorem
% 1.37/1.60 % SZS output start Proof
% 1.37/1.60 tff(point_equal_type, type, (
% 1.37/1.60 point_equal: ( $i * $i ) > $o)).
% 1.37/1.60 tff(o_type, type, (
% 1.37/1.60 o: $i)).
% 1.37/1.60 tff(a2_type, type, (
% 1.37/1.60 a2: $i)).
% 1.37/1.60 tff(incident_type, type, (
% 1.37/1.60 incident: ( $i * $i ) > $o)).
% 1.37/1.60 tff(oc_type, type, (
% 1.37/1.60 oc: $i)).
% 1.37/1.60 tff(b2_type, type, (
% 1.37/1.60 b2: $i)).
% 1.37/1.60 tff(c1_type, type, (
% 1.37/1.60 c1: $i)).
% 1.37/1.60 tff(b2c2_type, type, (
% 1.37/1.60 b2c2: $i)).
% 1.37/1.60 tff(a1_type, type, (
% 1.37/1.60 a1: $i)).
% 1.37/1.60 tff(a2c2_type, type, (
% 1.37/1.60 a2c2: $i)).
% 1.37/1.60 tff(b1_type, type, (
% 1.37/1.60 b1: $i)).
% 1.37/1.60 tff(oa_type, type, (
% 1.37/1.60 oa: $i)).
% 1.37/1.60 tff(ab_type, type, (
% 1.37/1.60 ab: $i)).
% 1.37/1.60 tff(line_equal_type, type, (
% 1.37/1.60 line_equal: ( $i * $i ) > $o)).
% 1.37/1.60 tff(a1b1_type, type, (
% 1.37/1.60 a1b1: $i)).
% 1.37/1.60 tff(ob_type, type, (
% 1.37/1.60 ob: $i)).
% 1.37/1.60 tff(c2_type, type, (
% 1.37/1.60 c2: $i)).
% 1.37/1.60 tff(goal_type, type, (
% 1.37/1.60 goal: $o)).
% 1.37/1.60 tff(a1c1_type, type, (
% 1.37/1.60 a1c1: $i)).
% 1.37/1.60 tff(ac_type, type, (
% 1.37/1.60 ac: $i)).
% 1.37/1.60 tff(bc_type, type, (
% 1.37/1.60 bc: $i)).
% 1.37/1.60 tff(a2b2_type, type, (
% 1.37/1.60 a2b2: $i)).
% 1.37/1.60 tff(b1c1_type, type, (
% 1.37/1.60 b1c1: $i)).
% 1.37/1.60 tff(1,assumption,(~point_equal(b2, c1)), introduced(assumption)).
% 1.37/1.60 tff(2,assumption,(~incident(b1, a2c2)), introduced(assumption)).
% 1.37/1.60 tff(3,plain,
% 1.37/1.60 ((incident(b1, a2c2) | incident(c2, a1b1)) <=> (incident(b1, a2c2) | incident(c2, a1b1))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(4,axiom,(incident(b1, a2c2) | incident(c2, a1b1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gap_b')).
% 1.37/1.60 tff(5,plain,
% 1.37/1.60 (incident(b1, a2c2) | incident(c2, a1b1)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.37/1.60 tff(6,plain,
% 1.37/1.60 (incident(c2, a1b1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[5, 2])).
% 1.37/1.60 tff(7,assumption,(line_equal(b2c2, a1b1)), introduced(assumption)).
% 1.37/1.60 tff(8,assumption,(~incident(b2, a1b1)), introduced(assumption)).
% 1.37/1.60 tff(9,plain,
% 1.37/1.60 (^[A: $i, B: $i, C: $i] : refl((incident(A, C) | (~line_equal(B, C)) | (~incident(A, B))) <=> (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(10,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B))) <=> ![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[9])).
% 1.37/1.60 tff(11,plain,
% 1.37/1.60 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((incident(A, B) & line_equal(B, C)) <=> (~((~incident(A, B)) | (~line_equal(B, C))))), ((~(incident(A, B) & line_equal(B, C))) <=> (~(~((~incident(A, B)) | (~line_equal(B, C))))))), rewrite((~(~((~incident(A, B)) | (~line_equal(B, C))))) <=> ((~incident(A, B)) | (~line_equal(B, C)))), ((~(incident(A, B) & line_equal(B, C))) <=> ((~incident(A, B)) | (~line_equal(B, C))))), (((~(incident(A, B) & line_equal(B, C))) | incident(A, C)) <=> (((~incident(A, B)) | (~line_equal(B, C))) | incident(A, C)))), rewrite((((~incident(A, B)) | (~line_equal(B, C))) | incident(A, C)) <=> (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))), (((~(incident(A, B) & line_equal(B, C))) | incident(A, C)) <=> (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(12,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i] : ((~(incident(A, B) & line_equal(B, C))) | incident(A, C)) <=> ![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[11])).
% 1.37/1.60 tff(13,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i] : ((~(incident(A, B) & line_equal(B, C))) | incident(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(incident(A, B) & line_equal(B, C))) | incident(A, C))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(14,plain,
% 1.37/1.60 (^[A: $i, B: $i, C: $i] : rewrite(((incident(A, B) & line_equal(B, C)) => incident(A, C)) <=> ((~(incident(A, B) & line_equal(B, C))) | incident(A, C)))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(15,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i] : ((incident(A, B) & line_equal(B, C)) => incident(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(incident(A, B) & line_equal(B, C))) | incident(A, C))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[14])).
% 1.37/1.60 tff(16,axiom,(![A: $i, B: $i, C: $i] : ((incident(A, B) & line_equal(B, C)) => incident(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lcon')).
% 1.37/1.60 tff(17,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i] : ((~(incident(A, B) & line_equal(B, C))) | incident(A, C))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.37/1.60 tff(18,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i] : ((~(incident(A, B) & line_equal(B, C))) | incident(A, C))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.37/1.60 tff(19,plain,(
% 1.37/1.60 ![A: $i, B: $i, C: $i] : ((~(incident(A, B) & line_equal(B, C))) | incident(A, C))),
% 1.37/1.60 inference(skolemize,[status(sab)],[18])).
% 1.37/1.60 tff(20,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.37/1.60 tff(21,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[20, 10])).
% 1.37/1.60 tff(22,plain,
% 1.37/1.60 (incident(b2, b2c2) <=> incident(b2, b2c2)),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(23,axiom,(incident(b2, b2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib2c2')).
% 1.37/1.60 tff(24,plain,
% 1.37/1.60 (incident(b2, b2c2)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.37/1.60 tff(25,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(b2, b2c2)) | incident(b2, a1b1) | (~line_equal(b2c2, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(b2, b2c2)) | incident(b2, a1b1) | (~line_equal(b2c2, a1b1)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(26,plain,
% 1.37/1.60 ((incident(b2, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(b2, b2c2))) <=> ((~incident(b2, b2c2)) | incident(b2, a1b1) | (~line_equal(b2c2, a1b1)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(27,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(b2, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(b2, b2c2)) | incident(b2, a1b1) | (~line_equal(b2c2, a1b1))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[26])).
% 1.37/1.60 tff(28,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(b2, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(b2, b2c2)) | incident(b2, a1b1) | (~line_equal(b2c2, a1b1)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[27, 25])).
% 1.37/1.60 tff(29,plain,
% 1.37/1.60 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(b2, b2c2)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(30,plain,
% 1.37/1.60 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(b2, b2c2)) | incident(b2, a1b1) | (~line_equal(b2c2, a1b1))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.37/1.60 tff(31,plain,
% 1.37/1.60 ($false),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[30, 24, 21, 8, 7])).
% 1.37/1.60 tff(32,plain,(incident(b2, a1b1) | (~line_equal(b2c2, a1b1))), inference(lemma,lemma(discharge,[]))).
% 1.37/1.60 tff(33,plain,
% 1.37/1.60 (incident(b2, a1b1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[32, 7])).
% 1.37/1.60 tff(34,plain,
% 1.37/1.60 (^[A: $i, B: $i, C: $i, D: $i] : refl((line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D))) <=> (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(35,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[34])).
% 1.37/1.60 tff(36,plain,
% 1.37/1.60 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D)) <=> (~((~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D))))), ((~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D))) <=> (~(~((~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D))))))), rewrite((~(~((~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D))))) <=> ((~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))), ((~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D))) <=> ((~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D))))), ((line_equal(C, D) | point_equal(A, B) | (~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D)))) <=> (line_equal(C, D) | point_equal(A, B) | ((~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))))), rewrite((line_equal(C, D) | point_equal(A, B) | ((~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) <=> (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))), ((line_equal(C, D) | point_equal(A, B) | (~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D)))) <=> (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(37,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[36])).
% 1.37/1.60 tff(38,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D))))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(39,plain,
% 1.37/1.60 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((incident(A, C) & incident(A, D)) & incident(B, C)) <=> (incident(A, C) & incident(A, D) & incident(B, C))), ((((incident(A, C) & incident(A, D)) & incident(B, C)) & incident(B, D)) <=> ((incident(A, C) & incident(A, D) & incident(B, C)) & incident(B, D)))), rewrite(((incident(A, C) & incident(A, D) & incident(B, C)) & incident(B, D)) <=> (incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D))), ((((incident(A, C) & incident(A, D)) & incident(B, C)) & incident(B, D)) <=> (incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D)))), rewrite((point_equal(A, B) | line_equal(C, D)) <=> (line_equal(C, D) | point_equal(A, B))), (((((incident(A, C) & incident(A, D)) & incident(B, C)) & incident(B, D)) => (point_equal(A, B) | line_equal(C, D))) <=> ((incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D)) => (line_equal(C, D) | point_equal(A, B))))), rewrite(((incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D)) => (line_equal(C, D) | point_equal(A, B))) <=> (line_equal(C, D) | point_equal(A, B) | (~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D))))), (((((incident(A, C) & incident(A, D)) & incident(B, C)) & incident(B, D)) => (point_equal(A, B) | line_equal(C, D))) <=> (line_equal(C, D) | point_equal(A, B) | (~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D))))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(40,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i, D: $i] : ((((incident(A, C) & incident(A, D)) & incident(B, C)) & incident(B, D)) => (point_equal(A, B) | line_equal(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D))))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[39])).
% 1.37/1.60 tff(41,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((incident(A, C) & incident(A, D)) & incident(B, C)) & incident(B, D)) => (point_equal(A, B) | line_equal(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unique')).
% 1.37/1.60 tff(42,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D))))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.37/1.60 tff(43,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D))))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[42, 38])).
% 1.37/1.60 tff(44,plain,(
% 1.37/1.60 ![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~(incident(A, C) & incident(A, D) & incident(B, C) & incident(B, D))))),
% 1.37/1.60 inference(skolemize,[status(sab)],[43])).
% 1.37/1.60 tff(45,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[44, 37])).
% 1.37/1.60 tff(46,plain,
% 1.37/1.60 (![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[45, 35])).
% 1.37/1.60 tff(47,plain,
% 1.37/1.60 ((~goal) <=> (~goal)),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(48,axiom,(~goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goal_to_be_proved')).
% 1.37/1.60 tff(49,plain,
% 1.37/1.60 (~goal),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.37/1.60 tff(50,plain,
% 1.37/1.60 ((goal | (~point_equal(b2, b1))) <=> (goal | (~point_equal(b2, b1)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(51,plain,
% 1.37/1.60 ((point_equal(b2, b1) => goal) <=> (goal | (~point_equal(b2, b1)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(52,axiom,(point_equal(b2, b1) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notbb')).
% 1.37/1.60 tff(53,plain,
% 1.37/1.60 (goal | (~point_equal(b2, b1))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.37/1.60 tff(54,plain,
% 1.37/1.60 (goal | (~point_equal(b2, b1))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[53, 50])).
% 1.37/1.60 tff(55,plain,
% 1.37/1.60 (~point_equal(b2, b1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[54, 49])).
% 1.37/1.60 tff(56,plain,
% 1.37/1.60 (incident(b2, ob) <=> incident(b2, ob)),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(57,axiom,(incident(b2, ob)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib2ob')).
% 1.37/1.60 tff(58,plain,
% 1.37/1.60 (incident(b2, ob)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.37/1.60 tff(59,plain,
% 1.37/1.60 (incident(b1, ob) <=> incident(b1, ob)),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(60,axiom,(incident(b1, ob)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib1ob')).
% 1.37/1.60 tff(61,plain,
% 1.37/1.60 (incident(b1, ob)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.37/1.60 tff(62,plain,
% 1.37/1.60 (incident(b1, a1b1) <=> incident(b1, a1b1)),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(63,axiom,(incident(b1, a1b1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib1a1')).
% 1.37/1.60 tff(64,plain,
% 1.37/1.60 (incident(b1, a1b1)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.37/1.60 tff(65,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(ob, a1b1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(ob, a1b1))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(66,plain,
% 1.37/1.60 ((line_equal(ob, a1b1) | point_equal(b2, b1) | (~incident(b1, ob)) | (~incident(b2, ob)) | (~incident(b2, a1b1)) | (~incident(b1, a1b1))) <=> (point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(ob, a1b1))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(67,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(b2, b1) | (~incident(b1, ob)) | (~incident(b2, ob)) | (~incident(b2, a1b1)) | (~incident(b1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(ob, a1b1)))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[66])).
% 1.37/1.60 tff(68,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(b2, b1) | (~incident(b1, ob)) | (~incident(b2, ob)) | (~incident(b2, a1b1)) | (~incident(b1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(ob, a1b1))),
% 1.37/1.60 inference(transitivity,[status(thm)],[67, 65])).
% 1.37/1.60 tff(69,plain,
% 1.37/1.60 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(b2, b1) | (~incident(b1, ob)) | (~incident(b2, ob)) | (~incident(b2, a1b1)) | (~incident(b1, a1b1)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(70,plain,
% 1.37/1.60 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(ob, a1b1)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.37/1.60 tff(71,plain,
% 1.37/1.60 ((~incident(b2, a1b1)) | line_equal(ob, a1b1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[70, 64, 61, 58, 55, 46])).
% 1.37/1.60 tff(72,plain,
% 1.37/1.60 (line_equal(ob, a1b1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[71, 33])).
% 1.37/1.60 tff(73,plain,
% 1.37/1.60 (incident(o, ob) <=> incident(o, ob)),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(74,axiom,(incident(o, ob)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ioob')).
% 1.37/1.60 tff(75,plain,
% 1.37/1.60 (incident(o, ob)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.37/1.60 tff(76,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, ob)) | (~line_equal(ob, a1b1)) | incident(o, a1b1))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | (~line_equal(ob, a1b1)) | incident(o, a1b1))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(77,plain,
% 1.37/1.60 ((incident(o, a1b1) | (~line_equal(ob, a1b1)) | (~incident(o, ob))) <=> ((~incident(o, ob)) | (~line_equal(ob, a1b1)) | incident(o, a1b1))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(78,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1b1) | (~line_equal(ob, a1b1)) | (~incident(o, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, ob)) | (~line_equal(ob, a1b1)) | incident(o, a1b1)))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[77])).
% 1.37/1.60 tff(79,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1b1) | (~line_equal(ob, a1b1)) | (~incident(o, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | (~line_equal(ob, a1b1)) | incident(o, a1b1))),
% 1.37/1.60 inference(transitivity,[status(thm)],[78, 76])).
% 1.37/1.60 tff(80,plain,
% 1.37/1.60 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1b1) | (~line_equal(ob, a1b1)) | (~incident(o, ob)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(81,plain,
% 1.37/1.60 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | (~line_equal(ob, a1b1)) | incident(o, a1b1)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.37/1.60 tff(82,plain,
% 1.37/1.60 ((~line_equal(ob, a1b1)) | incident(o, a1b1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[81, 75, 21])).
% 1.37/1.60 tff(83,plain,
% 1.37/1.60 (incident(o, a1b1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[82, 72])).
% 1.37/1.60 tff(84,assumption,(incident(c2, a1b1)), introduced(assumption)).
% 1.37/1.60 tff(85,plain,
% 1.37/1.60 (incident(bc, b2c2) <=> incident(bc, b2c2)),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(86,axiom,(incident(bc, b2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ibc2')).
% 1.37/1.60 tff(87,plain,
% 1.37/1.60 (incident(bc, b2c2)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.37/1.60 tff(88,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(bc, b2c2)) | incident(bc, a1b1) | (~line_equal(b2c2, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(bc, b2c2)) | incident(bc, a1b1) | (~line_equal(b2c2, a1b1)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(89,plain,
% 1.37/1.60 ((incident(bc, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(bc, b2c2))) <=> ((~incident(bc, b2c2)) | incident(bc, a1b1) | (~line_equal(b2c2, a1b1)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(90,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(bc, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(bc, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(bc, b2c2)) | incident(bc, a1b1) | (~line_equal(b2c2, a1b1))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[89])).
% 1.37/1.60 tff(91,plain,
% 1.37/1.60 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(bc, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(bc, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(bc, b2c2)) | incident(bc, a1b1) | (~line_equal(b2c2, a1b1)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[90, 88])).
% 1.37/1.60 tff(92,plain,
% 1.37/1.60 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(bc, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(bc, b2c2)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(93,plain,
% 1.37/1.60 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(bc, b2c2)) | incident(bc, a1b1) | (~line_equal(b2c2, a1b1))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.37/1.60 tff(94,plain,
% 1.37/1.60 (incident(bc, a1b1) | (~line_equal(b2c2, a1b1))),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[93, 87, 21])).
% 1.37/1.60 tff(95,plain,
% 1.37/1.60 (incident(bc, a1b1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[94, 7])).
% 1.37/1.60 tff(96,plain,
% 1.37/1.60 (^[A: $i, B: $i] : refl(((~incident(A, B)) | line_equal(B, B)) <=> ((~incident(A, B)) | line_equal(B, B)))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(97,plain,
% 1.37/1.60 (![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B)) <=> ![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[96])).
% 1.37/1.60 tff(98,plain,
% 1.37/1.60 (![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B)) <=> ![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(99,plain,
% 1.37/1.60 (^[A: $i, B: $i] : rewrite((incident(A, B) => line_equal(B, B)) <=> ((~incident(A, B)) | line_equal(B, B)))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(100,plain,
% 1.37/1.60 (![A: $i, B: $i] : (incident(A, B) => line_equal(B, B)) <=> ![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[99])).
% 1.37/1.60 tff(101,axiom,(![A: $i, B: $i] : (incident(A, B) => line_equal(B, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_of_line_equal')).
% 1.37/1.60 tff(102,plain,
% 1.37/1.60 (![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.37/1.60 tff(103,plain,
% 1.37/1.60 (![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[102, 98])).
% 1.37/1.60 tff(104,plain,(
% 1.37/1.60 ![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.37/1.60 inference(skolemize,[status(sab)],[103])).
% 1.37/1.60 tff(105,plain,
% 1.37/1.60 (![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[104, 97])).
% 1.37/1.60 tff(106,plain,
% 1.37/1.60 (incident(a1, a1b1) <=> incident(a1, a1b1)),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(107,axiom,(incident(a1, a1b1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia1b1')).
% 1.37/1.60 tff(108,plain,
% 1.37/1.60 (incident(a1, a1b1)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.37/1.60 tff(109,plain,
% 1.37/1.60 (((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(a1, a1b1)) | line_equal(a1b1, a1b1))) <=> ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(a1, a1b1)) | line_equal(a1b1, a1b1))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(110,plain,
% 1.37/1.60 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(a1, a1b1)) | line_equal(a1b1, a1b1))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(111,plain,
% 1.37/1.60 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(a1, a1b1)) | line_equal(a1b1, a1b1)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.37/1.60 tff(112,plain,
% 1.37/1.60 (line_equal(a1b1, a1b1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[111, 108, 105])).
% 1.37/1.60 tff(113,plain,
% 1.37/1.60 (incident(ab, a1b1) <=> incident(ab, a1b1)),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(114,axiom,(incident(ab, a1b1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iab1')).
% 1.37/1.60 tff(115,plain,
% 1.37/1.60 (incident(ab, a1b1)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.37/1.60 tff(116,plain,
% 1.37/1.60 (^[A: $i] : refl((goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A))) <=> (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(117,plain,
% 1.37/1.60 (![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A))) <=> ![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[116])).
% 1.37/1.60 tff(118,plain,
% 1.37/1.60 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)) <=> (~((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A))))), ((~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))) <=> (~(~((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A))))))), rewrite((~(~((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A))))) <=> ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))), ((~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))) <=> ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A))))), ((goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))) <=> (goal | ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))))), rewrite((goal | ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) <=> (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))), ((goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))) <=> (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(119,plain,
% 1.37/1.60 (![A: $i] : (goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))) <=> ![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[118])).
% 1.37/1.60 tff(120,plain,
% 1.37/1.60 (![A: $i] : (goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))) <=> ![A: $i] : (goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(121,plain,
% 1.37/1.60 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((line_equal(A, A) & incident(bc, A)) & incident(ac, A)) <=> (line_equal(A, A) & incident(bc, A) & incident(ac, A))), ((((line_equal(A, A) & incident(bc, A)) & incident(ac, A)) & incident(ab, A)) <=> ((line_equal(A, A) & incident(bc, A) & incident(ac, A)) & incident(ab, A)))), rewrite(((line_equal(A, A) & incident(bc, A) & incident(ac, A)) & incident(ab, A)) <=> (line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))), ((((line_equal(A, A) & incident(bc, A)) & incident(ac, A)) & incident(ab, A)) <=> (line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))), (((((line_equal(A, A) & incident(bc, A)) & incident(ac, A)) & incident(ab, A)) => goal) <=> ((line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)) => goal))), rewrite(((line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)) => goal) <=> (goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))))), (((((line_equal(A, A) & incident(bc, A)) & incident(ac, A)) & incident(ab, A)) => goal) <=> (goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(122,plain,
% 1.37/1.60 (![A: $i] : ((((line_equal(A, A) & incident(bc, A)) & incident(ac, A)) & incident(ab, A)) => goal) <=> ![A: $i] : (goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[121])).
% 1.37/1.60 tff(123,axiom,(![A: $i] : ((((line_equal(A, A) & incident(bc, A)) & incident(ac, A)) & incident(ab, A)) => goal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goal_normal')).
% 1.37/1.60 tff(124,plain,
% 1.37/1.60 (![A: $i] : (goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.37/1.60 tff(125,plain,
% 1.37/1.60 (![A: $i] : (goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[124, 120])).
% 1.37/1.60 tff(126,plain,(
% 1.37/1.60 ![A: $i] : (goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))))),
% 1.37/1.60 inference(skolemize,[status(sab)],[125])).
% 1.37/1.60 tff(127,plain,
% 1.37/1.60 (![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[126, 119])).
% 1.37/1.60 tff(128,plain,
% 1.37/1.60 (![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[127, 117])).
% 1.37/1.60 tff(129,plain,
% 1.37/1.60 (((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)))) <=> ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(130,plain,
% 1.37/1.60 ((goal | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ab, a1b1)) | (~incident(ac, a1b1))) <=> (goal | (~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(131,plain,
% 1.37/1.60 (((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ab, a1b1)) | (~incident(ac, a1b1)))) <=> ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[130])).
% 1.37/1.60 tff(132,plain,
% 1.37/1.60 (((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ab, a1b1)) | (~incident(ac, a1b1)))) <=> ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)))),
% 1.37/1.61 inference(transitivity,[status(thm)],[131, 129])).
% 1.37/1.61 tff(133,plain,
% 1.37/1.61 ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ab, a1b1)) | (~incident(ac, a1b1)))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(134,plain,
% 1.37/1.61 ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.37/1.61 tff(135,plain,
% 1.37/1.61 ((~incident(bc, a1b1)) | (~incident(ac, a1b1))),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[134, 128, 49, 115, 112])).
% 1.37/1.61 tff(136,plain,
% 1.37/1.61 (~incident(ac, a1b1)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[135, 95])).
% 1.37/1.61 tff(137,assumption,(point_equal(ac, c2)), introduced(assumption)).
% 1.37/1.61 tff(138,assumption,(~incident(ac, a1b1)), introduced(assumption)).
% 1.37/1.61 tff(139,plain,
% 1.37/1.61 (^[A: $i, B: $i, C: $i] : refl((incident(A, C) | (~incident(B, C)) | (~point_equal(A, B))) <=> (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B))))),
% 1.37/1.61 inference(bind,[status(th)],[])).
% 1.37/1.61 tff(140,plain,
% 1.37/1.61 (![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B))) <=> ![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))),
% 1.37/1.61 inference(quant_intro,[status(thm)],[139])).
% 1.37/1.61 tff(141,plain,
% 1.37/1.61 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((point_equal(A, B) & incident(B, C)) <=> (~((~incident(B, C)) | (~point_equal(A, B))))), ((~(point_equal(A, B) & incident(B, C))) <=> (~(~((~incident(B, C)) | (~point_equal(A, B))))))), rewrite((~(~((~incident(B, C)) | (~point_equal(A, B))))) <=> ((~incident(B, C)) | (~point_equal(A, B)))), ((~(point_equal(A, B) & incident(B, C))) <=> ((~incident(B, C)) | (~point_equal(A, B))))), (((~(point_equal(A, B) & incident(B, C))) | incident(A, C)) <=> (((~incident(B, C)) | (~point_equal(A, B))) | incident(A, C)))), rewrite((((~incident(B, C)) | (~point_equal(A, B))) | incident(A, C)) <=> (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))), (((~(point_equal(A, B) & incident(B, C))) | incident(A, C)) <=> (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))))),
% 1.37/1.61 inference(bind,[status(th)],[])).
% 1.37/1.61 tff(142,plain,
% 1.37/1.61 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & incident(B, C))) | incident(A, C)) <=> ![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))),
% 1.37/1.61 inference(quant_intro,[status(thm)],[141])).
% 1.37/1.61 tff(143,plain,
% 1.37/1.61 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & incident(B, C))) | incident(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & incident(B, C))) | incident(A, C))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(144,plain,
% 1.37/1.61 (^[A: $i, B: $i, C: $i] : rewrite(((point_equal(A, B) & incident(B, C)) => incident(A, C)) <=> ((~(point_equal(A, B) & incident(B, C))) | incident(A, C)))),
% 1.37/1.61 inference(bind,[status(th)],[])).
% 1.37/1.61 tff(145,plain,
% 1.37/1.61 (![A: $i, B: $i, C: $i] : ((point_equal(A, B) & incident(B, C)) => incident(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & incident(B, C))) | incident(A, C))),
% 1.37/1.61 inference(quant_intro,[status(thm)],[144])).
% 1.37/1.61 tff(146,axiom,(![A: $i, B: $i, C: $i] : ((point_equal(A, B) & incident(B, C)) => incident(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pcon')).
% 1.37/1.61 tff(147,plain,
% 1.37/1.61 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & incident(B, C))) | incident(A, C))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[146, 145])).
% 1.37/1.61 tff(148,plain,
% 1.37/1.61 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & incident(B, C))) | incident(A, C))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[147, 143])).
% 1.37/1.61 tff(149,plain,(
% 1.37/1.61 ![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & incident(B, C))) | incident(A, C))),
% 1.37/1.61 inference(skolemize,[status(sab)],[148])).
% 1.37/1.61 tff(150,plain,
% 1.37/1.61 (![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[149, 142])).
% 1.37/1.61 tff(151,plain,
% 1.37/1.61 (![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[150, 140])).
% 1.37/1.61 tff(152,plain,
% 1.37/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c2, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c2, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, c2)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(153,plain,
% 1.37/1.61 ((incident(ac, a1b1) | (~incident(c2, a1b1)) | (~point_equal(ac, c2))) <=> ((~incident(c2, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, c2)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(154,plain,
% 1.37/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, a1b1) | (~incident(c2, a1b1)) | (~point_equal(ac, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c2, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, c2))))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[153])).
% 1.37/1.61 tff(155,plain,
% 1.37/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, a1b1) | (~incident(c2, a1b1)) | (~point_equal(ac, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c2, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, c2)))),
% 1.37/1.61 inference(transitivity,[status(thm)],[154, 152])).
% 1.37/1.61 tff(156,plain,
% 1.37/1.61 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, a1b1) | (~incident(c2, a1b1)) | (~point_equal(ac, c2)))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(157,plain,
% 1.37/1.61 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c2, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, c2))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.37/1.61 tff(158,plain,
% 1.37/1.61 ($false),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[157, 84, 151, 138, 137])).
% 1.37/1.61 tff(159,plain,(incident(ac, a1b1) | (~incident(c2, a1b1)) | (~point_equal(ac, c2))), inference(lemma,lemma(discharge,[]))).
% 1.37/1.61 tff(160,plain,
% 1.37/1.61 (~point_equal(ac, c2)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[159, 136, 84])).
% 1.37/1.61 tff(161,assumption,(~point_equal(ac, c2)), introduced(assumption)).
% 1.37/1.61 tff(162,assumption,(incident(c2, a1c1)), introduced(assumption)).
% 1.37/1.61 tff(163,plain,
% 1.37/1.61 ((goal | (~line_equal(a1c1, a2c2))) <=> (goal | (~line_equal(a1c1, a2c2)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(164,plain,
% 1.37/1.61 ((line_equal(a1c1, a2c2) => goal) <=> (goal | (~line_equal(a1c1, a2c2)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(165,axiom,(line_equal(a1c1, a2c2) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notac')).
% 1.37/1.61 tff(166,plain,
% 1.37/1.61 (goal | (~line_equal(a1c1, a2c2))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.37/1.61 tff(167,plain,
% 1.37/1.61 (goal | (~line_equal(a1c1, a2c2))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[166, 163])).
% 1.37/1.61 tff(168,plain,
% 1.37/1.61 (~line_equal(a1c1, a2c2)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[167, 49])).
% 1.37/1.61 tff(169,plain,
% 1.37/1.61 (incident(ac, a2c2) <=> incident(ac, a2c2)),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(170,axiom,(incident(ac, a2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iac2')).
% 1.37/1.61 tff(171,plain,
% 1.37/1.61 (incident(ac, a2c2)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.37/1.61 tff(172,plain,
% 1.37/1.61 (incident(ac, a1c1) <=> incident(ac, a1c1)),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(173,axiom,(incident(ac, a1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iac1')).
% 1.37/1.61 tff(174,plain,
% 1.37/1.61 (incident(ac, a1c1)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.37/1.61 tff(175,plain,
% 1.37/1.61 (incident(c2, a2c2) <=> incident(c2, a2c2)),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(176,axiom,(incident(c2, a2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic2a2')).
% 1.37/1.61 tff(177,plain,
% 1.37/1.61 (incident(c2, a2c2)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.37/1.61 tff(178,plain,
% 1.37/1.61 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, c2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, c2))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(179,plain,
% 1.37/1.61 ((line_equal(a1c1, a2c2) | point_equal(ac, c2) | (~incident(c2, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | (~incident(c2, a2c2))) <=> (line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, c2))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(180,plain,
% 1.37/1.61 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | point_equal(ac, c2) | (~incident(c2, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | (~incident(c2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, c2)))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[179])).
% 1.37/1.61 tff(181,plain,
% 1.37/1.61 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | point_equal(ac, c2) | (~incident(c2, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | (~incident(c2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, c2))),
% 1.37/1.61 inference(transitivity,[status(thm)],[180, 178])).
% 1.37/1.61 tff(182,plain,
% 1.37/1.61 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | point_equal(ac, c2) | (~incident(c2, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | (~incident(c2, a2c2)))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(183,plain,
% 1.37/1.61 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, c2)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.37/1.61 tff(184,plain,
% 1.37/1.61 ($false),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[183, 177, 174, 171, 168, 46, 162, 161])).
% 1.37/1.61 tff(185,plain,(point_equal(ac, c2) | (~incident(c2, a1c1))), inference(lemma,lemma(discharge,[]))).
% 1.37/1.61 tff(186,plain,
% 1.37/1.61 (~incident(c2, a1c1)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[185, 160])).
% 1.37/1.61 tff(187,plain,
% 1.37/1.61 (incident(c2, oc) <=> incident(c2, oc)),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(188,axiom,(incident(c2, oc)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic2oc')).
% 1.37/1.61 tff(189,plain,
% 1.37/1.61 (incident(c2, oc)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.37/1.61 tff(190,plain,
% 1.37/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, a1c1) | (~incident(c2, oc)) | (~line_equal(oc, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, a1c1) | (~incident(c2, oc)) | (~line_equal(oc, a1c1)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(191,plain,
% 1.37/1.61 ((incident(c2, a1c1) | (~line_equal(oc, a1c1)) | (~incident(c2, oc))) <=> (incident(c2, a1c1) | (~incident(c2, oc)) | (~line_equal(oc, a1c1)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(192,plain,
% 1.37/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, a1c1) | (~line_equal(oc, a1c1)) | (~incident(c2, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, a1c1) | (~incident(c2, oc)) | (~line_equal(oc, a1c1))))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[191])).
% 1.37/1.61 tff(193,plain,
% 1.37/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, a1c1) | (~line_equal(oc, a1c1)) | (~incident(c2, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, a1c1) | (~incident(c2, oc)) | (~line_equal(oc, a1c1)))),
% 1.37/1.61 inference(transitivity,[status(thm)],[192, 190])).
% 1.37/1.61 tff(194,plain,
% 1.37/1.61 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, a1c1) | (~line_equal(oc, a1c1)) | (~incident(c2, oc)))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(195,plain,
% 1.37/1.61 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, a1c1) | (~incident(c2, oc)) | (~line_equal(oc, a1c1))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.37/1.61 tff(196,plain,
% 1.37/1.61 (incident(c2, a1c1) | (~line_equal(oc, a1c1))),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[195, 189, 21])).
% 1.37/1.61 tff(197,plain,
% 1.37/1.61 (~line_equal(oc, a1c1)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[196, 186])).
% 1.37/1.61 tff(198,plain,
% 1.37/1.61 (^[A: $i] : refl((goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A))) <=> (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A))))),
% 1.37/1.61 inference(bind,[status(th)],[])).
% 1.37/1.61 tff(199,plain,
% 1.37/1.61 (![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A))) <=> ![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))),
% 1.37/1.61 inference(quant_intro,[status(thm)],[198])).
% 1.37/1.61 tff(200,plain,
% 1.37/1.61 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((incident(a1, A) & incident(b1, A) & incident(c1, A)) <=> (~((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A))))), ((~(incident(a1, A) & incident(b1, A) & incident(c1, A))) <=> (~(~((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A))))))), rewrite((~(~((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A))))) <=> ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))), ((~(incident(a1, A) & incident(b1, A) & incident(c1, A))) <=> ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A))))), ((goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))) <=> (goal | ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))))), rewrite((goal | ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) <=> (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))), ((goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))) <=> (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))))),
% 1.37/1.61 inference(bind,[status(th)],[])).
% 1.37/1.61 tff(201,plain,
% 1.37/1.61 (![A: $i] : (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))) <=> ![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))),
% 1.37/1.61 inference(quant_intro,[status(thm)],[200])).
% 1.37/1.61 tff(202,plain,
% 1.37/1.61 (![A: $i] : (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))) <=> ![A: $i] : (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(203,plain,
% 1.45/1.61 (^[A: $i] : trans(monotonicity(rewrite(((incident(a1, A) & incident(b1, A)) & incident(c1, A)) <=> (incident(a1, A) & incident(b1, A) & incident(c1, A))), ((((incident(a1, A) & incident(b1, A)) & incident(c1, A)) => goal) <=> ((incident(a1, A) & incident(b1, A) & incident(c1, A)) => goal))), rewrite(((incident(a1, A) & incident(b1, A) & incident(c1, A)) => goal) <=> (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A))))), ((((incident(a1, A) & incident(b1, A)) & incident(c1, A)) => goal) <=> (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A))))))),
% 1.45/1.61 inference(bind,[status(th)],[])).
% 1.45/1.61 tff(204,plain,
% 1.45/1.61 (![A: $i] : (((incident(a1, A) & incident(b1, A)) & incident(c1, A)) => goal) <=> ![A: $i] : (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A))))),
% 1.45/1.61 inference(quant_intro,[status(thm)],[203])).
% 1.45/1.61 tff(205,axiom,(![A: $i] : (((incident(a1, A) & incident(b1, A)) & incident(c1, A)) => goal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','triangle1')).
% 1.45/1.61 tff(206,plain,
% 1.45/1.61 (![A: $i] : (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.45/1.61 tff(207,plain,
% 1.45/1.61 (![A: $i] : (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[206, 202])).
% 1.45/1.61 tff(208,plain,(
% 1.45/1.61 ![A: $i] : (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A))))),
% 1.45/1.61 inference(skolemize,[status(sab)],[207])).
% 1.45/1.61 tff(209,plain,
% 1.45/1.61 (![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[208, 201])).
% 1.45/1.61 tff(210,plain,
% 1.45/1.61 (![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[209, 199])).
% 1.45/1.61 tff(211,plain,
% 1.45/1.61 (((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(c1, a1b1)))) <=> ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(c1, a1b1)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(212,plain,
% 1.45/1.61 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(c1, a1b1)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(213,plain,
% 1.45/1.61 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(c1, a1b1))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.45/1.61 tff(214,plain,
% 1.45/1.61 (~incident(c1, a1b1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[213, 49, 108, 64, 210])).
% 1.45/1.61 tff(215,plain,
% 1.45/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, a1)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(216,plain,
% 1.45/1.61 ((incident(c1, a1b1) | (~incident(a1, a1b1)) | (~point_equal(c1, a1))) <=> ((~incident(a1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, a1)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(217,plain,
% 1.45/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, a1b1) | (~incident(a1, a1b1)) | (~point_equal(c1, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, a1))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[216])).
% 1.45/1.61 tff(218,plain,
% 1.45/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, a1b1) | (~incident(a1, a1b1)) | (~point_equal(c1, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, a1)))),
% 1.45/1.61 inference(transitivity,[status(thm)],[217, 215])).
% 1.45/1.61 tff(219,plain,
% 1.45/1.61 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, a1b1) | (~incident(a1, a1b1)) | (~point_equal(c1, a1)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(220,plain,
% 1.45/1.61 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, a1))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[219, 218])).
% 1.45/1.61 tff(221,plain,
% 1.45/1.61 (~point_equal(c1, a1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[220, 108, 151, 214])).
% 1.45/1.61 tff(222,plain,
% 1.45/1.61 (incident(c1, oc) <=> incident(c1, oc)),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(223,axiom,(incident(c1, oc)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic1oc')).
% 1.45/1.61 tff(224,plain,
% 1.45/1.61 (incident(c1, oc)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.45/1.61 tff(225,plain,
% 1.45/1.61 (incident(c1, a1c1) <=> incident(c1, a1c1)),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(226,axiom,(incident(c1, a1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic1a1')).
% 1.45/1.61 tff(227,plain,
% 1.45/1.61 (incident(c1, a1c1)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[226, 225])).
% 1.45/1.61 tff(228,plain,
% 1.45/1.61 (incident(a1, a1c1) <=> incident(a1, a1c1)),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(229,axiom,(incident(a1, a1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia1c1')).
% 1.45/1.61 tff(230,plain,
% 1.45/1.61 (incident(a1, a1c1)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[229, 228])).
% 1.45/1.61 tff(231,plain,
% 1.45/1.61 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, oc)) | (~incident(c1, oc)) | point_equal(c1, a1) | line_equal(oc, a1c1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, oc)) | (~incident(c1, oc)) | point_equal(c1, a1) | line_equal(oc, a1c1))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(232,plain,
% 1.45/1.61 ((line_equal(oc, a1c1) | point_equal(c1, a1) | (~incident(a1, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(a1, a1c1))) <=> ((~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, oc)) | (~incident(c1, oc)) | point_equal(c1, a1) | line_equal(oc, a1c1))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(233,plain,
% 1.45/1.61 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, a1c1) | point_equal(c1, a1) | (~incident(a1, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(a1, a1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, oc)) | (~incident(c1, oc)) | point_equal(c1, a1) | line_equal(oc, a1c1)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[232])).
% 1.45/1.61 tff(234,plain,
% 1.45/1.61 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, a1c1) | point_equal(c1, a1) | (~incident(a1, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(a1, a1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, oc)) | (~incident(c1, oc)) | point_equal(c1, a1) | line_equal(oc, a1c1))),
% 1.45/1.61 inference(transitivity,[status(thm)],[233, 231])).
% 1.45/1.61 tff(235,plain,
% 1.45/1.61 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, a1c1) | point_equal(c1, a1) | (~incident(a1, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(a1, a1c1)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(236,plain,
% 1.45/1.61 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, oc)) | (~incident(c1, oc)) | point_equal(c1, a1) | line_equal(oc, a1c1)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[235, 234])).
% 1.45/1.61 tff(237,plain,
% 1.45/1.61 (~incident(a1, oc)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[236, 230, 227, 224, 46, 221, 197])).
% 1.45/1.61 tff(238,plain,
% 1.45/1.61 (incident(o, oc) <=> incident(o, oc)),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(239,axiom,(incident(o, oc)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iooc')).
% 1.45/1.61 tff(240,plain,
% 1.45/1.61 (incident(o, oc)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.45/1.61 tff(241,plain,
% 1.45/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, oc)) | incident(a1, oc) | (~point_equal(a1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oc)) | incident(a1, oc) | (~point_equal(a1, o)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(242,plain,
% 1.45/1.61 ((incident(a1, oc) | (~incident(o, oc)) | (~point_equal(a1, o))) <=> ((~incident(o, oc)) | incident(a1, oc) | (~point_equal(a1, o)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(243,plain,
% 1.45/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a1, oc) | (~incident(o, oc)) | (~point_equal(a1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, oc)) | incident(a1, oc) | (~point_equal(a1, o))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[242])).
% 1.45/1.61 tff(244,plain,
% 1.45/1.61 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a1, oc) | (~incident(o, oc)) | (~point_equal(a1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oc)) | incident(a1, oc) | (~point_equal(a1, o)))),
% 1.45/1.61 inference(transitivity,[status(thm)],[243, 241])).
% 1.45/1.61 tff(245,plain,
% 1.45/1.61 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a1, oc) | (~incident(o, oc)) | (~point_equal(a1, o)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(246,plain,
% 1.45/1.61 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oc)) | incident(a1, oc) | (~point_equal(a1, o))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[245, 244])).
% 1.45/1.61 tff(247,plain,
% 1.45/1.61 (~point_equal(a1, o)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[246, 240, 151, 237])).
% 1.45/1.61 tff(248,plain,
% 1.45/1.61 (incident(a1, oa) <=> incident(a1, oa)),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(249,axiom,(incident(a1, oa)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia1oa')).
% 1.45/1.61 tff(250,plain,
% 1.45/1.61 (incident(a1, oa)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[249, 248])).
% 1.45/1.61 tff(251,plain,
% 1.45/1.61 (incident(o, oa) <=> incident(o, oa)),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(252,axiom,(incident(o, oa)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iooa')).
% 1.45/1.61 tff(253,plain,
% 1.45/1.61 (incident(o, oa)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[252, 251])).
% 1.45/1.61 tff(254,plain,
% 1.45/1.61 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, a1b1)) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(o, a1b1)) | line_equal(oa, a1b1) | point_equal(a1, o))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, a1b1)) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(o, a1b1)) | line_equal(oa, a1b1) | point_equal(a1, o))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(255,plain,
% 1.45/1.62 ((line_equal(oa, a1b1) | point_equal(a1, o) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(a1, a1b1)) | (~incident(o, a1b1))) <=> ((~incident(a1, a1b1)) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(o, a1b1)) | line_equal(oa, a1b1) | point_equal(a1, o))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(256,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, a1b1) | point_equal(a1, o) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(a1, a1b1)) | (~incident(o, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, a1b1)) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(o, a1b1)) | line_equal(oa, a1b1) | point_equal(a1, o)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[255])).
% 1.45/1.62 tff(257,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, a1b1) | point_equal(a1, o) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(a1, a1b1)) | (~incident(o, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, a1b1)) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(o, a1b1)) | line_equal(oa, a1b1) | point_equal(a1, o))),
% 1.45/1.62 inference(transitivity,[status(thm)],[256, 254])).
% 1.45/1.62 tff(258,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, a1b1) | point_equal(a1, o) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(a1, a1b1)) | (~incident(o, a1b1)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(259,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, a1b1)) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(o, a1b1)) | line_equal(oa, a1b1) | point_equal(a1, o)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[258, 257])).
% 1.45/1.62 tff(260,plain,
% 1.45/1.62 ((~incident(o, a1b1)) | line_equal(oa, a1b1) | point_equal(a1, o)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[259, 108, 253, 250, 46])).
% 1.45/1.62 tff(261,plain,
% 1.45/1.62 (line_equal(oa, a1b1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[260, 247, 83])).
% 1.45/1.62 tff(262,plain,
% 1.45/1.62 (^[A: $i] : refl((goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A))) <=> (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A))))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(263,plain,
% 1.45/1.62 (![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A))) <=> ![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[262])).
% 1.45/1.62 tff(264,plain,
% 1.45/1.62 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((incident(a2, A) & incident(b2, A) & incident(c2, A)) <=> (~((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A))))), ((~(incident(a2, A) & incident(b2, A) & incident(c2, A))) <=> (~(~((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A))))))), rewrite((~(~((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A))))) <=> ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))), ((~(incident(a2, A) & incident(b2, A) & incident(c2, A))) <=> ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A))))), ((goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))) <=> (goal | ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))))), rewrite((goal | ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) <=> (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))), ((goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))) <=> (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(265,plain,
% 1.45/1.62 (![A: $i] : (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))) <=> ![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[264])).
% 1.45/1.62 tff(266,plain,
% 1.45/1.62 (![A: $i] : (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))) <=> ![A: $i] : (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(267,plain,
% 1.45/1.62 (^[A: $i] : trans(monotonicity(rewrite(((incident(a2, A) & incident(b2, A)) & incident(c2, A)) <=> (incident(a2, A) & incident(b2, A) & incident(c2, A))), ((((incident(a2, A) & incident(b2, A)) & incident(c2, A)) => goal) <=> ((incident(a2, A) & incident(b2, A) & incident(c2, A)) => goal))), rewrite(((incident(a2, A) & incident(b2, A) & incident(c2, A)) => goal) <=> (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A))))), ((((incident(a2, A) & incident(b2, A)) & incident(c2, A)) => goal) <=> (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A))))))),
% 1.45/1.62 inference(bind,[status(th)],[])).
% 1.45/1.62 tff(268,plain,
% 1.45/1.62 (![A: $i] : (((incident(a2, A) & incident(b2, A)) & incident(c2, A)) => goal) <=> ![A: $i] : (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A))))),
% 1.45/1.62 inference(quant_intro,[status(thm)],[267])).
% 1.45/1.62 tff(269,axiom,(![A: $i] : (((incident(a2, A) & incident(b2, A)) & incident(c2, A)) => goal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','triangle2')).
% 1.45/1.62 tff(270,plain,
% 1.45/1.62 (![A: $i] : (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[269, 268])).
% 1.45/1.62 tff(271,plain,
% 1.45/1.62 (![A: $i] : (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[270, 266])).
% 1.45/1.62 tff(272,plain,(
% 1.45/1.62 ![A: $i] : (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A))))),
% 1.45/1.62 inference(skolemize,[status(sab)],[271])).
% 1.45/1.62 tff(273,plain,
% 1.45/1.62 (![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[272, 265])).
% 1.45/1.62 tff(274,plain,
% 1.45/1.62 (![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[273, 263])).
% 1.45/1.62 tff(275,plain,
% 1.45/1.62 (incident(a2, a2c2) <=> incident(a2, a2c2)),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(276,axiom,(incident(a2, a2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia2c2')).
% 1.45/1.62 tff(277,plain,
% 1.45/1.62 (incident(a2, a2c2)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.45/1.62 tff(278,plain,
% 1.45/1.62 (((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (goal | (~incident(a2, a2c2)) | (~incident(b2, a2c2)) | (~incident(c2, a2c2)))) <=> ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | goal | (~incident(a2, a2c2)) | (~incident(b2, a2c2)) | (~incident(c2, a2c2)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(279,plain,
% 1.45/1.62 ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (goal | (~incident(a2, a2c2)) | (~incident(b2, a2c2)) | (~incident(c2, a2c2)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(280,plain,
% 1.45/1.62 ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | goal | (~incident(a2, a2c2)) | (~incident(b2, a2c2)) | (~incident(c2, a2c2))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[279, 278])).
% 1.45/1.62 tff(281,plain,
% 1.45/1.62 (~incident(b2, a2c2)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[280, 49, 277, 177, 274])).
% 1.45/1.62 tff(282,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, a2c2)) | incident(b2, a2c2) | (~point_equal(b2, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2c2)) | incident(b2, a2c2) | (~point_equal(b2, a2)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(283,plain,
% 1.45/1.62 ((incident(b2, a2c2) | (~incident(a2, a2c2)) | (~point_equal(b2, a2))) <=> ((~incident(a2, a2c2)) | incident(b2, a2c2) | (~point_equal(b2, a2)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(284,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, a2c2) | (~incident(a2, a2c2)) | (~point_equal(b2, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, a2c2)) | incident(b2, a2c2) | (~point_equal(b2, a2))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[283])).
% 1.45/1.62 tff(285,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, a2c2) | (~incident(a2, a2c2)) | (~point_equal(b2, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2c2)) | incident(b2, a2c2) | (~point_equal(b2, a2)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[284, 282])).
% 1.45/1.62 tff(286,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, a2c2) | (~incident(a2, a2c2)) | (~point_equal(b2, a2)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(287,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2c2)) | incident(b2, a2c2) | (~point_equal(b2, a2))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[286, 285])).
% 1.45/1.62 tff(288,plain,
% 1.45/1.62 (~point_equal(b2, a2)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[287, 277, 151, 281])).
% 1.45/1.62 tff(289,plain,
% 1.45/1.62 ((goal | (~line_equal(a1b1, a2b2))) <=> (goal | (~line_equal(a1b1, a2b2)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(290,plain,
% 1.45/1.62 ((line_equal(a1b1, a2b2) => goal) <=> (goal | (~line_equal(a1b1, a2b2)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(291,axiom,(line_equal(a1b1, a2b2) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notab')).
% 1.45/1.62 tff(292,plain,
% 1.45/1.62 (goal | (~line_equal(a1b1, a2b2))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[291, 290])).
% 1.45/1.62 tff(293,plain,
% 1.45/1.62 (goal | (~line_equal(a1b1, a2b2))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[292, 289])).
% 1.45/1.62 tff(294,plain,
% 1.45/1.62 (~line_equal(a1b1, a2b2)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[293, 49])).
% 1.45/1.62 tff(295,plain,
% 1.45/1.62 (incident(b2, a2b2) <=> incident(b2, a2b2)),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(296,axiom,(incident(b2, a2b2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib2a2')).
% 1.45/1.62 tff(297,plain,
% 1.45/1.62 (incident(b2, a2b2)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[296, 295])).
% 1.45/1.62 tff(298,plain,
% 1.45/1.62 (incident(a2, a2b2) <=> incident(a2, a2b2)),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(299,axiom,(incident(a2, a2b2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia2b2')).
% 1.45/1.62 tff(300,plain,
% 1.45/1.62 (incident(a2, a2b2)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[299, 298])).
% 1.45/1.62 tff(301,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(b2, a1b1)) | (~incident(b2, a2b2)) | point_equal(b2, a2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(b2, a1b1)) | (~incident(b2, a2b2)) | point_equal(b2, a2))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(302,plain,
% 1.45/1.62 ((line_equal(a1b1, a2b2) | point_equal(b2, a2) | (~incident(a2, a1b1)) | (~incident(b2, a1b1)) | (~incident(b2, a2b2)) | (~incident(a2, a2b2))) <=> (line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(b2, a1b1)) | (~incident(b2, a2b2)) | point_equal(b2, a2))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(303,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(b2, a2) | (~incident(a2, a1b1)) | (~incident(b2, a1b1)) | (~incident(b2, a2b2)) | (~incident(a2, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(b2, a1b1)) | (~incident(b2, a2b2)) | point_equal(b2, a2)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[302])).
% 1.45/1.62 tff(304,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(b2, a2) | (~incident(a2, a1b1)) | (~incident(b2, a1b1)) | (~incident(b2, a2b2)) | (~incident(a2, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(b2, a1b1)) | (~incident(b2, a2b2)) | point_equal(b2, a2))),
% 1.45/1.62 inference(transitivity,[status(thm)],[303, 301])).
% 1.45/1.62 tff(305,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(b2, a2) | (~incident(a2, a1b1)) | (~incident(b2, a1b1)) | (~incident(b2, a2b2)) | (~incident(a2, a2b2)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(306,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(b2, a1b1)) | (~incident(b2, a2b2)) | point_equal(b2, a2)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.45/1.62 tff(307,plain,
% 1.45/1.62 ((~incident(a2, a1b1)) | (~incident(b2, a1b1))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[306, 300, 297, 294, 46, 288])).
% 1.45/1.62 tff(308,plain,
% 1.45/1.62 (~incident(a2, a1b1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[307, 33])).
% 1.45/1.62 tff(309,plain,
% 1.45/1.62 (incident(a2, oa) <=> incident(a2, oa)),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(310,axiom,(incident(a2, oa)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia2oa')).
% 1.45/1.62 tff(311,plain,
% 1.45/1.62 (incident(a2, oa)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[310, 309])).
% 1.45/1.62 tff(312,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, a1b1) | (~incident(a2, oa)) | (~line_equal(oa, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a2, a1b1) | (~incident(a2, oa)) | (~line_equal(oa, a1b1)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(313,plain,
% 1.45/1.62 ((incident(a2, a1b1) | (~line_equal(oa, a1b1)) | (~incident(a2, oa))) <=> (incident(a2, a1b1) | (~incident(a2, oa)) | (~line_equal(oa, a1b1)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(314,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, a1b1) | (~line_equal(oa, a1b1)) | (~incident(a2, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, a1b1) | (~incident(a2, oa)) | (~line_equal(oa, a1b1))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[313])).
% 1.45/1.62 tff(315,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, a1b1) | (~line_equal(oa, a1b1)) | (~incident(a2, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a2, a1b1) | (~incident(a2, oa)) | (~line_equal(oa, a1b1)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[314, 312])).
% 1.45/1.62 tff(316,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, a1b1) | (~line_equal(oa, a1b1)) | (~incident(a2, oa)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(317,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a2, a1b1) | (~incident(a2, oa)) | (~line_equal(oa, a1b1))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[316, 315])).
% 1.45/1.62 tff(318,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[317, 311, 21, 308, 261])).
% 1.45/1.62 tff(319,plain,((~line_equal(b2c2, a1b1)) | (~incident(c2, a1b1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(320,plain,
% 1.45/1.62 (~line_equal(b2c2, a1b1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[319, 6])).
% 1.45/1.62 tff(321,plain,
% 1.45/1.62 (((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (goal | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(c2, a2b2)))) <=> ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | goal | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(c2, a2b2)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(322,plain,
% 1.45/1.62 ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (goal | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(c2, a2b2)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(323,plain,
% 1.45/1.62 ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | goal | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(c2, a2b2))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[322, 321])).
% 1.45/1.62 tff(324,plain,
% 1.45/1.62 (~incident(c2, a2b2)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[323, 49, 300, 297, 274])).
% 1.45/1.62 tff(325,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, b2)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(326,plain,
% 1.45/1.62 ((incident(c2, a2b2) | (~incident(b2, a2b2)) | (~point_equal(c2, b2))) <=> ((~incident(b2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, b2)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(327,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, a2b2) | (~incident(b2, a2b2)) | (~point_equal(c2, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, b2))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[326])).
% 1.45/1.62 tff(328,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, a2b2) | (~incident(b2, a2b2)) | (~point_equal(c2, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, b2)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[327, 325])).
% 1.45/1.62 tff(329,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, a2b2) | (~incident(b2, a2b2)) | (~point_equal(c2, b2)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(330,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, b2))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[329, 328])).
% 1.45/1.62 tff(331,plain,
% 1.45/1.62 (~point_equal(c2, b2)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[330, 297, 151, 324])).
% 1.45/1.62 tff(332,plain,
% 1.45/1.62 (incident(c2, b2c2) <=> incident(c2, b2c2)),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(333,axiom,(incident(c2, b2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic2b2')).
% 1.45/1.62 tff(334,plain,
% 1.45/1.62 (incident(c2, b2c2)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.45/1.62 tff(335,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c2, a1b1)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, a1b1)) | point_equal(c2, b2) | line_equal(b2c2, a1b1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c2, a1b1)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, a1b1)) | point_equal(c2, b2) | line_equal(b2c2, a1b1))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(336,plain,
% 1.45/1.62 ((line_equal(b2c2, a1b1) | point_equal(c2, b2) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(c2, a1b1)) | (~incident(b2, a1b1))) <=> ((~incident(c2, a1b1)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, a1b1)) | point_equal(c2, b2) | line_equal(b2c2, a1b1))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(337,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b2c2, a1b1) | point_equal(c2, b2) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(c2, a1b1)) | (~incident(b2, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c2, a1b1)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, a1b1)) | point_equal(c2, b2) | line_equal(b2c2, a1b1)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[336])).
% 1.45/1.62 tff(338,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b2c2, a1b1) | point_equal(c2, b2) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(c2, a1b1)) | (~incident(b2, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c2, a1b1)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, a1b1)) | point_equal(c2, b2) | line_equal(b2c2, a1b1))),
% 1.45/1.62 inference(transitivity,[status(thm)],[337, 335])).
% 1.45/1.62 tff(339,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b2c2, a1b1) | point_equal(c2, b2) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(c2, a1b1)) | (~incident(b2, a1b1)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(340,plain,
% 1.45/1.62 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c2, a1b1)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, a1b1)) | point_equal(c2, b2) | line_equal(b2c2, a1b1)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.45/1.62 tff(341,plain,
% 1.45/1.62 (~incident(b2, a1b1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[340, 6, 334, 24, 46, 331, 320])).
% 1.45/1.62 tff(342,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, a1b1) | (~incident(b2, ob)) | (~line_equal(ob, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b2, a1b1) | (~incident(b2, ob)) | (~line_equal(ob, a1b1)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(343,plain,
% 1.45/1.62 ((incident(b2, a1b1) | (~line_equal(ob, a1b1)) | (~incident(b2, ob))) <=> (incident(b2, a1b1) | (~incident(b2, ob)) | (~line_equal(ob, a1b1)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(344,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, a1b1) | (~line_equal(ob, a1b1)) | (~incident(b2, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, a1b1) | (~incident(b2, ob)) | (~line_equal(ob, a1b1))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[343])).
% 1.45/1.62 tff(345,plain,
% 1.45/1.62 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, a1b1) | (~line_equal(ob, a1b1)) | (~incident(b2, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b2, a1b1) | (~incident(b2, ob)) | (~line_equal(ob, a1b1)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[344, 342])).
% 1.45/1.63 tff(346,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, a1b1) | (~line_equal(ob, a1b1)) | (~incident(b2, ob)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(347,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b2, a1b1) | (~incident(b2, ob)) | (~line_equal(ob, a1b1))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[346, 345])).
% 1.45/1.63 tff(348,plain,
% 1.45/1.63 (incident(b2, a1b1) | (~line_equal(ob, a1b1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[347, 58, 21])).
% 1.45/1.63 tff(349,plain,
% 1.45/1.63 (~line_equal(ob, a1b1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[348, 341])).
% 1.45/1.63 tff(350,assumption,(~incident(ab, ob)), introduced(assumption)).
% 1.45/1.63 tff(351,assumption,(line_equal(a1b1, ob)), introduced(assumption)).
% 1.45/1.63 tff(352,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ab, a1b1)) | incident(ab, ob) | (~line_equal(a1b1, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ab, a1b1)) | incident(ab, ob) | (~line_equal(a1b1, ob)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(353,plain,
% 1.45/1.63 ((incident(ab, ob) | (~line_equal(a1b1, ob)) | (~incident(ab, a1b1))) <=> ((~incident(ab, a1b1)) | incident(ab, ob) | (~line_equal(a1b1, ob)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(354,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, ob) | (~line_equal(a1b1, ob)) | (~incident(ab, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ab, a1b1)) | incident(ab, ob) | (~line_equal(a1b1, ob))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[353])).
% 1.45/1.63 tff(355,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, ob) | (~line_equal(a1b1, ob)) | (~incident(ab, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ab, a1b1)) | incident(ab, ob) | (~line_equal(a1b1, ob)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[354, 352])).
% 1.45/1.63 tff(356,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, ob) | (~line_equal(a1b1, ob)) | (~incident(ab, a1b1)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(357,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ab, a1b1)) | incident(ab, ob) | (~line_equal(a1b1, ob))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[356, 355])).
% 1.45/1.63 tff(358,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[357, 115, 21, 350, 351])).
% 1.45/1.63 tff(359,plain,((~line_equal(a1b1, ob)) | incident(ab, ob)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(360,plain,
% 1.45/1.63 (~line_equal(a1b1, ob)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[359, 350])).
% 1.45/1.63 tff(361,plain,
% 1.45/1.63 (incident(ab, a2b2) <=> incident(ab, a2b2)),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(362,axiom,(incident(ab, a2b2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iab2')).
% 1.45/1.63 tff(363,plain,
% 1.45/1.63 (incident(ab, a2b2)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[362, 361])).
% 1.45/1.63 tff(364,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ab, a2b2)) | incident(ab, ob) | (~line_equal(a2b2, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ab, a2b2)) | incident(ab, ob) | (~line_equal(a2b2, ob)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(365,plain,
% 1.45/1.63 ((incident(ab, ob) | (~line_equal(a2b2, ob)) | (~incident(ab, a2b2))) <=> ((~incident(ab, a2b2)) | incident(ab, ob) | (~line_equal(a2b2, ob)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(366,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, ob) | (~line_equal(a2b2, ob)) | (~incident(ab, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ab, a2b2)) | incident(ab, ob) | (~line_equal(a2b2, ob))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[365])).
% 1.45/1.63 tff(367,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, ob) | (~line_equal(a2b2, ob)) | (~incident(ab, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ab, a2b2)) | incident(ab, ob) | (~line_equal(a2b2, ob)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[366, 364])).
% 1.45/1.63 tff(368,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, ob) | (~line_equal(a2b2, ob)) | (~incident(ab, a2b2)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(369,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ab, a2b2)) | incident(ab, ob) | (~line_equal(a2b2, ob))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.45/1.63 tff(370,plain,
% 1.45/1.63 (incident(ab, ob) | (~line_equal(a2b2, ob))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[369, 363, 21])).
% 1.45/1.63 tff(371,plain,
% 1.45/1.63 (~line_equal(a2b2, ob)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[370, 350])).
% 1.45/1.63 tff(372,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(a2, ob)) | (~incident(b2, ob)) | point_equal(b2, a2) | line_equal(a2b2, ob))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(a2, ob)) | (~incident(b2, ob)) | point_equal(b2, a2) | line_equal(a2b2, ob))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(373,plain,
% 1.45/1.63 ((line_equal(a2b2, ob) | point_equal(b2, a2) | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(a2, ob))) <=> ((~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(a2, ob)) | (~incident(b2, ob)) | point_equal(b2, a2) | line_equal(a2b2, ob))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(374,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2b2, ob) | point_equal(b2, a2) | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(a2, ob)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(a2, ob)) | (~incident(b2, ob)) | point_equal(b2, a2) | line_equal(a2b2, ob)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[373])).
% 1.45/1.63 tff(375,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2b2, ob) | point_equal(b2, a2) | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(a2, ob)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(a2, ob)) | (~incident(b2, ob)) | point_equal(b2, a2) | line_equal(a2b2, ob))),
% 1.45/1.63 inference(transitivity,[status(thm)],[374, 372])).
% 1.45/1.63 tff(376,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2b2, ob) | point_equal(b2, a2) | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(a2, ob)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(377,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(a2, ob)) | (~incident(b2, ob)) | point_equal(b2, a2) | line_equal(a2b2, ob)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.45/1.63 tff(378,plain,
% 1.45/1.63 (~incident(a2, ob)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[377, 300, 297, 58, 46, 288, 371])).
% 1.45/1.63 tff(379,assumption,(~line_equal(a2b2, ob)), introduced(assumption)).
% 1.45/1.63 tff(380,assumption,(incident(b1, a2b2)), introduced(assumption)).
% 1.45/1.63 tff(381,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(b2, b1) | (~incident(b2, a2b2)) | (~incident(b1, a2b2)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | (~incident(b2, a2b2)) | (~incident(b1, a2b2)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(382,plain,
% 1.45/1.63 ((line_equal(a2b2, ob) | point_equal(b2, b1) | (~incident(b1, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(b1, ob))) <=> (point_equal(b2, b1) | (~incident(b2, a2b2)) | (~incident(b1, a2b2)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(383,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2b2, ob) | point_equal(b2, b1) | (~incident(b1, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(b1, ob)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(b2, b1) | (~incident(b2, a2b2)) | (~incident(b1, a2b2)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[382])).
% 1.45/1.63 tff(384,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2b2, ob) | point_equal(b2, b1) | (~incident(b1, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(b1, ob)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | (~incident(b2, a2b2)) | (~incident(b1, a2b2)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob))),
% 1.45/1.63 inference(transitivity,[status(thm)],[383, 381])).
% 1.45/1.63 tff(385,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2b2, ob) | point_equal(b2, b1) | (~incident(b1, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(b1, ob)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(386,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | (~incident(b2, a2b2)) | (~incident(b1, a2b2)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[385, 384])).
% 1.45/1.63 tff(387,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[386, 297, 61, 58, 55, 46, 380, 379])).
% 1.45/1.63 tff(388,plain,(line_equal(a2b2, ob) | (~incident(b1, a2b2))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(389,plain,
% 1.45/1.63 (~incident(b1, a2b2)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[388, 371])).
% 1.45/1.63 tff(390,assumption,(point_equal(b1, a2)), introduced(assumption)).
% 1.45/1.63 tff(391,assumption,(~incident(b1, a2b2)), introduced(assumption)).
% 1.45/1.63 tff(392,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, a2b2)) | incident(b1, a2b2) | (~point_equal(b1, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2b2)) | incident(b1, a2b2) | (~point_equal(b1, a2)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(393,plain,
% 1.45/1.63 ((incident(b1, a2b2) | (~incident(a2, a2b2)) | (~point_equal(b1, a2))) <=> ((~incident(a2, a2b2)) | incident(b1, a2b2) | (~point_equal(b1, a2)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(394,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a2b2) | (~incident(a2, a2b2)) | (~point_equal(b1, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, a2b2)) | incident(b1, a2b2) | (~point_equal(b1, a2))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[393])).
% 1.45/1.63 tff(395,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a2b2) | (~incident(a2, a2b2)) | (~point_equal(b1, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2b2)) | incident(b1, a2b2) | (~point_equal(b1, a2)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[394, 392])).
% 1.45/1.63 tff(396,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a2b2) | (~incident(a2, a2b2)) | (~point_equal(b1, a2)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(397,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2b2)) | incident(b1, a2b2) | (~point_equal(b1, a2))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.45/1.63 tff(398,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[397, 300, 151, 391, 390])).
% 1.45/1.63 tff(399,plain,(incident(b1, a2b2) | (~point_equal(b1, a2))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(400,plain,
% 1.45/1.63 (~point_equal(b1, a2)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[399, 389])).
% 1.45/1.63 tff(401,assumption,(~incident(b1, b2c2)), introduced(assumption)).
% 1.45/1.63 tff(402,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, b2c2) | (~incident(bc, b2c2)) | (~point_equal(b1, bc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, b2c2) | (~incident(bc, b2c2)) | (~point_equal(b1, bc)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(403,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, b2c2) | (~incident(bc, b2c2)) | (~point_equal(b1, bc)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(404,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, b2c2) | (~incident(bc, b2c2)) | (~point_equal(b1, bc))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[403, 402])).
% 1.45/1.63 tff(405,plain,
% 1.45/1.63 (incident(b1, b2c2) | (~point_equal(b1, bc))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[404, 87, 151])).
% 1.45/1.63 tff(406,plain,
% 1.45/1.63 (~point_equal(b1, bc)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[405, 401])).
% 1.45/1.63 tff(407,assumption,(~incident(a2, ob)), introduced(assumption)).
% 1.45/1.63 tff(408,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, ob)) | incident(a2, ob) | (~point_equal(a2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(a2, ob) | (~point_equal(a2, o)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(409,plain,
% 1.45/1.63 ((incident(a2, ob) | (~incident(o, ob)) | (~point_equal(a2, o))) <=> ((~incident(o, ob)) | incident(a2, ob) | (~point_equal(a2, o)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(410,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, ob) | (~incident(o, ob)) | (~point_equal(a2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, ob)) | incident(a2, ob) | (~point_equal(a2, o))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[409])).
% 1.45/1.63 tff(411,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, ob) | (~incident(o, ob)) | (~point_equal(a2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(a2, ob) | (~point_equal(a2, o)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[410, 408])).
% 1.45/1.63 tff(412,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, ob) | (~incident(o, ob)) | (~point_equal(a2, o)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(413,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(a2, ob) | (~point_equal(a2, o))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.45/1.63 tff(414,plain,
% 1.45/1.63 (~point_equal(a2, o)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[413, 75, 151, 407])).
% 1.45/1.63 tff(415,assumption,(~point_equal(b1, a2)), introduced(assumption)).
% 1.45/1.63 tff(416,assumption,(~line_equal(a1b1, ob)), introduced(assumption)).
% 1.45/1.63 tff(417,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, b2c2) | (~incident(c2, b2c2)) | (~point_equal(b1, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, b2c2) | (~incident(c2, b2c2)) | (~point_equal(b1, c2)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(418,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, b2c2) | (~incident(c2, b2c2)) | (~point_equal(b1, c2)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(419,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, b2c2) | (~incident(c2, b2c2)) | (~point_equal(b1, c2))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.45/1.63 tff(420,plain,
% 1.45/1.63 (~point_equal(b1, c2)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[419, 334, 151, 401])).
% 1.45/1.63 tff(421,plain,
% 1.45/1.63 (^[A: $i, B: $i] : refl(((~point_equal(A, B)) | point_equal(B, A)) <=> ((~point_equal(A, B)) | point_equal(B, A)))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(422,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A)) <=> ![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[421])).
% 1.45/1.63 tff(423,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A)) <=> ![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(424,plain,
% 1.45/1.63 (^[A: $i, B: $i] : rewrite((point_equal(A, B) => point_equal(B, A)) <=> ((~point_equal(A, B)) | point_equal(B, A)))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(425,plain,
% 1.45/1.63 (![A: $i, B: $i] : (point_equal(A, B) => point_equal(B, A)) <=> ![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[424])).
% 1.45/1.63 tff(426,axiom,(![A: $i, B: $i] : (point_equal(A, B) => point_equal(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_of_point_equal')).
% 1.45/1.63 tff(427,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[426, 425])).
% 1.45/1.63 tff(428,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[427, 423])).
% 1.45/1.63 tff(429,plain,(
% 1.45/1.63 ![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.45/1.63 inference(skolemize,[status(sab)],[428])).
% 1.45/1.63 tff(430,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[429, 422])).
% 1.45/1.63 tff(431,plain,
% 1.45/1.63 (((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(c2, b1)) | point_equal(b1, c2))) <=> ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(c2, b1)) | point_equal(b1, c2))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(432,plain,
% 1.45/1.63 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(c2, b1)) | point_equal(b1, c2))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(433,plain,
% 1.45/1.63 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(c2, b1)) | point_equal(b1, c2)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[432, 431])).
% 1.45/1.63 tff(434,plain,
% 1.45/1.63 (~point_equal(c2, b1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[433, 430, 420])).
% 1.45/1.63 tff(435,assumption,(~incident(b2, b1c1)), introduced(assumption)).
% 1.45/1.63 tff(436,assumption,(point_equal(b2, c1)), introduced(assumption)).
% 1.45/1.63 tff(437,plain,
% 1.45/1.63 (incident(c1, b1c1) <=> incident(c1, b1c1)),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(438,axiom,(incident(c1, b1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic1b1')).
% 1.45/1.63 tff(439,plain,
% 1.45/1.63 (incident(c1, b1c1)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[438, 437])).
% 1.45/1.63 tff(440,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, b1c1) | (~incident(c1, b1c1)) | (~point_equal(b2, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b2, b1c1) | (~incident(c1, b1c1)) | (~point_equal(b2, c1)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(441,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, b1c1) | (~incident(c1, b1c1)) | (~point_equal(b2, c1)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(442,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b2, b1c1) | (~incident(c1, b1c1)) | (~point_equal(b2, c1))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[441, 440])).
% 1.45/1.63 tff(443,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[442, 439, 151, 435, 436])).
% 1.45/1.63 tff(444,plain,(incident(b2, b1c1) | (~point_equal(b2, c1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(445,plain,
% 1.45/1.63 (~point_equal(b2, c1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[444, 435])).
% 1.45/1.63 tff(446,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a1b1, ob))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a1b1, ob))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(447,plain,
% 1.45/1.63 ((line_equal(a1b1, ob) | point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b2, ob)) | (~incident(b1, ob))) <=> (point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a1b1, ob))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(448,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, ob) | point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b2, ob)) | (~incident(b1, ob)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a1b1, ob)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[447])).
% 1.45/1.63 tff(449,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, ob) | point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b2, ob)) | (~incident(b1, ob)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a1b1, ob))),
% 1.45/1.63 inference(transitivity,[status(thm)],[448, 446])).
% 1.45/1.63 tff(450,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, ob) | point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b2, ob)) | (~incident(b1, ob)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(451,plain,
% 1.45/1.63 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | (~incident(b1, a1b1)) | (~incident(b2, a1b1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(a1b1, ob)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[450, 449])).
% 1.45/1.63 tff(452,plain,
% 1.45/1.63 ((~incident(b2, a1b1)) | line_equal(a1b1, ob)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[451, 64, 61, 58, 55, 46])).
% 1.45/1.63 tff(453,plain,
% 1.45/1.63 (~incident(b2, a1b1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[452, 416])).
% 1.45/1.63 tff(454,plain,
% 1.45/1.63 (~line_equal(b2c2, a1b1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[32, 453])).
% 1.45/1.63 tff(455,plain,
% 1.45/1.63 (^[A: $i, B: $i] : refl(((~line_equal(A, B)) | line_equal(B, A)) <=> ((~line_equal(A, B)) | line_equal(B, A)))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(456,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A)) <=> ![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[455])).
% 1.45/1.63 tff(457,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A)) <=> ![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(458,plain,
% 1.45/1.63 (^[A: $i, B: $i] : rewrite((line_equal(A, B) => line_equal(B, A)) <=> ((~line_equal(A, B)) | line_equal(B, A)))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(459,plain,
% 1.45/1.63 (![A: $i, B: $i] : (line_equal(A, B) => line_equal(B, A)) <=> ![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[458])).
% 1.45/1.63 tff(460,axiom,(![A: $i, B: $i] : (line_equal(A, B) => line_equal(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_of_line_equal')).
% 1.45/1.63 tff(461,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[460, 459])).
% 1.45/1.63 tff(462,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[461, 457])).
% 1.45/1.63 tff(463,plain,(
% 1.45/1.63 ![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.45/1.63 inference(skolemize,[status(sab)],[462])).
% 1.45/1.63 tff(464,plain,
% 1.45/1.63 (![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[463, 456])).
% 1.45/1.63 tff(465,plain,
% 1.45/1.63 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a1b1, b2c2)) | line_equal(b2c2, a1b1))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a1b1, b2c2)) | line_equal(b2c2, a1b1))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(466,plain,
% 1.45/1.63 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a1b1, b2c2)) | line_equal(b2c2, a1b1))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(467,plain,
% 1.45/1.63 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a1b1, b2c2)) | line_equal(b2c2, a1b1)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[466, 465])).
% 1.45/1.63 tff(468,plain,
% 1.45/1.63 (~line_equal(a1b1, b2c2)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[467, 464, 454])).
% 1.45/1.63 tff(469,plain,
% 1.45/1.63 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, b1c1) | (~incident(b2, ob)) | (~line_equal(ob, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b2, b1c1) | (~incident(b2, ob)) | (~line_equal(ob, b1c1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(470,plain,
% 1.45/1.64 ((incident(b2, b1c1) | (~line_equal(ob, b1c1)) | (~incident(b2, ob))) <=> (incident(b2, b1c1) | (~incident(b2, ob)) | (~line_equal(ob, b1c1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(471,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, b1c1) | (~line_equal(ob, b1c1)) | (~incident(b2, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, b1c1) | (~incident(b2, ob)) | (~line_equal(ob, b1c1))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[470])).
% 1.45/1.64 tff(472,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, b1c1) | (~line_equal(ob, b1c1)) | (~incident(b2, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b2, b1c1) | (~incident(b2, ob)) | (~line_equal(ob, b1c1)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[471, 469])).
% 1.45/1.64 tff(473,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b2, b1c1) | (~line_equal(ob, b1c1)) | (~incident(b2, ob)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(474,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b2, b1c1) | (~incident(b2, ob)) | (~line_equal(ob, b1c1))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[473, 472])).
% 1.45/1.64 tff(475,plain,
% 1.45/1.64 (incident(b2, b1c1) | (~line_equal(ob, b1c1))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[474, 58, 21])).
% 1.45/1.64 tff(476,plain,
% 1.45/1.64 (~line_equal(ob, b1c1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[475, 435])).
% 1.45/1.64 tff(477,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, b1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(478,plain,
% 1.45/1.64 ((incident(c1, a1b1) | (~incident(b1, a1b1)) | (~point_equal(c1, b1))) <=> ((~incident(b1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, b1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(479,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, a1b1) | (~incident(b1, a1b1)) | (~point_equal(c1, b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, b1))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[478])).
% 1.45/1.64 tff(480,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, a1b1) | (~incident(b1, a1b1)) | (~point_equal(c1, b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, b1)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[479, 477])).
% 1.45/1.64 tff(481,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, a1b1) | (~incident(b1, a1b1)) | (~point_equal(c1, b1)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(482,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, b1))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[481, 480])).
% 1.45/1.64 tff(483,plain,
% 1.45/1.64 (~point_equal(c1, b1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[482, 64, 151, 214])).
% 1.45/1.64 tff(484,plain,
% 1.45/1.64 (incident(b1, b1c1) <=> incident(b1, b1c1)),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(485,axiom,(incident(b1, b1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib1c1')).
% 1.45/1.64 tff(486,plain,
% 1.45/1.64 (incident(b1, b1c1)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.45/1.64 tff(487,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, ob)) | (~incident(c1, ob)) | point_equal(c1, b1) | line_equal(ob, b1c1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, ob)) | (~incident(c1, ob)) | point_equal(c1, b1) | line_equal(ob, b1c1))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(488,plain,
% 1.45/1.64 ((line_equal(ob, b1c1) | point_equal(c1, b1) | (~incident(b1, ob)) | (~incident(c1, ob)) | (~incident(c1, b1c1)) | (~incident(b1, b1c1))) <=> ((~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, ob)) | (~incident(c1, ob)) | point_equal(c1, b1) | line_equal(ob, b1c1))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(489,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, b1c1) | point_equal(c1, b1) | (~incident(b1, ob)) | (~incident(c1, ob)) | (~incident(c1, b1c1)) | (~incident(b1, b1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, ob)) | (~incident(c1, ob)) | point_equal(c1, b1) | line_equal(ob, b1c1)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[488])).
% 1.45/1.64 tff(490,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, b1c1) | point_equal(c1, b1) | (~incident(b1, ob)) | (~incident(c1, ob)) | (~incident(c1, b1c1)) | (~incident(b1, b1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, ob)) | (~incident(c1, ob)) | point_equal(c1, b1) | line_equal(ob, b1c1))),
% 1.45/1.64 inference(transitivity,[status(thm)],[489, 487])).
% 1.45/1.64 tff(491,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, b1c1) | point_equal(c1, b1) | (~incident(b1, ob)) | (~incident(c1, ob)) | (~incident(c1, b1c1)) | (~incident(b1, b1c1)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(492,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, ob)) | (~incident(c1, ob)) | point_equal(c1, b1) | line_equal(ob, b1c1)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.45/1.64 tff(493,plain,
% 1.45/1.64 ((~incident(c1, ob)) | line_equal(ob, b1c1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[492, 439, 486, 61, 46, 483])).
% 1.45/1.64 tff(494,plain,
% 1.45/1.64 (~incident(c1, ob)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[493, 476])).
% 1.45/1.64 tff(495,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, ob)) | incident(c1, ob) | (~point_equal(c1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(c1, ob) | (~point_equal(c1, o)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(496,plain,
% 1.45/1.64 ((incident(c1, ob) | (~incident(o, ob)) | (~point_equal(c1, o))) <=> ((~incident(o, ob)) | incident(c1, ob) | (~point_equal(c1, o)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(497,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, ob) | (~incident(o, ob)) | (~point_equal(c1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, ob)) | incident(c1, ob) | (~point_equal(c1, o))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[496])).
% 1.45/1.64 tff(498,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, ob) | (~incident(o, ob)) | (~point_equal(c1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(c1, ob) | (~point_equal(c1, o)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[497, 495])).
% 1.45/1.64 tff(499,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, ob) | (~incident(o, ob)) | (~point_equal(c1, o)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(500,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(c1, ob) | (~point_equal(c1, o))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[499, 498])).
% 1.45/1.64 tff(501,plain,
% 1.45/1.64 (incident(c1, ob) | (~point_equal(c1, o))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[500, 75, 151])).
% 1.45/1.64 tff(502,plain,
% 1.45/1.64 (~point_equal(c1, o)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[501, 494])).
% 1.45/1.64 tff(503,assumption,(incident(a2, a1c1)), introduced(assumption)).
% 1.45/1.64 tff(504,plain,
% 1.45/1.64 ((goal | (~point_equal(a2, a1))) <=> (goal | (~point_equal(a2, a1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(505,plain,
% 1.45/1.64 ((point_equal(a2, a1) => goal) <=> (goal | (~point_equal(a2, a1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(506,axiom,(point_equal(a2, a1) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notaa')).
% 1.45/1.64 tff(507,plain,
% 1.45/1.64 (goal | (~point_equal(a2, a1))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[506, 505])).
% 1.45/1.64 tff(508,plain,
% 1.45/1.64 (goal | (~point_equal(a2, a1))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[507, 504])).
% 1.45/1.64 tff(509,plain,
% 1.45/1.64 (~point_equal(a2, a1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[508, 49])).
% 1.45/1.64 tff(510,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(a2, a1) | (~incident(a1, a1c1)) | (~incident(a2, a1c1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | line_equal(a1c1, oa))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(a2, a1) | (~incident(a1, a1c1)) | (~incident(a2, a1c1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | line_equal(a1c1, oa))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(511,plain,
% 1.45/1.64 ((line_equal(a1c1, oa) | point_equal(a2, a1) | (~incident(a1, a1c1)) | (~incident(a2, a1c1)) | (~incident(a2, oa)) | (~incident(a1, oa))) <=> (point_equal(a2, a1) | (~incident(a1, a1c1)) | (~incident(a2, a1c1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | line_equal(a1c1, oa))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(512,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, oa) | point_equal(a2, a1) | (~incident(a1, a1c1)) | (~incident(a2, a1c1)) | (~incident(a2, oa)) | (~incident(a1, oa)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(a2, a1) | (~incident(a1, a1c1)) | (~incident(a2, a1c1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | line_equal(a1c1, oa)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[511])).
% 1.45/1.64 tff(513,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, oa) | point_equal(a2, a1) | (~incident(a1, a1c1)) | (~incident(a2, a1c1)) | (~incident(a2, oa)) | (~incident(a1, oa)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(a2, a1) | (~incident(a1, a1c1)) | (~incident(a2, a1c1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | line_equal(a1c1, oa))),
% 1.45/1.64 inference(transitivity,[status(thm)],[512, 510])).
% 1.45/1.64 tff(514,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, oa) | point_equal(a2, a1) | (~incident(a1, a1c1)) | (~incident(a2, a1c1)) | (~incident(a2, oa)) | (~incident(a1, oa)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(515,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(a2, a1) | (~incident(a1, a1c1)) | (~incident(a2, a1c1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | line_equal(a1c1, oa)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[514, 513])).
% 1.45/1.64 tff(516,plain,
% 1.45/1.64 ((~incident(a2, a1c1)) | line_equal(a1c1, oa)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[515, 230, 250, 311, 509, 46])).
% 1.45/1.64 tff(517,plain,
% 1.45/1.64 (line_equal(a1c1, oa)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[516, 503])).
% 1.45/1.64 tff(518,plain,
% 1.45/1.64 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a1c1, oa)) | line_equal(oa, a1c1))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a1c1, oa)) | line_equal(oa, a1c1))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(519,plain,
% 1.45/1.64 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a1c1, oa)) | line_equal(oa, a1c1))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(520,plain,
% 1.45/1.64 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a1c1, oa)) | line_equal(oa, a1c1)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[519, 518])).
% 1.45/1.64 tff(521,plain,
% 1.45/1.64 (line_equal(oa, a1c1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[520, 464, 517])).
% 1.45/1.64 tff(522,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, a2)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(523,plain,
% 1.45/1.64 ((incident(c2, a2b2) | (~incident(a2, a2b2)) | (~point_equal(c2, a2))) <=> ((~incident(a2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, a2)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(524,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, a2b2) | (~incident(a2, a2b2)) | (~point_equal(c2, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, a2))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[523])).
% 1.45/1.64 tff(525,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, a2b2) | (~incident(a2, a2b2)) | (~point_equal(c2, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, a2)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[524, 522])).
% 1.45/1.64 tff(526,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, a2b2) | (~incident(a2, a2b2)) | (~point_equal(c2, a2)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(527,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, a2))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[526, 525])).
% 1.45/1.64 tff(528,plain,
% 1.45/1.64 (~point_equal(c2, a2)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[527, 300, 151, 324])).
% 1.45/1.64 tff(529,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | point_equal(c2, a2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | point_equal(c2, a2))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(530,plain,
% 1.45/1.64 ((line_equal(a1c1, a2c2) | point_equal(c2, a2) | (~incident(a2, a1c1)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(a2, a2c2))) <=> (line_equal(a1c1, a2c2) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | point_equal(c2, a2))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(531,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | point_equal(c2, a2) | (~incident(a2, a1c1)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(a2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | point_equal(c2, a2)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[530])).
% 1.45/1.64 tff(532,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | point_equal(c2, a2) | (~incident(a2, a1c1)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(a2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | point_equal(c2, a2))),
% 1.45/1.64 inference(transitivity,[status(thm)],[531, 529])).
% 1.45/1.64 tff(533,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | point_equal(c2, a2) | (~incident(a2, a1c1)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(a2, a2c2)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(534,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | point_equal(c2, a2)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.45/1.64 tff(535,plain,
% 1.45/1.64 ((~incident(a2, a1c1)) | (~incident(c2, a1c1))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[534, 277, 177, 168, 46, 528])).
% 1.45/1.64 tff(536,plain,
% 1.45/1.64 (~incident(c2, a1c1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[535, 503])).
% 1.45/1.64 tff(537,plain,
% 1.45/1.64 (~line_equal(oc, a1c1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[196, 536])).
% 1.45/1.64 tff(538,assumption,(~point_equal(c1, o)), introduced(assumption)).
% 1.45/1.64 tff(539,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c1, a1c1)) | (~incident(o, oc)) | (~incident(c1, oc)) | (~incident(o, a1c1)) | line_equal(oc, a1c1) | point_equal(c1, o))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a1c1)) | (~incident(o, oc)) | (~incident(c1, oc)) | (~incident(o, a1c1)) | line_equal(oc, a1c1) | point_equal(c1, o))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(540,plain,
% 1.45/1.64 ((line_equal(oc, a1c1) | point_equal(c1, o) | (~incident(o, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(o, a1c1))) <=> ((~incident(c1, a1c1)) | (~incident(o, oc)) | (~incident(c1, oc)) | (~incident(o, a1c1)) | line_equal(oc, a1c1) | point_equal(c1, o))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(541,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, a1c1) | point_equal(c1, o) | (~incident(o, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(o, a1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c1, a1c1)) | (~incident(o, oc)) | (~incident(c1, oc)) | (~incident(o, a1c1)) | line_equal(oc, a1c1) | point_equal(c1, o)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[540])).
% 1.45/1.64 tff(542,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, a1c1) | point_equal(c1, o) | (~incident(o, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(o, a1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a1c1)) | (~incident(o, oc)) | (~incident(c1, oc)) | (~incident(o, a1c1)) | line_equal(oc, a1c1) | point_equal(c1, o))),
% 1.45/1.64 inference(transitivity,[status(thm)],[541, 539])).
% 1.45/1.64 tff(543,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, a1c1) | point_equal(c1, o) | (~incident(o, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(o, a1c1)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(544,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a1c1)) | (~incident(o, oc)) | (~incident(c1, oc)) | (~incident(o, a1c1)) | line_equal(oc, a1c1) | point_equal(c1, o)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.45/1.64 tff(545,plain,
% 1.45/1.64 (~incident(o, a1c1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[544, 227, 240, 224, 46, 538, 537])).
% 1.45/1.64 tff(546,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oa)) | incident(o, a1c1) | (~line_equal(oa, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a1c1) | (~line_equal(oa, a1c1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(547,plain,
% 1.45/1.64 ((incident(o, a1c1) | (~line_equal(oa, a1c1)) | (~incident(o, oa))) <=> ((~incident(o, oa)) | incident(o, a1c1) | (~line_equal(oa, a1c1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(548,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1c1) | (~line_equal(oa, a1c1)) | (~incident(o, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oa)) | incident(o, a1c1) | (~line_equal(oa, a1c1))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[547])).
% 1.45/1.64 tff(549,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1c1) | (~line_equal(oa, a1c1)) | (~incident(o, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a1c1) | (~line_equal(oa, a1c1)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[548, 546])).
% 1.45/1.64 tff(550,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1c1) | (~line_equal(oa, a1c1)) | (~incident(o, oa)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(551,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a1c1) | (~line_equal(oa, a1c1))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[550, 549])).
% 1.45/1.64 tff(552,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[551, 253, 21, 545, 521])).
% 1.45/1.64 tff(553,plain,((~incident(a2, a1c1)) | point_equal(c1, o)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(554,plain,
% 1.45/1.64 (~incident(a2, a1c1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[553, 502])).
% 1.45/1.64 tff(555,assumption,(line_equal(a2b2, a1c1)), introduced(assumption)).
% 1.45/1.64 tff(556,assumption,(~incident(a2, a1c1)), introduced(assumption)).
% 1.45/1.64 tff(557,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, a1c1) | (~incident(a2, a2b2)) | (~line_equal(a2b2, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a2, a1c1) | (~incident(a2, a2b2)) | (~line_equal(a2b2, a1c1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(558,plain,
% 1.45/1.64 ((incident(a2, a1c1) | (~line_equal(a2b2, a1c1)) | (~incident(a2, a2b2))) <=> (incident(a2, a1c1) | (~incident(a2, a2b2)) | (~line_equal(a2b2, a1c1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(559,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, a1c1) | (~line_equal(a2b2, a1c1)) | (~incident(a2, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, a1c1) | (~incident(a2, a2b2)) | (~line_equal(a2b2, a1c1))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[558])).
% 1.45/1.64 tff(560,plain,
% 1.45/1.64 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, a1c1) | (~line_equal(a2b2, a1c1)) | (~incident(a2, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a2, a1c1) | (~incident(a2, a2b2)) | (~line_equal(a2b2, a1c1)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[559, 557])).
% 1.45/1.64 tff(561,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, a1c1) | (~line_equal(a2b2, a1c1)) | (~incident(a2, a2b2)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(562,plain,
% 1.45/1.64 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a2, a1c1) | (~incident(a2, a2b2)) | (~line_equal(a2b2, a1c1))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[561, 560])).
% 1.45/1.64 tff(563,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[562, 300, 21, 556, 555])).
% 1.45/1.64 tff(564,plain,(incident(a2, a1c1) | (~line_equal(a2b2, a1c1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(565,plain,
% 1.45/1.64 (~line_equal(a2b2, a1c1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[564, 554])).
% 1.45/1.64 tff(566,plain,
% 1.45/1.64 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a1c1, a2b2)) | line_equal(a2b2, a1c1))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a1c1, a2b2)) | line_equal(a2b2, a1c1))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(567,plain,
% 1.45/1.64 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a1c1, a2b2)) | line_equal(a2b2, a1c1))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(568,plain,
% 1.45/1.64 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a1c1, a2b2)) | line_equal(a2b2, a1c1)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[567, 566])).
% 1.45/1.64 tff(569,plain,
% 1.45/1.64 (~line_equal(a1c1, a2b2)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[568, 464, 565])).
% 1.45/1.64 tff(570,assumption,(~point_equal(a2, o)), introduced(assumption)).
% 1.45/1.64 tff(571,assumption,(~line_equal(a1c1, a2b2)), introduced(assumption)).
% 1.45/1.64 tff(572,plain,
% 1.45/1.64 (((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(a2, b1)) | point_equal(b1, a2))) <=> ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(a2, b1)) | point_equal(b1, a2))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(573,plain,
% 1.45/1.65 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(a2, b1)) | point_equal(b1, a2))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(574,plain,
% 1.45/1.65 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(a2, b1)) | point_equal(b1, a2)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[573, 572])).
% 1.45/1.65 tff(575,plain,
% 1.45/1.65 (~point_equal(a2, b1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[574, 430, 415])).
% 1.45/1.65 tff(576,assumption,(incident(b1, a2c2)), introduced(assumption)).
% 1.45/1.65 tff(577,assumption,(line_equal(a2c2, oc)), introduced(assumption)).
% 1.45/1.65 tff(578,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a2, a2c2)) | incident(a2, oc) | (~line_equal(a2c2, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a2, a2c2)) | incident(a2, oc) | (~line_equal(a2c2, oc)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(579,plain,
% 1.45/1.65 ((incident(a2, oc) | (~line_equal(a2c2, oc)) | (~incident(a2, a2c2))) <=> ((~incident(a2, a2c2)) | incident(a2, oc) | (~line_equal(a2c2, oc)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(580,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, oc) | (~line_equal(a2c2, oc)) | (~incident(a2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a2, a2c2)) | incident(a2, oc) | (~line_equal(a2c2, oc))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[579])).
% 1.45/1.65 tff(581,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, oc) | (~line_equal(a2c2, oc)) | (~incident(a2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a2, a2c2)) | incident(a2, oc) | (~line_equal(a2c2, oc)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[580, 578])).
% 1.45/1.65 tff(582,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, oc) | (~line_equal(a2c2, oc)) | (~incident(a2, a2c2)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(583,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a2, a2c2)) | incident(a2, oc) | (~line_equal(a2c2, oc))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[582, 581])).
% 1.45/1.65 tff(584,plain,
% 1.45/1.65 (incident(a2, oc) | (~line_equal(a2c2, oc))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[583, 277, 21])).
% 1.45/1.65 tff(585,plain,
% 1.45/1.65 (incident(a2, oc)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[584, 577])).
% 1.45/1.65 tff(586,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(o, oa)) | (~incident(o, oc)) | (~incident(a2, oa)) | (~incident(a2, oc)) | line_equal(oa, oc) | point_equal(a2, o))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(o, oa)) | (~incident(o, oc)) | (~incident(a2, oa)) | (~incident(a2, oc)) | line_equal(oa, oc) | point_equal(a2, o))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(587,plain,
% 1.45/1.65 ((line_equal(oa, oc) | point_equal(a2, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, oc)) | (~incident(o, oc))) <=> ((~incident(o, oa)) | (~incident(o, oc)) | (~incident(a2, oa)) | (~incident(a2, oc)) | line_equal(oa, oc) | point_equal(a2, o))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(588,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, oc) | point_equal(a2, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, oc)) | (~incident(o, oc)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(o, oa)) | (~incident(o, oc)) | (~incident(a2, oa)) | (~incident(a2, oc)) | line_equal(oa, oc) | point_equal(a2, o)))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[587])).
% 1.45/1.65 tff(589,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, oc) | point_equal(a2, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, oc)) | (~incident(o, oc)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(o, oa)) | (~incident(o, oc)) | (~incident(a2, oa)) | (~incident(a2, oc)) | line_equal(oa, oc) | point_equal(a2, o))),
% 1.45/1.65 inference(transitivity,[status(thm)],[588, 586])).
% 1.45/1.65 tff(590,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, oc) | point_equal(a2, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, oc)) | (~incident(o, oc)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(591,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(o, oa)) | (~incident(o, oc)) | (~incident(a2, oa)) | (~incident(a2, oc)) | line_equal(oa, oc) | point_equal(a2, o)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[590, 589])).
% 1.45/1.65 tff(592,plain,
% 1.45/1.65 ((~incident(a2, oc)) | line_equal(oa, oc) | point_equal(a2, o)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[591, 253, 240, 311, 46])).
% 1.45/1.65 tff(593,plain,
% 1.45/1.65 (line_equal(oa, oc)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[592, 585, 570])).
% 1.45/1.65 tff(594,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(b1, a2c2)) | incident(b1, oc) | (~line_equal(a2c2, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(b1, a2c2)) | incident(b1, oc) | (~line_equal(a2c2, oc)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(595,plain,
% 1.45/1.65 ((incident(b1, oc) | (~line_equal(a2c2, oc)) | (~incident(b1, a2c2))) <=> ((~incident(b1, a2c2)) | incident(b1, oc) | (~line_equal(a2c2, oc)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(596,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, oc) | (~line_equal(a2c2, oc)) | (~incident(b1, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(b1, a2c2)) | incident(b1, oc) | (~line_equal(a2c2, oc))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[595])).
% 1.45/1.65 tff(597,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, oc) | (~line_equal(a2c2, oc)) | (~incident(b1, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(b1, a2c2)) | incident(b1, oc) | (~line_equal(a2c2, oc)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[596, 594])).
% 1.45/1.65 tff(598,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, oc) | (~line_equal(a2c2, oc)) | (~incident(b1, a2c2)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(599,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(b1, a2c2)) | incident(b1, oc) | (~line_equal(a2c2, oc))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[598, 597])).
% 1.45/1.65 tff(600,plain,
% 1.45/1.65 ((~incident(b1, a2c2)) | incident(b1, oc) | (~line_equal(a2c2, oc))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[599, 21])).
% 1.45/1.65 tff(601,plain,
% 1.45/1.65 (incident(b1, oc)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[600, 577, 576])).
% 1.45/1.65 tff(602,plain,
% 1.45/1.65 (((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, oc)) | (~incident(b1, oc)) | (~incident(c1, oc)))) <=> ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, oc)) | (~incident(b1, oc)) | (~incident(c1, oc)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(603,plain,
% 1.45/1.65 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, oc)) | (~incident(b1, oc)) | (~incident(c1, oc)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(604,plain,
% 1.45/1.65 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, oc)) | (~incident(b1, oc)) | (~incident(c1, oc))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[603, 602])).
% 1.45/1.65 tff(605,plain,
% 1.45/1.65 ((~incident(a1, oc)) | (~incident(b1, oc))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[604, 49, 224, 210])).
% 1.45/1.65 tff(606,plain,
% 1.45/1.65 (~incident(a1, oc)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[605, 601])).
% 1.45/1.65 tff(607,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a1, oa)) | incident(a1, oc) | (~line_equal(oa, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a1, oa)) | incident(a1, oc) | (~line_equal(oa, oc)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(608,plain,
% 1.45/1.65 ((incident(a1, oc) | (~line_equal(oa, oc)) | (~incident(a1, oa))) <=> ((~incident(a1, oa)) | incident(a1, oc) | (~line_equal(oa, oc)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(609,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, oc) | (~line_equal(oa, oc)) | (~incident(a1, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a1, oa)) | incident(a1, oc) | (~line_equal(oa, oc))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[608])).
% 1.45/1.65 tff(610,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, oc) | (~line_equal(oa, oc)) | (~incident(a1, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a1, oa)) | incident(a1, oc) | (~line_equal(oa, oc)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[609, 607])).
% 1.45/1.65 tff(611,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, oc) | (~line_equal(oa, oc)) | (~incident(a1, oa)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(612,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a1, oa)) | incident(a1, oc) | (~line_equal(oa, oc))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[611, 610])).
% 1.45/1.65 tff(613,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[612, 250, 21, 606, 593])).
% 1.45/1.65 tff(614,plain,((~line_equal(a2c2, oc)) | point_equal(a2, o) | (~incident(b1, a2c2))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(615,plain,
% 1.45/1.65 (~line_equal(a2c2, oc)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[614, 576, 570])).
% 1.45/1.65 tff(616,assumption,(~line_equal(a2c2, oc)), introduced(assumption)).
% 1.45/1.65 tff(617,assumption,(incident(c1, a2c2)), introduced(assumption)).
% 1.45/1.65 tff(618,plain,
% 1.45/1.65 ((goal | (~point_equal(c2, c1))) <=> (goal | (~point_equal(c2, c1)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(619,plain,
% 1.45/1.65 ((point_equal(c2, c1) => goal) <=> (goal | (~point_equal(c2, c1)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(620,axiom,(point_equal(c2, c1) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notcc')).
% 1.45/1.65 tff(621,plain,
% 1.45/1.65 (goal | (~point_equal(c2, c1))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[620, 619])).
% 1.45/1.65 tff(622,plain,
% 1.45/1.65 (goal | (~point_equal(c2, c1))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[621, 618])).
% 1.45/1.65 tff(623,plain,
% 1.45/1.65 (~point_equal(c2, c1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[622, 49])).
% 1.45/1.65 tff(624,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(c2, c1) | (~incident(c2, a2c2)) | (~incident(c1, a2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a2c2, oc))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(c2, c1) | (~incident(c2, a2c2)) | (~incident(c1, a2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a2c2, oc))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(625,plain,
% 1.45/1.65 ((line_equal(a2c2, oc) | point_equal(c2, c1) | (~incident(c1, a2c2)) | (~incident(c2, a2c2)) | (~incident(c2, oc)) | (~incident(c1, oc))) <=> (point_equal(c2, c1) | (~incident(c2, a2c2)) | (~incident(c1, a2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a2c2, oc))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(626,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2c2, oc) | point_equal(c2, c1) | (~incident(c1, a2c2)) | (~incident(c2, a2c2)) | (~incident(c2, oc)) | (~incident(c1, oc)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(c2, c1) | (~incident(c2, a2c2)) | (~incident(c1, a2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a2c2, oc)))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[625])).
% 1.45/1.65 tff(627,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2c2, oc) | point_equal(c2, c1) | (~incident(c1, a2c2)) | (~incident(c2, a2c2)) | (~incident(c2, oc)) | (~incident(c1, oc)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(c2, c1) | (~incident(c2, a2c2)) | (~incident(c1, a2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a2c2, oc))),
% 1.45/1.65 inference(transitivity,[status(thm)],[626, 624])).
% 1.45/1.65 tff(628,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2c2, oc) | point_equal(c2, c1) | (~incident(c1, a2c2)) | (~incident(c2, a2c2)) | (~incident(c2, oc)) | (~incident(c1, oc)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(629,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(c2, c1) | (~incident(c2, a2c2)) | (~incident(c1, a2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a2c2, oc)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[628, 627])).
% 1.45/1.65 tff(630,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[629, 177, 224, 189, 623, 46, 617, 616])).
% 1.45/1.65 tff(631,plain,(line_equal(a2c2, oc) | (~incident(c1, a2c2))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(632,plain,
% 1.45/1.65 (~incident(c1, a2c2)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[631, 615])).
% 1.45/1.65 tff(633,assumption,(line_equal(b1c1, a2c2)), introduced(assumption)).
% 1.45/1.65 tff(634,assumption,(~incident(c1, a2c2)), introduced(assumption)).
% 1.45/1.65 tff(635,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(c1, b1c1)) | incident(c1, a2c2) | (~line_equal(b1c1, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c1, b1c1)) | incident(c1, a2c2) | (~line_equal(b1c1, a2c2)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(636,plain,
% 1.45/1.65 ((incident(c1, a2c2) | (~line_equal(b1c1, a2c2)) | (~incident(c1, b1c1))) <=> ((~incident(c1, b1c1)) | incident(c1, a2c2) | (~line_equal(b1c1, a2c2)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(637,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, a2c2) | (~line_equal(b1c1, a2c2)) | (~incident(c1, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(c1, b1c1)) | incident(c1, a2c2) | (~line_equal(b1c1, a2c2))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[636])).
% 1.45/1.65 tff(638,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, a2c2) | (~line_equal(b1c1, a2c2)) | (~incident(c1, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c1, b1c1)) | incident(c1, a2c2) | (~line_equal(b1c1, a2c2)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[637, 635])).
% 1.45/1.65 tff(639,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, a2c2) | (~line_equal(b1c1, a2c2)) | (~incident(c1, b1c1)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(640,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c1, b1c1)) | incident(c1, a2c2) | (~line_equal(b1c1, a2c2))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.45/1.65 tff(641,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[640, 439, 21, 634, 633])).
% 1.45/1.65 tff(642,plain,(incident(c1, a2c2) | (~line_equal(b1c1, a2c2))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(643,plain,
% 1.45/1.65 (~line_equal(b1c1, a2c2)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[642, 632])).
% 1.45/1.65 tff(644,assumption,(incident(a1, b2c2)), introduced(assumption)).
% 1.45/1.65 tff(645,plain,
% 1.45/1.65 ((goal | ((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2)))) <=> (goal | (~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(646,plain,
% 1.45/1.65 ((~(~((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2))))) <=> ((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(647,plain,
% 1.45/1.65 ((incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)) <=> (~((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(648,plain,
% 1.45/1.65 ((~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))) <=> (~(~((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2)))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[647])).
% 1.45/1.65 tff(649,plain,
% 1.45/1.65 ((~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))) <=> ((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[648, 646])).
% 1.45/1.65 tff(650,plain,
% 1.45/1.65 ((goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))) <=> (goal | ((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[649])).
% 1.45/1.65 tff(651,plain,
% 1.45/1.65 ((goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))) <=> (goal | (~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[650, 645])).
% 1.45/1.65 tff(652,plain,
% 1.45/1.65 ((goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))) <=> (goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(653,plain,
% 1.45/1.65 (((incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)) => goal) <=> (goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(654,plain,
% 1.45/1.65 (((incident(a1, b2c2) & incident(b1, a2c2)) & incident(c1, a2b2)) <=> (incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(655,plain,
% 1.45/1.65 ((((incident(a1, b2c2) & incident(b1, a2c2)) & incident(c1, a2b2)) => goal) <=> ((incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)) => goal)),
% 1.45/1.65 inference(monotonicity,[status(thm)],[654])).
% 1.45/1.65 tff(656,plain,
% 1.45/1.65 ((((incident(a1, b2c2) & incident(b1, a2c2)) & incident(c1, a2b2)) => goal) <=> (goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[655, 653])).
% 1.45/1.65 tff(657,axiom,(((incident(a1, b2c2) & incident(b1, a2c2)) & incident(c1, a2b2)) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1in2')).
% 1.45/1.65 tff(658,plain,
% 1.45/1.65 (goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[657, 656])).
% 1.45/1.65 tff(659,plain,
% 1.45/1.65 (goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[658, 652])).
% 1.45/1.65 tff(660,plain,
% 1.45/1.65 (goal | (~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[659, 651])).
% 1.45/1.65 tff(661,plain,
% 1.45/1.65 ((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[660, 49])).
% 1.45/1.65 tff(662,plain,
% 1.45/1.65 (~incident(c1, a2b2)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[661, 576, 644])).
% 1.45/1.65 tff(663,assumption,(~point_equal(a2, b1)), introduced(assumption)).
% 1.45/1.65 tff(664,assumption,(~line_equal(b1c1, a2c2)), introduced(assumption)).
% 1.45/1.65 tff(665,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(a2, b1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(a2, b1))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(666,plain,
% 1.45/1.65 ((line_equal(b1c1, a2c2) | point_equal(a2, b1) | (~incident(b1, b1c1)) | (~incident(a2, b1c1)) | (~incident(a2, a2c2)) | (~incident(b1, a2c2))) <=> ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(a2, b1))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(667,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, a2c2) | point_equal(a2, b1) | (~incident(b1, b1c1)) | (~incident(a2, b1c1)) | (~incident(a2, a2c2)) | (~incident(b1, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(a2, b1)))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[666])).
% 1.45/1.65 tff(668,plain,
% 1.45/1.65 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, a2c2) | point_equal(a2, b1) | (~incident(b1, b1c1)) | (~incident(a2, b1c1)) | (~incident(a2, a2c2)) | (~incident(b1, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(a2, b1))),
% 1.45/1.65 inference(transitivity,[status(thm)],[667, 665])).
% 1.45/1.65 tff(669,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, a2c2) | point_equal(a2, b1) | (~incident(b1, b1c1)) | (~incident(a2, b1c1)) | (~incident(a2, a2c2)) | (~incident(b1, a2c2)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(670,plain,
% 1.45/1.65 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(a2, b1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[669, 668])).
% 1.45/1.66 tff(671,plain,
% 1.45/1.66 ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | line_equal(b1c1, a2c2) | point_equal(a2, b1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[670, 277, 486, 46])).
% 1.45/1.66 tff(672,plain,
% 1.45/1.66 (~incident(a2, b1c1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[671, 576, 664, 663])).
% 1.45/1.66 tff(673,plain,
% 1.45/1.66 ((incident(c1, a2b2) | incident(a2, b1c1)) <=> (incident(c1, a2b2) | incident(a2, b1c1))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(674,axiom,(incident(c1, a2b2) | incident(a2, b1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gap_c')).
% 1.45/1.66 tff(675,plain,
% 1.45/1.66 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[674, 673])).
% 1.45/1.66 tff(676,plain,
% 1.45/1.66 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[675, 673])).
% 1.45/1.66 tff(677,plain,
% 1.45/1.66 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[676, 673])).
% 1.45/1.66 tff(678,plain,
% 1.45/1.66 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[677, 673])).
% 1.45/1.66 tff(679,plain,
% 1.45/1.66 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[678, 673])).
% 1.45/1.66 tff(680,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[679, 672, 662])).
% 1.45/1.66 tff(681,plain,((~incident(b1, a2c2)) | line_equal(b1c1, a2c2) | point_equal(a2, b1) | (~incident(a1, b2c2))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(682,plain,
% 1.45/1.66 (~incident(a1, b2c2)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[681, 643, 576, 575])).
% 1.45/1.66 tff(683,plain,
% 1.45/1.66 ((incident(a1, b2c2) | incident(b2, a1c1)) <=> (incident(a1, b2c2) | incident(b2, a1c1))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(684,axiom,(incident(a1, b2c2) | incident(b2, a1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gap_a')).
% 1.45/1.66 tff(685,plain,
% 1.45/1.66 (incident(a1, b2c2) | incident(b2, a1c1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[684, 683])).
% 1.45/1.66 tff(686,plain,
% 1.45/1.66 (incident(b2, a1c1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[685, 682])).
% 1.45/1.66 tff(687,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(b1, a2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(b1, a2))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(688,plain,
% 1.45/1.66 ((line_equal(b1c1, a2c2) | point_equal(b1, a2) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, a2c2)) | (~incident(a2, a2c2))) <=> ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(b1, a2))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(689,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, a2c2) | point_equal(b1, a2) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, a2c2)) | (~incident(a2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(b1, a2)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[688])).
% 1.45/1.66 tff(690,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, a2c2) | point_equal(b1, a2) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, a2c2)) | (~incident(a2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(b1, a2))),
% 1.45/1.66 inference(transitivity,[status(thm)],[689, 687])).
% 1.45/1.66 tff(691,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, a2c2) | point_equal(b1, a2) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, a2c2)) | (~incident(a2, a2c2)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(692,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(b1c1, a2c2) | point_equal(b1, a2)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[691, 690])).
% 1.45/1.66 tff(693,plain,
% 1.45/1.66 ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | line_equal(b1c1, a2c2) | point_equal(b1, a2)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[692, 277, 486, 46])).
% 1.45/1.66 tff(694,plain,
% 1.45/1.66 (~incident(a2, b1c1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[693, 643, 415, 576])).
% 1.45/1.66 tff(695,plain,
% 1.45/1.66 (incident(c1, a2b2)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[679, 694])).
% 1.45/1.66 tff(696,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a1c1, a2b2) | point_equal(b2, c1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a1c1, a2b2) | point_equal(b2, c1))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(697,plain,
% 1.45/1.66 ((line_equal(a1c1, a2b2) | point_equal(b2, c1) | (~incident(c1, a1c1)) | (~incident(b2, a1c1)) | (~incident(b2, a2b2)) | (~incident(c1, a2b2))) <=> ((~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a1c1, a2b2) | point_equal(b2, c1))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(698,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2b2) | point_equal(b2, c1) | (~incident(c1, a1c1)) | (~incident(b2, a1c1)) | (~incident(b2, a2b2)) | (~incident(c1, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a1c1, a2b2) | point_equal(b2, c1)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[697])).
% 1.45/1.66 tff(699,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2b2) | point_equal(b2, c1) | (~incident(c1, a1c1)) | (~incident(b2, a1c1)) | (~incident(b2, a2b2)) | (~incident(c1, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a1c1, a2b2) | point_equal(b2, c1))),
% 1.45/1.66 inference(transitivity,[status(thm)],[698, 696])).
% 1.45/1.66 tff(700,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2b2) | point_equal(b2, c1) | (~incident(c1, a1c1)) | (~incident(b2, a1c1)) | (~incident(b2, a2b2)) | (~incident(c1, a2b2)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(701,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a1c1, a2b2) | point_equal(b2, c1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[700, 699])).
% 1.45/1.66 tff(702,plain,
% 1.45/1.66 ((~incident(c1, a2b2)) | (~incident(b2, a1c1)) | line_equal(a1c1, a2b2) | point_equal(b2, c1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[701, 297, 227, 46])).
% 1.45/1.66 tff(703,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[702, 695, 686, 1, 571])).
% 1.45/1.66 tff(704,plain,((~incident(b1, a2c2)) | point_equal(b2, c1) | line_equal(a1c1, a2b2) | point_equal(b1, a2) | point_equal(a2, o)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(705,plain,
% 1.45/1.66 (~incident(b1, a2c2)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[704, 445, 569, 415, 570])).
% 1.45/1.66 tff(706,plain,
% 1.45/1.66 (incident(c2, a1b1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5, 705])).
% 1.45/1.66 tff(707,assumption,(~point_equal(c2, a1)), introduced(assumption)).
% 1.45/1.66 tff(708,assumption,(~line_equal(a1b1, b2c2)), introduced(assumption)).
% 1.45/1.66 tff(709,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(a1b1, b2c2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(a1b1, b2c2))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(710,plain,
% 1.45/1.66 ((line_equal(a1b1, b2c2) | point_equal(c2, a1) | (~incident(a1, a1b1)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, b2c2))) <=> ((~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(a1b1, b2c2))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(711,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, b2c2) | point_equal(c2, a1) | (~incident(a1, a1b1)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(a1b1, b2c2)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[710])).
% 1.45/1.66 tff(712,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, b2c2) | point_equal(c2, a1) | (~incident(a1, a1b1)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(a1b1, b2c2))),
% 1.45/1.66 inference(transitivity,[status(thm)],[711, 709])).
% 1.45/1.66 tff(713,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, b2c2) | point_equal(c2, a1) | (~incident(a1, a1b1)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, b2c2)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(714,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(a1b1, b2c2)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[713, 712])).
% 1.45/1.66 tff(715,plain,
% 1.45/1.66 ((~incident(a1, b2c2)) | (~incident(c2, a1b1)) | point_equal(c2, a1) | line_equal(a1b1, b2c2)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[714, 108, 334, 46])).
% 1.45/1.66 tff(716,plain,
% 1.45/1.66 (~incident(a1, b2c2)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[715, 84, 708, 707])).
% 1.45/1.66 tff(717,plain,
% 1.45/1.66 (incident(b2, a1c1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[685, 716])).
% 1.45/1.66 tff(718,plain,
% 1.45/1.66 (~incident(c1, a2b2)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[702, 717, 1, 571])).
% 1.45/1.66 tff(719,plain,
% 1.45/1.66 ((goal | ((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1)))) <=> (goal | (~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(720,plain,
% 1.45/1.66 ((~(~((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1))))) <=> ((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(721,plain,
% 1.45/1.66 ((incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)) <=> (~((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(722,plain,
% 1.45/1.66 ((~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))) <=> (~(~((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1)))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[721])).
% 1.45/1.66 tff(723,plain,
% 1.45/1.66 ((~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))) <=> ((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[722, 720])).
% 1.45/1.66 tff(724,plain,
% 1.45/1.66 ((goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))) <=> (goal | ((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[723])).
% 1.45/1.66 tff(725,plain,
% 1.45/1.66 ((goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))) <=> (goal | (~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[724, 719])).
% 1.45/1.66 tff(726,plain,
% 1.45/1.66 ((goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))) <=> (goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(727,plain,
% 1.45/1.66 (((incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)) => goal) <=> (goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(728,plain,
% 1.45/1.66 (((incident(a2, b1c1) & incident(b2, a1c1)) & incident(c2, a1b1)) <=> (incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(729,plain,
% 1.45/1.66 ((((incident(a2, b1c1) & incident(b2, a1c1)) & incident(c2, a1b1)) => goal) <=> ((incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)) => goal)),
% 1.45/1.66 inference(monotonicity,[status(thm)],[728])).
% 1.45/1.66 tff(730,plain,
% 1.45/1.66 ((((incident(a2, b1c1) & incident(b2, a1c1)) & incident(c2, a1b1)) => goal) <=> (goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[729, 727])).
% 1.45/1.66 tff(731,axiom,(((incident(a2, b1c1) & incident(b2, a1c1)) & incident(c2, a1b1)) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2in1')).
% 1.45/1.66 tff(732,plain,
% 1.45/1.66 (goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[731, 730])).
% 1.45/1.66 tff(733,plain,
% 1.45/1.66 (goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[732, 726])).
% 1.45/1.66 tff(734,plain,
% 1.45/1.66 (goal | (~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[733, 725])).
% 1.45/1.66 tff(735,plain,
% 1.45/1.66 ((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[734, 49])).
% 1.45/1.66 tff(736,plain,
% 1.45/1.66 (~incident(a2, b1c1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[735, 717, 84])).
% 1.45/1.66 tff(737,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[679, 736, 718])).
% 1.45/1.66 tff(738,plain,((~incident(c2, a1b1)) | point_equal(b2, c1) | line_equal(a1c1, a2b2) | line_equal(a1b1, b2c2) | point_equal(c2, a1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(739,plain,
% 1.45/1.66 (point_equal(c2, a1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[738, 706, 569, 468, 445])).
% 1.45/1.66 tff(740,assumption,(point_equal(c2, a1)), introduced(assumption)).
% 1.45/1.66 tff(741,assumption,(~incident(c2, a1c1)), introduced(assumption)).
% 1.45/1.66 tff(742,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, a1c1)) | incident(c2, a1c1) | (~point_equal(c2, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1c1)) | incident(c2, a1c1) | (~point_equal(c2, a1)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(743,plain,
% 1.45/1.66 ((incident(c2, a1c1) | (~incident(a1, a1c1)) | (~point_equal(c2, a1))) <=> ((~incident(a1, a1c1)) | incident(c2, a1c1) | (~point_equal(c2, a1)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(744,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, a1c1) | (~incident(a1, a1c1)) | (~point_equal(c2, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, a1c1)) | incident(c2, a1c1) | (~point_equal(c2, a1))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[743])).
% 1.45/1.66 tff(745,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, a1c1) | (~incident(a1, a1c1)) | (~point_equal(c2, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1c1)) | incident(c2, a1c1) | (~point_equal(c2, a1)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[744, 742])).
% 1.45/1.66 tff(746,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, a1c1) | (~incident(a1, a1c1)) | (~point_equal(c2, a1)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(747,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1c1)) | incident(c2, a1c1) | (~point_equal(c2, a1))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[746, 745])).
% 1.45/1.66 tff(748,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[747, 230, 151, 741, 740])).
% 1.45/1.66 tff(749,plain,(incident(c2, a1c1) | (~point_equal(c2, a1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(750,plain,
% 1.45/1.66 (incident(c2, a1c1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[749, 739])).
% 1.45/1.66 tff(751,plain,
% 1.45/1.66 (((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(c1, c2)) | point_equal(c2, c1))) <=> ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(c1, c2)) | point_equal(c2, c1))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(752,plain,
% 1.45/1.66 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(c1, c2)) | point_equal(c2, c1))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(753,plain,
% 1.45/1.66 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(c1, c2)) | point_equal(c2, c1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[752, 751])).
% 1.45/1.66 tff(754,plain,
% 1.45/1.66 (~point_equal(c1, c2)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[753, 623, 430])).
% 1.45/1.66 tff(755,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | line_equal(oc, a1c1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | line_equal(oc, a1c1))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(756,plain,
% 1.45/1.66 ((line_equal(oc, a1c1) | point_equal(c1, c2) | (~incident(c2, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(c2, a1c1))) <=> ((~incident(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | line_equal(oc, a1c1))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(757,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, a1c1) | point_equal(c1, c2) | (~incident(c2, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(c2, a1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | line_equal(oc, a1c1)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[756])).
% 1.45/1.66 tff(758,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, a1c1) | point_equal(c1, c2) | (~incident(c2, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(c2, a1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | line_equal(oc, a1c1))),
% 1.45/1.66 inference(transitivity,[status(thm)],[757, 755])).
% 1.45/1.66 tff(759,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, a1c1) | point_equal(c1, c2) | (~incident(c2, oc)) | (~incident(c1, oc)) | (~incident(c1, a1c1)) | (~incident(c2, a1c1)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(760,plain,
% 1.45/1.66 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | line_equal(oc, a1c1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[759, 758])).
% 1.45/1.66 tff(761,plain,
% 1.45/1.66 ((~incident(c2, a1c1)) | line_equal(oc, a1c1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[760, 227, 224, 189, 46, 754])).
% 1.45/1.66 tff(762,plain,
% 1.45/1.66 (line_equal(oc, a1c1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[761, 750])).
% 1.45/1.66 tff(763,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oc)) | incident(o, a1c1) | (~line_equal(oc, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oc)) | incident(o, a1c1) | (~line_equal(oc, a1c1)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(764,plain,
% 1.45/1.66 ((incident(o, a1c1) | (~line_equal(oc, a1c1)) | (~incident(o, oc))) <=> ((~incident(o, oc)) | incident(o, a1c1) | (~line_equal(oc, a1c1)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(765,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1c1) | (~line_equal(oc, a1c1)) | (~incident(o, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oc)) | incident(o, a1c1) | (~line_equal(oc, a1c1))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[764])).
% 1.45/1.66 tff(766,plain,
% 1.45/1.66 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1c1) | (~line_equal(oc, a1c1)) | (~incident(o, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oc)) | incident(o, a1c1) | (~line_equal(oc, a1c1)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[765, 763])).
% 1.45/1.67 tff(767,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1c1) | (~line_equal(oc, a1c1)) | (~incident(o, oc)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(768,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oc)) | incident(o, a1c1) | (~line_equal(oc, a1c1))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[767, 766])).
% 1.45/1.67 tff(769,plain,
% 1.45/1.67 (incident(o, a1c1) | (~line_equal(oc, a1c1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[768, 240, 21])).
% 1.45/1.67 tff(770,plain,
% 1.45/1.67 (incident(o, a1c1)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[769, 762])).
% 1.45/1.67 tff(771,assumption,(~point_equal(c2, b1)), introduced(assumption)).
% 1.45/1.67 tff(772,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(a1b1, ob))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(a1b1, ob))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(773,plain,
% 1.45/1.67 ((line_equal(a1b1, ob) | point_equal(c2, b1) | (~incident(b1, a1b1)) | (~incident(c2, a1b1)) | (~incident(c2, ob)) | (~incident(b1, ob))) <=> ((~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(a1b1, ob))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(774,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, ob) | point_equal(c2, b1) | (~incident(b1, a1b1)) | (~incident(c2, a1b1)) | (~incident(c2, ob)) | (~incident(b1, ob)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(a1b1, ob)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[773])).
% 1.45/1.67 tff(775,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, ob) | point_equal(c2, b1) | (~incident(b1, a1b1)) | (~incident(c2, a1b1)) | (~incident(c2, ob)) | (~incident(b1, ob)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(a1b1, ob))),
% 1.45/1.67 inference(transitivity,[status(thm)],[774, 772])).
% 1.45/1.67 tff(776,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, ob) | point_equal(c2, b1) | (~incident(b1, a1b1)) | (~incident(c2, a1b1)) | (~incident(c2, ob)) | (~incident(b1, ob)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(777,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(a1b1, ob)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[776, 775])).
% 1.45/1.67 tff(778,plain,
% 1.45/1.67 ((~incident(c2, a1b1)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(a1b1, ob)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[777, 64, 61, 46])).
% 1.45/1.67 tff(779,plain,
% 1.45/1.67 (~incident(c2, ob)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[778, 706, 416, 771])).
% 1.45/1.67 tff(780,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, ob)) | incident(c2, ob) | (~point_equal(c2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(c2, ob) | (~point_equal(c2, o)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(781,plain,
% 1.45/1.67 ((incident(c2, ob) | (~incident(o, ob)) | (~point_equal(c2, o))) <=> ((~incident(o, ob)) | incident(c2, ob) | (~point_equal(c2, o)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(782,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, ob) | (~incident(o, ob)) | (~point_equal(c2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, ob)) | incident(c2, ob) | (~point_equal(c2, o))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[781])).
% 1.45/1.67 tff(783,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, ob) | (~incident(o, ob)) | (~point_equal(c2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(c2, ob) | (~point_equal(c2, o)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[782, 780])).
% 1.45/1.67 tff(784,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, ob) | (~incident(o, ob)) | (~point_equal(c2, o)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(785,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(c2, ob) | (~point_equal(c2, o))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[784, 783])).
% 1.45/1.67 tff(786,plain,
% 1.45/1.67 (incident(c2, ob) | (~point_equal(c2, o))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[785, 75, 151])).
% 1.45/1.67 tff(787,plain,
% 1.45/1.67 (~point_equal(c2, o)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[786, 779])).
% 1.45/1.67 tff(788,assumption,(~incident(c2, oa)), introduced(assumption)).
% 1.45/1.67 tff(789,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, oa)) | incident(c2, oa) | (~point_equal(c2, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, oa)) | incident(c2, oa) | (~point_equal(c2, a1)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(790,plain,
% 1.45/1.67 ((incident(c2, oa) | (~incident(a1, oa)) | (~point_equal(c2, a1))) <=> ((~incident(a1, oa)) | incident(c2, oa) | (~point_equal(c2, a1)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(791,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, oa) | (~incident(a1, oa)) | (~point_equal(c2, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, oa)) | incident(c2, oa) | (~point_equal(c2, a1))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[790])).
% 1.45/1.67 tff(792,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, oa) | (~incident(a1, oa)) | (~point_equal(c2, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, oa)) | incident(c2, oa) | (~point_equal(c2, a1)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[791, 789])).
% 1.45/1.67 tff(793,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, oa) | (~incident(a1, oa)) | (~point_equal(c2, a1)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(794,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, oa)) | incident(c2, oa) | (~point_equal(c2, a1))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[793, 792])).
% 1.45/1.67 tff(795,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[794, 250, 151, 788, 740])).
% 1.45/1.67 tff(796,plain,(incident(c2, oa) | (~point_equal(c2, a1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(797,plain,
% 1.45/1.67 (incident(c2, oa)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[796, 739])).
% 1.45/1.67 tff(798,plain,
% 1.45/1.67 (((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (goal | (~incident(a2, b2c2)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)))) <=> ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | goal | (~incident(a2, b2c2)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(799,plain,
% 1.45/1.67 ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (goal | (~incident(a2, b2c2)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(800,plain,
% 1.45/1.67 ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | goal | (~incident(a2, b2c2)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[799, 798])).
% 1.45/1.67 tff(801,plain,
% 1.45/1.67 (~incident(a2, b2c2)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[800, 49, 334, 24, 274])).
% 1.45/1.67 tff(802,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, b2c2) | (~incident(c2, b2c2)) | (~point_equal(a2, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a2, b2c2) | (~incident(c2, b2c2)) | (~point_equal(a2, c2)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(803,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, b2c2) | (~incident(c2, b2c2)) | (~point_equal(a2, c2)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(804,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a2, b2c2) | (~incident(c2, b2c2)) | (~point_equal(a2, c2))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[803, 802])).
% 1.45/1.67 tff(805,plain,
% 1.45/1.67 (~point_equal(a2, c2)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[804, 334, 151, 801])).
% 1.45/1.67 tff(806,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oa)) | (~incident(c2, oa)) | point_equal(a2, c2) | line_equal(oa, a2c2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oa)) | (~incident(c2, oa)) | point_equal(a2, c2) | line_equal(oa, a2c2))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(807,plain,
% 1.45/1.67 ((line_equal(oa, a2c2) | point_equal(a2, c2) | (~incident(c2, oa)) | (~incident(a2, oa)) | (~incident(a2, a2c2)) | (~incident(c2, a2c2))) <=> ((~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oa)) | (~incident(c2, oa)) | point_equal(a2, c2) | line_equal(oa, a2c2))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(808,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, a2c2) | point_equal(a2, c2) | (~incident(c2, oa)) | (~incident(a2, oa)) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oa)) | (~incident(c2, oa)) | point_equal(a2, c2) | line_equal(oa, a2c2)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[807])).
% 1.45/1.67 tff(809,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, a2c2) | point_equal(a2, c2) | (~incident(c2, oa)) | (~incident(a2, oa)) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oa)) | (~incident(c2, oa)) | point_equal(a2, c2) | line_equal(oa, a2c2))),
% 1.45/1.67 inference(transitivity,[status(thm)],[808, 806])).
% 1.45/1.67 tff(810,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, a2c2) | point_equal(a2, c2) | (~incident(c2, oa)) | (~incident(a2, oa)) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(811,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oa)) | (~incident(c2, oa)) | point_equal(a2, c2) | line_equal(oa, a2c2)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.45/1.67 tff(812,plain,
% 1.45/1.67 ((~incident(c2, oa)) | line_equal(oa, a2c2)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[811, 277, 177, 311, 46, 805])).
% 1.45/1.67 tff(813,plain,
% 1.45/1.67 (line_equal(oa, a2c2)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[812, 797])).
% 1.45/1.67 tff(814,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oa)) | incident(o, a2c2) | (~line_equal(oa, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a2c2) | (~line_equal(oa, a2c2)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(815,plain,
% 1.45/1.67 ((incident(o, a2c2) | (~line_equal(oa, a2c2)) | (~incident(o, oa))) <=> ((~incident(o, oa)) | incident(o, a2c2) | (~line_equal(oa, a2c2)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(816,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2c2) | (~line_equal(oa, a2c2)) | (~incident(o, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oa)) | incident(o, a2c2) | (~line_equal(oa, a2c2))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[815])).
% 1.45/1.67 tff(817,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2c2) | (~line_equal(oa, a2c2)) | (~incident(o, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a2c2) | (~line_equal(oa, a2c2)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[816, 814])).
% 1.45/1.67 tff(818,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2c2) | (~line_equal(oa, a2c2)) | (~incident(o, oa)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(819,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a2c2) | (~line_equal(oa, a2c2))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[818, 817])).
% 1.45/1.67 tff(820,plain,
% 1.45/1.67 (incident(o, a2c2) | (~line_equal(oa, a2c2))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[819, 253, 21])).
% 1.45/1.67 tff(821,plain,
% 1.45/1.67 (incident(o, a2c2)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[820, 813])).
% 1.45/1.67 tff(822,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(o, a1c1)) | (~incident(o, a2c2)) | point_equal(c2, o))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(o, a1c1)) | (~incident(o, a2c2)) | point_equal(c2, o))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(823,plain,
% 1.45/1.67 ((line_equal(a1c1, a2c2) | point_equal(c2, o) | (~incident(o, a1c1)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(o, a2c2))) <=> (line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(o, a1c1)) | (~incident(o, a2c2)) | point_equal(c2, o))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(824,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | point_equal(c2, o) | (~incident(o, a1c1)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(o, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(o, a1c1)) | (~incident(o, a2c2)) | point_equal(c2, o)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[823])).
% 1.45/1.67 tff(825,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | point_equal(c2, o) | (~incident(o, a1c1)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(o, a2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(o, a1c1)) | (~incident(o, a2c2)) | point_equal(c2, o))),
% 1.45/1.67 inference(transitivity,[status(thm)],[824, 822])).
% 1.45/1.67 tff(826,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2c2) | point_equal(c2, o) | (~incident(o, a1c1)) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(o, a2c2)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(827,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(o, a1c1)) | (~incident(o, a2c2)) | point_equal(c2, o)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[826, 825])).
% 1.45/1.67 tff(828,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[827, 177, 168, 46, 750, 821, 787, 770])).
% 1.45/1.67 tff(829,plain,(incident(b2, b1c1) | line_equal(a1b1, ob) | point_equal(c2, b1) | point_equal(b1, a2) | point_equal(a2, o)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(830,plain,
% 1.45/1.67 (incident(b2, b1c1)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[829, 434, 416, 415, 414])).
% 1.45/1.67 tff(831,assumption,(~point_equal(bc, b2)), introduced(assumption)).
% 1.45/1.67 tff(832,assumption,(incident(b2, b1c1)), introduced(assumption)).
% 1.45/1.67 tff(833,plain,
% 1.45/1.67 ((goal | (~line_equal(b1c1, b2c2))) <=> (goal | (~line_equal(b1c1, b2c2)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(834,plain,
% 1.45/1.67 ((line_equal(b1c1, b2c2) => goal) <=> (goal | (~line_equal(b1c1, b2c2)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(835,axiom,(line_equal(b1c1, b2c2) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notbc')).
% 1.45/1.67 tff(836,plain,
% 1.45/1.67 (goal | (~line_equal(b1c1, b2c2))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[835, 834])).
% 1.45/1.67 tff(837,plain,
% 1.45/1.67 (goal | (~line_equal(b1c1, b2c2))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[836, 833])).
% 1.45/1.67 tff(838,plain,
% 1.45/1.67 (~line_equal(b1c1, b2c2)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[837, 49])).
% 1.45/1.67 tff(839,plain,
% 1.45/1.67 (incident(bc, b1c1) <=> incident(bc, b1c1)),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(840,axiom,(incident(bc, b1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ibc1')).
% 1.45/1.67 tff(841,plain,
% 1.45/1.67 (incident(bc, b1c1)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[840, 839])).
% 1.45/1.67 tff(842,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, b2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, b2))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(843,plain,
% 1.45/1.67 ((line_equal(b1c1, b2c2) | point_equal(bc, b2) | (~incident(b2, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(b2, b2c2))) <=> (line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, b2))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(844,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(bc, b2) | (~incident(b2, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(b2, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, b2)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[843])).
% 1.45/1.67 tff(845,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(bc, b2) | (~incident(b2, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(b2, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, b2))),
% 1.45/1.67 inference(transitivity,[status(thm)],[844, 842])).
% 1.45/1.67 tff(846,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(bc, b2) | (~incident(b2, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(b2, b2c2)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(847,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, b2)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[846, 845])).
% 1.45/1.67 tff(848,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[847, 24, 841, 87, 838, 46, 832, 831])).
% 1.45/1.67 tff(849,plain,(point_equal(bc, b2) | (~incident(b2, b1c1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(850,plain,
% 1.45/1.67 (point_equal(bc, b2)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[849, 830])).
% 1.45/1.67 tff(851,assumption,(point_equal(bc, b2)), introduced(assumption)).
% 1.45/1.67 tff(852,assumption,(~incident(bc, ob)), introduced(assumption)).
% 1.45/1.67 tff(853,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, ob)) | incident(bc, ob) | (~point_equal(bc, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, ob)) | incident(bc, ob) | (~point_equal(bc, b2)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(854,plain,
% 1.45/1.67 ((incident(bc, ob) | (~incident(b2, ob)) | (~point_equal(bc, b2))) <=> ((~incident(b2, ob)) | incident(bc, ob) | (~point_equal(bc, b2)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(855,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, ob) | (~incident(b2, ob)) | (~point_equal(bc, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, ob)) | incident(bc, ob) | (~point_equal(bc, b2))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[854])).
% 1.45/1.67 tff(856,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, ob) | (~incident(b2, ob)) | (~point_equal(bc, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, ob)) | incident(bc, ob) | (~point_equal(bc, b2)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[855, 853])).
% 1.45/1.67 tff(857,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, ob) | (~incident(b2, ob)) | (~point_equal(bc, b2)))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(858,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, ob)) | incident(bc, ob) | (~point_equal(bc, b2))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[857, 856])).
% 1.45/1.67 tff(859,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[858, 58, 151, 852, 851])).
% 1.45/1.67 tff(860,plain,(incident(bc, ob) | (~point_equal(bc, b2))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(861,plain,
% 1.45/1.67 (incident(bc, ob)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[860, 850])).
% 1.45/1.67 tff(862,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(ob, b1c1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(ob, b1c1))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(863,plain,
% 1.45/1.67 ((line_equal(ob, b1c1) | point_equal(b1, bc) | (~incident(bc, ob)) | (~incident(b1, ob)) | (~incident(b1, b1c1)) | (~incident(bc, b1c1))) <=> ((~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(ob, b1c1))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(864,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, b1c1) | point_equal(b1, bc) | (~incident(bc, ob)) | (~incident(b1, ob)) | (~incident(b1, b1c1)) | (~incident(bc, b1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(ob, b1c1)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[863])).
% 1.45/1.67 tff(865,plain,
% 1.45/1.67 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, b1c1) | point_equal(b1, bc) | (~incident(bc, ob)) | (~incident(b1, ob)) | (~incident(b1, b1c1)) | (~incident(bc, b1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(ob, b1c1))),
% 1.45/1.67 inference(transitivity,[status(thm)],[864, 862])).
% 1.45/1.67 tff(866,plain,
% 1.45/1.67 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, b1c1) | point_equal(b1, bc) | (~incident(bc, ob)) | (~incident(b1, ob)) | (~incident(b1, b1c1)) | (~incident(bc, b1c1)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(867,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(ob, b1c1)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[866, 865])).
% 1.45/1.68 tff(868,plain,
% 1.45/1.68 ((~incident(bc, ob)) | point_equal(b1, bc) | line_equal(ob, b1c1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[867, 486, 61, 841, 46])).
% 1.45/1.68 tff(869,plain,
% 1.45/1.68 (line_equal(ob, b1c1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[868, 861, 406])).
% 1.45/1.68 tff(870,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, ob)) | incident(o, b1c1) | (~line_equal(ob, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | incident(o, b1c1) | (~line_equal(ob, b1c1)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(871,plain,
% 1.45/1.68 ((incident(o, b1c1) | (~line_equal(ob, b1c1)) | (~incident(o, ob))) <=> ((~incident(o, ob)) | incident(o, b1c1) | (~line_equal(ob, b1c1)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(872,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, b1c1) | (~line_equal(ob, b1c1)) | (~incident(o, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, ob)) | incident(o, b1c1) | (~line_equal(ob, b1c1))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[871])).
% 1.45/1.68 tff(873,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, b1c1) | (~line_equal(ob, b1c1)) | (~incident(o, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | incident(o, b1c1) | (~line_equal(ob, b1c1)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[872, 870])).
% 1.45/1.68 tff(874,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, b1c1) | (~line_equal(ob, b1c1)) | (~incident(o, ob)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(875,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | incident(o, b1c1) | (~line_equal(ob, b1c1))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[874, 873])).
% 1.45/1.68 tff(876,plain,
% 1.45/1.68 (incident(o, b1c1) | (~line_equal(ob, b1c1))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[875, 75, 21])).
% 1.45/1.68 tff(877,plain,
% 1.45/1.68 (incident(o, b1c1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[876, 869])).
% 1.45/1.68 tff(878,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | point_equal(c2, b2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | point_equal(c2, b2))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(879,plain,
% 1.45/1.68 ((line_equal(b1c1, b2c2) | point_equal(c2, b2) | (~incident(b2, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(b2, b2c2))) <=> (line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | point_equal(c2, b2))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(880,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(c2, b2) | (~incident(b2, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(b2, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | point_equal(c2, b2)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[879])).
% 1.45/1.68 tff(881,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(c2, b2) | (~incident(b2, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(b2, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | point_equal(c2, b2))),
% 1.45/1.68 inference(transitivity,[status(thm)],[880, 878])).
% 1.45/1.68 tff(882,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(c2, b2) | (~incident(b2, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(b2, b2c2)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(883,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | point_equal(c2, b2)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[882, 881])).
% 1.45/1.68 tff(884,plain,
% 1.45/1.68 ((~incident(b2, b1c1)) | (~incident(c2, b1c1))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[883, 334, 24, 838, 46, 331])).
% 1.45/1.68 tff(885,plain,
% 1.45/1.68 (~incident(c2, b1c1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[884, 830])).
% 1.45/1.68 tff(886,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, b1c1) | (~incident(o, b1c1)) | (~point_equal(c2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(c2, b1c1) | (~incident(o, b1c1)) | (~point_equal(c2, o)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(887,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, b1c1) | (~incident(o, b1c1)) | (~point_equal(c2, o)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(888,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(c2, b1c1) | (~incident(o, b1c1)) | (~point_equal(c2, o))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[887, 886])).
% 1.45/1.68 tff(889,plain,
% 1.45/1.68 (~point_equal(c2, o)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[888, 151, 885, 877])).
% 1.45/1.68 tff(890,plain,
% 1.45/1.68 (incident(c2, a1c1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[749, 740])).
% 1.45/1.68 tff(891,plain,
% 1.45/1.68 (line_equal(oc, a1c1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[761, 890])).
% 1.45/1.68 tff(892,plain,
% 1.45/1.68 (incident(o, a1c1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[769, 891])).
% 1.45/1.68 tff(893,plain,
% 1.45/1.68 (incident(c2, oa)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[796, 740])).
% 1.45/1.68 tff(894,plain,
% 1.45/1.68 (line_equal(oa, a2c2)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[812, 893])).
% 1.45/1.68 tff(895,plain,
% 1.45/1.68 (incident(o, a2c2)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[820, 894])).
% 1.45/1.68 tff(896,assumption,(~point_equal(c2, o)), introduced(assumption)).
% 1.45/1.68 tff(897,plain,
% 1.45/1.68 ((~incident(c2, a1c1)) | (~incident(o, a1c1)) | (~incident(o, a2c2))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[827, 177, 168, 46, 896])).
% 1.45/1.68 tff(898,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[897, 895, 892, 890])).
% 1.45/1.68 tff(899,plain,((~point_equal(c2, a1)) | point_equal(c2, o)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(900,plain,
% 1.45/1.68 (~point_equal(c2, a1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[899, 889])).
% 1.45/1.68 tff(901,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, a2b2)) | incident(bc, a2b2) | (~point_equal(bc, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a2b2)) | incident(bc, a2b2) | (~point_equal(bc, b2)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(902,plain,
% 1.45/1.68 ((incident(bc, a2b2) | (~incident(b2, a2b2)) | (~point_equal(bc, b2))) <=> ((~incident(b2, a2b2)) | incident(bc, a2b2) | (~point_equal(bc, b2)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(903,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, a2b2) | (~incident(b2, a2b2)) | (~point_equal(bc, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, a2b2)) | incident(bc, a2b2) | (~point_equal(bc, b2))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[902])).
% 1.45/1.68 tff(904,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, a2b2) | (~incident(b2, a2b2)) | (~point_equal(bc, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a2b2)) | incident(bc, a2b2) | (~point_equal(bc, b2)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[903, 901])).
% 1.45/1.68 tff(905,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, a2b2) | (~incident(b2, a2b2)) | (~point_equal(bc, b2)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(906,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a2b2)) | incident(bc, a2b2) | (~point_equal(bc, b2))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[905, 904])).
% 1.45/1.68 tff(907,plain,
% 1.45/1.68 (incident(bc, a2b2) | (~point_equal(bc, b2))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[906, 297, 151])).
% 1.45/1.68 tff(908,plain,
% 1.45/1.68 (incident(bc, a2b2)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[907, 850])).
% 1.45/1.68 tff(909,plain,
% 1.45/1.68 (((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(a2, a2b2)) | line_equal(a2b2, a2b2))) <=> ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(a2, a2b2)) | line_equal(a2b2, a2b2))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(910,plain,
% 1.45/1.68 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(a2, a2b2)) | line_equal(a2b2, a2b2))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(911,plain,
% 1.45/1.68 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(a2, a2b2)) | line_equal(a2b2, a2b2)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[910, 909])).
% 1.45/1.68 tff(912,plain,
% 1.45/1.68 (line_equal(a2b2, a2b2)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[911, 300, 105])).
% 1.45/1.68 tff(913,plain,
% 1.45/1.68 (((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(a2b2, a2b2)) | (~incident(bc, a2b2)) | (~incident(ab, a2b2)) | (~incident(ac, a2b2)))) <=> ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~line_equal(a2b2, a2b2)) | (~incident(bc, a2b2)) | (~incident(ab, a2b2)) | (~incident(ac, a2b2)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(914,plain,
% 1.45/1.68 ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(a2b2, a2b2)) | (~incident(bc, a2b2)) | (~incident(ab, a2b2)) | (~incident(ac, a2b2)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(915,plain,
% 1.45/1.68 ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~line_equal(a2b2, a2b2)) | (~incident(bc, a2b2)) | (~incident(ab, a2b2)) | (~incident(ac, a2b2))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[914, 913])).
% 1.45/1.68 tff(916,plain,
% 1.45/1.68 ((~incident(bc, a2b2)) | (~incident(ac, a2b2))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[915, 128, 49, 363, 912])).
% 1.45/1.68 tff(917,plain,
% 1.45/1.68 (~incident(ac, a2b2)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[916, 908])).
% 1.45/1.68 tff(918,assumption,(line_equal(a1c1, a2b2)), introduced(assumption)).
% 1.45/1.68 tff(919,assumption,(~incident(ac, a2b2)), introduced(assumption)).
% 1.45/1.68 tff(920,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ac, a1c1)) | incident(ac, a2b2) | (~line_equal(a1c1, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ac, a1c1)) | incident(ac, a2b2) | (~line_equal(a1c1, a2b2)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(921,plain,
% 1.45/1.68 ((incident(ac, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(ac, a1c1))) <=> ((~incident(ac, a1c1)) | incident(ac, a2b2) | (~line_equal(a1c1, a2b2)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(922,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(ac, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ac, a1c1)) | incident(ac, a2b2) | (~line_equal(a1c1, a2b2))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[921])).
% 1.45/1.68 tff(923,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(ac, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ac, a1c1)) | incident(ac, a2b2) | (~line_equal(a1c1, a2b2)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[922, 920])).
% 1.45/1.68 tff(924,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(ac, a1c1)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(925,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ac, a1c1)) | incident(ac, a2b2) | (~line_equal(a1c1, a2b2))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[924, 923])).
% 1.45/1.68 tff(926,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[925, 174, 21, 919, 918])).
% 1.45/1.68 tff(927,plain,(incident(ac, a2b2) | (~line_equal(a1c1, a2b2))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(928,plain,
% 1.45/1.68 (~line_equal(a1c1, a2b2)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[927, 917])).
% 1.45/1.68 tff(929,plain,
% 1.45/1.68 (~incident(b1, a2c2)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[704, 1, 571, 415, 570])).
% 1.45/1.68 tff(930,plain,
% 1.45/1.68 (~incident(c2, a1b1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[738, 1, 571, 708, 707])).
% 1.45/1.68 tff(931,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5, 930, 929])).
% 1.45/1.68 tff(932,plain,(point_equal(b2, c1) | line_equal(a1c1, a2b2) | line_equal(a1b1, b2c2) | point_equal(c2, a1) | point_equal(b1, a2) | point_equal(a2, o)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(933,plain,
% 1.45/1.68 (point_equal(b2, c1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[932, 928, 468, 900, 415, 414])).
% 1.45/1.68 tff(934,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(b1c1, ob))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(b1c1, ob))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(935,plain,
% 1.45/1.68 ((line_equal(b1c1, ob) | point_equal(b1, bc) | (~incident(bc, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, ob))) <=> ((~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(b1c1, ob))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(936,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, ob) | point_equal(b1, bc) | (~incident(bc, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, ob)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(b1c1, ob)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[935])).
% 1.45/1.68 tff(937,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, ob) | point_equal(b1, bc) | (~incident(bc, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, ob)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(b1c1, ob))),
% 1.45/1.68 inference(transitivity,[status(thm)],[936, 934])).
% 1.45/1.68 tff(938,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, ob) | point_equal(b1, bc) | (~incident(bc, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, ob)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(939,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(bc, b1c1)) | (~incident(bc, ob)) | point_equal(b1, bc) | line_equal(b1c1, ob)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[938, 937])).
% 1.45/1.68 tff(940,plain,
% 1.45/1.68 ((~incident(bc, ob)) | point_equal(b1, bc) | line_equal(b1c1, ob)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[939, 486, 61, 841, 46])).
% 1.45/1.68 tff(941,plain,
% 1.45/1.68 (line_equal(b1c1, ob)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[940, 861, 406])).
% 1.45/1.68 tff(942,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a2, b1c1)) | incident(a2, ob) | (~line_equal(b1c1, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a2, b1c1)) | incident(a2, ob) | (~line_equal(b1c1, ob)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(943,plain,
% 1.45/1.68 ((incident(a2, ob) | (~line_equal(b1c1, ob)) | (~incident(a2, b1c1))) <=> ((~incident(a2, b1c1)) | incident(a2, ob) | (~line_equal(b1c1, ob)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(944,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, ob) | (~line_equal(b1c1, ob)) | (~incident(a2, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a2, b1c1)) | incident(a2, ob) | (~line_equal(b1c1, ob))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[943])).
% 1.45/1.68 tff(945,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, ob) | (~line_equal(b1c1, ob)) | (~incident(a2, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a2, b1c1)) | incident(a2, ob) | (~line_equal(b1c1, ob)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[944, 942])).
% 1.45/1.68 tff(946,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, ob) | (~line_equal(b1c1, ob)) | (~incident(a2, b1c1)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(947,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a2, b1c1)) | incident(a2, ob) | (~line_equal(b1c1, ob))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[946, 945])).
% 1.45/1.68 tff(948,plain,
% 1.45/1.68 (~incident(a2, b1c1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[947, 21, 407, 941])).
% 1.45/1.68 tff(949,plain,
% 1.45/1.68 (incident(c1, a2b2)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[679, 948])).
% 1.45/1.68 tff(950,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c1, a2b2)) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, a2b2)) | point_equal(c1, a1) | line_equal(a1c1, a2b2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a2b2)) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, a2b2)) | point_equal(c1, a1) | line_equal(a1c1, a2b2))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(951,plain,
% 1.45/1.68 ((line_equal(a1c1, a2b2) | point_equal(c1, a1) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2b2)) | (~incident(a1, a2b2))) <=> ((~incident(c1, a2b2)) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, a2b2)) | point_equal(c1, a1) | line_equal(a1c1, a2b2))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(952,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2b2) | point_equal(c1, a1) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2b2)) | (~incident(a1, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c1, a2b2)) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, a2b2)) | point_equal(c1, a1) | line_equal(a1c1, a2b2)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[951])).
% 1.45/1.68 tff(953,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2b2) | point_equal(c1, a1) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2b2)) | (~incident(a1, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a2b2)) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, a2b2)) | point_equal(c1, a1) | line_equal(a1c1, a2b2))),
% 1.45/1.68 inference(transitivity,[status(thm)],[952, 950])).
% 1.45/1.68 tff(954,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2b2) | point_equal(c1, a1) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2b2)) | (~incident(a1, a2b2)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(955,plain,
% 1.45/1.68 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a2b2)) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(a1, a2b2)) | point_equal(c1, a1) | line_equal(a1c1, a2b2)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[954, 953])).
% 1.45/1.68 tff(956,plain,
% 1.45/1.68 ((~incident(c1, a2b2)) | (~incident(a1, a2b2))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[955, 230, 227, 46, 221, 928])).
% 1.45/1.68 tff(957,plain,
% 1.45/1.68 (~incident(a1, a2b2)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[956, 949])).
% 1.45/1.68 tff(958,assumption,(line_equal(oa, a2b2)), introduced(assumption)).
% 1.45/1.68 tff(959,assumption,(~incident(a1, a2b2)), introduced(assumption)).
% 1.45/1.68 tff(960,plain,
% 1.45/1.68 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2b2) | (~incident(a1, oa)) | (~line_equal(oa, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a1, a2b2) | (~incident(a1, oa)) | (~line_equal(oa, a2b2)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(961,plain,
% 1.45/1.69 ((incident(a1, a2b2) | (~line_equal(oa, a2b2)) | (~incident(a1, oa))) <=> (incident(a1, a2b2) | (~incident(a1, oa)) | (~line_equal(oa, a2b2)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(962,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2b2) | (~line_equal(oa, a2b2)) | (~incident(a1, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2b2) | (~incident(a1, oa)) | (~line_equal(oa, a2b2))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[961])).
% 1.45/1.69 tff(963,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2b2) | (~line_equal(oa, a2b2)) | (~incident(a1, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a1, a2b2) | (~incident(a1, oa)) | (~line_equal(oa, a2b2)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[962, 960])).
% 1.45/1.69 tff(964,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2b2) | (~line_equal(oa, a2b2)) | (~incident(a1, oa)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(965,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a1, a2b2) | (~incident(a1, oa)) | (~line_equal(oa, a2b2))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[964, 963])).
% 1.45/1.69 tff(966,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[965, 250, 21, 959, 958])).
% 1.45/1.69 tff(967,plain,((~line_equal(oa, a2b2)) | incident(a1, a2b2)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(968,plain,
% 1.45/1.69 (~line_equal(oa, a2b2)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[967, 957])).
% 1.45/1.69 tff(969,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a2, a2b2)) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2b2)) | point_equal(a2, o) | line_equal(oa, a2b2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2b2)) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2b2)) | point_equal(a2, o) | line_equal(oa, a2b2))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(970,plain,
% 1.45/1.69 ((line_equal(oa, a2b2) | point_equal(a2, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, a2b2)) | (~incident(o, a2b2))) <=> ((~incident(a2, a2b2)) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2b2)) | point_equal(a2, o) | line_equal(oa, a2b2))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(971,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, a2b2) | point_equal(a2, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, a2b2)) | (~incident(o, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a2, a2b2)) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2b2)) | point_equal(a2, o) | line_equal(oa, a2b2)))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[970])).
% 1.45/1.69 tff(972,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, a2b2) | point_equal(a2, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, a2b2)) | (~incident(o, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2b2)) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2b2)) | point_equal(a2, o) | line_equal(oa, a2b2))),
% 1.45/1.69 inference(transitivity,[status(thm)],[971, 969])).
% 1.45/1.69 tff(973,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oa, a2b2) | point_equal(a2, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, a2b2)) | (~incident(o, a2b2)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(974,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2b2)) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2b2)) | point_equal(a2, o) | line_equal(oa, a2b2)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[973, 972])).
% 1.45/1.69 tff(975,plain,
% 1.45/1.69 ((~incident(o, a2b2)) | point_equal(a2, o) | line_equal(oa, a2b2)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[974, 300, 253, 311, 46])).
% 1.45/1.69 tff(976,plain,
% 1.45/1.69 (~incident(o, a2b2)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[975, 968, 414])).
% 1.45/1.69 tff(977,plain,
% 1.45/1.69 (incident(b2, b1c1)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[444, 436])).
% 1.45/1.69 tff(978,plain,
% 1.45/1.69 (point_equal(bc, b2)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[849, 977])).
% 1.45/1.69 tff(979,plain,
% 1.45/1.69 (incident(bc, ob)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[860, 978])).
% 1.45/1.69 tff(980,assumption,(incident(b2, a1c1)), introduced(assumption)).
% 1.45/1.69 tff(981,assumption,(~incident(bc, a1c1)), introduced(assumption)).
% 1.45/1.69 tff(982,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, b2)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(983,plain,
% 1.45/1.69 ((incident(bc, a1c1) | (~incident(b2, a1c1)) | (~point_equal(bc, b2))) <=> ((~incident(b2, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, b2)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(984,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, a1c1) | (~incident(b2, a1c1)) | (~point_equal(bc, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, b2))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[983])).
% 1.45/1.69 tff(985,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, a1c1) | (~incident(b2, a1c1)) | (~point_equal(bc, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, b2)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[984, 982])).
% 1.45/1.69 tff(986,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, a1c1) | (~incident(b2, a1c1)) | (~point_equal(bc, b2)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(987,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, b2))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[986, 985])).
% 1.45/1.69 tff(988,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[987, 980, 151, 981, 851])).
% 1.45/1.69 tff(989,plain,(incident(bc, a1c1) | (~incident(b2, a1c1)) | (~point_equal(bc, b2))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(990,plain,
% 1.45/1.69 (incident(bc, a1c1)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[989, 978, 980])).
% 1.45/1.69 tff(991,plain,
% 1.45/1.69 (((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, a1c1)) | (~incident(b1, a1c1)) | (~incident(c1, a1c1)))) <=> ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, a1c1)) | (~incident(b1, a1c1)) | (~incident(c1, a1c1)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(992,plain,
% 1.45/1.69 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, a1c1)) | (~incident(b1, a1c1)) | (~incident(c1, a1c1)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(993,plain,
% 1.45/1.69 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, a1c1)) | (~incident(b1, a1c1)) | (~incident(c1, a1c1))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[992, 991])).
% 1.45/1.69 tff(994,plain,
% 1.45/1.69 (~incident(b1, a1c1)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[993, 49, 230, 227, 210])).
% 1.45/1.69 tff(995,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a1c1) | (~incident(bc, a1c1)) | (~point_equal(b1, bc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, a1c1) | (~incident(bc, a1c1)) | (~point_equal(b1, bc)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(996,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a1c1) | (~incident(bc, a1c1)) | (~point_equal(b1, bc)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(997,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, a1c1) | (~incident(bc, a1c1)) | (~point_equal(b1, bc))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[996, 995])).
% 1.45/1.69 tff(998,plain,
% 1.45/1.69 (~point_equal(b1, bc)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[997, 151, 994, 990])).
% 1.45/1.69 tff(999,plain,
% 1.45/1.69 (line_equal(ob, b1c1)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[868, 998, 979])).
% 1.45/1.69 tff(1000,plain,
% 1.45/1.69 (incident(o, b1c1)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[876, 999])).
% 1.45/1.69 tff(1001,assumption,(~incident(o, a2b2)), introduced(assumption)).
% 1.45/1.69 tff(1002,plain,
% 1.45/1.69 (incident(bc, a2b2)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[907, 978])).
% 1.45/1.69 tff(1003,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(bc, a2b2)) | incident(o, a2b2) | (~point_equal(o, bc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(bc, a2b2)) | incident(o, a2b2) | (~point_equal(o, bc)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(1004,plain,
% 1.45/1.69 ((incident(o, a2b2) | (~incident(bc, a2b2)) | (~point_equal(o, bc))) <=> ((~incident(bc, a2b2)) | incident(o, a2b2) | (~point_equal(o, bc)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(1005,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a2b2) | (~incident(bc, a2b2)) | (~point_equal(o, bc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(bc, a2b2)) | incident(o, a2b2) | (~point_equal(o, bc))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[1004])).
% 1.45/1.69 tff(1006,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a2b2) | (~incident(bc, a2b2)) | (~point_equal(o, bc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(bc, a2b2)) | incident(o, a2b2) | (~point_equal(o, bc)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[1005, 1003])).
% 1.45/1.69 tff(1007,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a2b2) | (~incident(bc, a2b2)) | (~point_equal(o, bc)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(1008,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(bc, a2b2)) | incident(o, a2b2) | (~point_equal(o, bc))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 1.45/1.69 tff(1009,plain,
% 1.45/1.69 (~point_equal(o, bc)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1008, 151, 1002, 1001])).
% 1.45/1.69 tff(1010,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c1, oc)) | incident(b2, oc) | (~point_equal(b2, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, oc)) | incident(b2, oc) | (~point_equal(b2, c1)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(1011,plain,
% 1.45/1.69 ((incident(b2, oc) | (~incident(c1, oc)) | (~point_equal(b2, c1))) <=> ((~incident(c1, oc)) | incident(b2, oc) | (~point_equal(b2, c1)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(1012,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, oc) | (~incident(c1, oc)) | (~point_equal(b2, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c1, oc)) | incident(b2, oc) | (~point_equal(b2, c1))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[1011])).
% 1.45/1.69 tff(1013,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, oc) | (~incident(c1, oc)) | (~point_equal(b2, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, oc)) | incident(b2, oc) | (~point_equal(b2, c1)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[1012, 1010])).
% 1.45/1.69 tff(1014,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, oc) | (~incident(c1, oc)) | (~point_equal(b2, c1)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(1015,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, oc)) | incident(b2, oc) | (~point_equal(b2, c1))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 1.45/1.69 tff(1016,plain,
% 1.45/1.69 (incident(b2, oc) | (~point_equal(b2, c1))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1015, 224, 151])).
% 1.45/1.69 tff(1017,plain,
% 1.45/1.69 (incident(b2, oc)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1016, 436])).
% 1.45/1.69 tff(1018,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, oc)) | (~incident(c2, oc)) | point_equal(c2, b2) | line_equal(oc, b2c2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, oc)) | (~incident(c2, oc)) | point_equal(c2, b2) | line_equal(oc, b2c2))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(1019,plain,
% 1.45/1.69 ((line_equal(oc, b2c2) | point_equal(c2, b2) | (~incident(b2, oc)) | (~incident(c2, oc)) | (~incident(c2, b2c2)) | (~incident(b2, b2c2))) <=> ((~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, oc)) | (~incident(c2, oc)) | point_equal(c2, b2) | line_equal(oc, b2c2))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(1020,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, b2c2) | point_equal(c2, b2) | (~incident(b2, oc)) | (~incident(c2, oc)) | (~incident(c2, b2c2)) | (~incident(b2, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, oc)) | (~incident(c2, oc)) | point_equal(c2, b2) | line_equal(oc, b2c2)))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[1019])).
% 1.45/1.69 tff(1021,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, b2c2) | point_equal(c2, b2) | (~incident(b2, oc)) | (~incident(c2, oc)) | (~incident(c2, b2c2)) | (~incident(b2, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, oc)) | (~incident(c2, oc)) | point_equal(c2, b2) | line_equal(oc, b2c2))),
% 1.45/1.69 inference(transitivity,[status(thm)],[1020, 1018])).
% 1.45/1.69 tff(1022,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(oc, b2c2) | point_equal(c2, b2) | (~incident(b2, oc)) | (~incident(c2, oc)) | (~incident(c2, b2c2)) | (~incident(b2, b2c2)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(1023,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, oc)) | (~incident(c2, oc)) | point_equal(c2, b2) | line_equal(oc, b2c2)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 1.45/1.69 tff(1024,plain,
% 1.45/1.69 ((~incident(b2, oc)) | line_equal(oc, b2c2)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1023, 334, 24, 189, 46, 331])).
% 1.45/1.69 tff(1025,plain,
% 1.45/1.69 (line_equal(oc, b2c2)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1024, 1017])).
% 1.45/1.69 tff(1026,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(b2, b1) | line_equal(b1c1, b2c2) | (~incident(b1, b1c1)) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(b1, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | line_equal(b1c1, b2c2) | (~incident(b1, b1c1)) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(b1, b2c2)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(1027,plain,
% 1.45/1.69 ((line_equal(b1c1, b2c2) | point_equal(b2, b1) | (~incident(b1, b1c1)) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(b1, b2c2))) <=> (point_equal(b2, b1) | line_equal(b1c1, b2c2) | (~incident(b1, b1c1)) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(b1, b2c2)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(1028,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(b2, b1) | (~incident(b1, b1c1)) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(b1, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (point_equal(b2, b1) | line_equal(b1c1, b2c2) | (~incident(b1, b1c1)) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(b1, b2c2))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[1027])).
% 1.45/1.69 tff(1029,plain,
% 1.45/1.69 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(b2, b1) | (~incident(b1, b1c1)) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(b1, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | line_equal(b1c1, b2c2) | (~incident(b1, b1c1)) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(b1, b2c2)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[1028, 1026])).
% 1.45/1.69 tff(1030,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(b2, b1) | (~incident(b1, b1c1)) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(b1, b2c2)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(1031,plain,
% 1.45/1.69 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(b2, b1) | line_equal(b1c1, b2c2) | (~incident(b1, b1c1)) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(b1, b2c2))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 1.53/1.69 tff(1032,plain,
% 1.53/1.69 ((~incident(b2, b1c1)) | (~incident(b1, b2c2))),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[1031, 486, 24, 55, 838, 46])).
% 1.53/1.69 tff(1033,plain,
% 1.53/1.69 (~incident(b1, b2c2)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[1032, 977])).
% 1.53/1.69 tff(1034,plain,
% 1.53/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, b2c2) | (~incident(b1, oc)) | (~line_equal(oc, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b1, b2c2) | (~incident(b1, oc)) | (~line_equal(oc, b2c2)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(1035,plain,
% 1.53/1.69 ((incident(b1, b2c2) | (~line_equal(oc, b2c2)) | (~incident(b1, oc))) <=> (incident(b1, b2c2) | (~incident(b1, oc)) | (~line_equal(oc, b2c2)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(1036,plain,
% 1.53/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, b2c2) | (~line_equal(oc, b2c2)) | (~incident(b1, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, b2c2) | (~incident(b1, oc)) | (~line_equal(oc, b2c2))))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[1035])).
% 1.53/1.69 tff(1037,plain,
% 1.53/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, b2c2) | (~line_equal(oc, b2c2)) | (~incident(b1, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b1, b2c2) | (~incident(b1, oc)) | (~line_equal(oc, b2c2)))),
% 1.53/1.69 inference(transitivity,[status(thm)],[1036, 1034])).
% 1.53/1.69 tff(1038,plain,
% 1.53/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, b2c2) | (~line_equal(oc, b2c2)) | (~incident(b1, oc)))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(1039,plain,
% 1.53/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b1, b2c2) | (~incident(b1, oc)) | (~line_equal(oc, b2c2))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 1.53/1.69 tff(1040,plain,
% 1.53/1.69 (~incident(b1, oc)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[1039, 21, 1033, 1025])).
% 1.53/1.69 tff(1041,plain,
% 1.53/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(b1, b1c1)) | incident(b1, oc) | (~line_equal(b1c1, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(b1, b1c1)) | incident(b1, oc) | (~line_equal(b1c1, oc)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(1042,plain,
% 1.53/1.69 ((incident(b1, oc) | (~line_equal(b1c1, oc)) | (~incident(b1, b1c1))) <=> ((~incident(b1, b1c1)) | incident(b1, oc) | (~line_equal(b1c1, oc)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(1043,plain,
% 1.53/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, oc) | (~line_equal(b1c1, oc)) | (~incident(b1, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(b1, b1c1)) | incident(b1, oc) | (~line_equal(b1c1, oc))))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[1042])).
% 1.53/1.69 tff(1044,plain,
% 1.53/1.69 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, oc) | (~line_equal(b1c1, oc)) | (~incident(b1, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(b1, b1c1)) | incident(b1, oc) | (~line_equal(b1c1, oc)))),
% 1.53/1.69 inference(transitivity,[status(thm)],[1043, 1041])).
% 1.53/1.69 tff(1045,plain,
% 1.53/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, oc) | (~line_equal(b1c1, oc)) | (~incident(b1, b1c1)))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(1046,plain,
% 1.53/1.69 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(b1, b1c1)) | incident(b1, oc) | (~line_equal(b1c1, oc))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 1.53/1.70 tff(1047,plain,
% 1.53/1.70 (incident(b1, oc) | (~line_equal(b1c1, oc))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1046, 486, 21])).
% 1.53/1.70 tff(1048,plain,
% 1.53/1.70 (~line_equal(b1c1, oc)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1047, 1040])).
% 1.53/1.70 tff(1049,plain,
% 1.53/1.70 (((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(b2, c1)) | point_equal(c1, b2))) <=> ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(b2, c1)) | point_equal(c1, b2))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1050,plain,
% 1.53/1.70 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(b2, c1)) | point_equal(c1, b2))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(1051,plain,
% 1.53/1.70 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(b2, c1)) | point_equal(c1, b2)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 1.53/1.70 tff(1052,plain,
% 1.53/1.70 (point_equal(c1, b2)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1051, 430, 436])).
% 1.53/1.70 tff(1053,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, b2c2)) | incident(c1, b2c2) | (~point_equal(c1, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, b2c2)) | incident(c1, b2c2) | (~point_equal(c1, b2)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1054,plain,
% 1.53/1.70 ((incident(c1, b2c2) | (~incident(b2, b2c2)) | (~point_equal(c1, b2))) <=> ((~incident(b2, b2c2)) | incident(c1, b2c2) | (~point_equal(c1, b2)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1055,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, b2c2) | (~incident(b2, b2c2)) | (~point_equal(c1, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, b2c2)) | incident(c1, b2c2) | (~point_equal(c1, b2))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1054])).
% 1.53/1.70 tff(1056,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, b2c2) | (~incident(b2, b2c2)) | (~point_equal(c1, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, b2c2)) | incident(c1, b2c2) | (~point_equal(c1, b2)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[1055, 1053])).
% 1.53/1.70 tff(1057,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, b2c2) | (~incident(b2, b2c2)) | (~point_equal(c1, b2)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(1058,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, b2c2)) | incident(c1, b2c2) | (~point_equal(c1, b2))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 1.53/1.70 tff(1059,plain,
% 1.53/1.70 (incident(c1, b2c2) | (~point_equal(c1, b2))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1058, 24, 151])).
% 1.53/1.70 tff(1060,plain,
% 1.53/1.70 (incident(c1, b2c2)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1059, 1052])).
% 1.53/1.70 tff(1061,assumption,(~point_equal(bc, c1)), introduced(assumption)).
% 1.53/1.70 tff(1062,assumption,(incident(c1, b2c2)), introduced(assumption)).
% 1.53/1.70 tff(1063,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c1, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, c1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c1, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, c1))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1064,plain,
% 1.53/1.70 ((line_equal(b1c1, b2c2) | point_equal(bc, c1) | (~incident(c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(c1, b2c2))) <=> (line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c1, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, c1))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1065,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(bc, c1) | (~incident(c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(c1, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c1, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, c1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1064])).
% 1.53/1.70 tff(1066,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(bc, c1) | (~incident(c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(c1, b2c2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c1, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, c1))),
% 1.53/1.70 inference(transitivity,[status(thm)],[1065, 1063])).
% 1.53/1.70 tff(1067,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, b2c2) | point_equal(bc, c1) | (~incident(c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(c1, b2c2)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(1068,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c1, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, c1)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 1.53/1.70 tff(1069,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1068, 439, 841, 87, 838, 46, 1062, 1061])).
% 1.53/1.70 tff(1070,plain,(point_equal(bc, c1) | (~incident(c1, b2c2))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(1071,plain,
% 1.53/1.70 (point_equal(bc, c1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1070, 1060])).
% 1.53/1.70 tff(1072,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c1, oc)) | incident(bc, oc) | (~point_equal(bc, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, oc)) | incident(bc, oc) | (~point_equal(bc, c1)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1073,plain,
% 1.53/1.70 ((incident(bc, oc) | (~incident(c1, oc)) | (~point_equal(bc, c1))) <=> ((~incident(c1, oc)) | incident(bc, oc) | (~point_equal(bc, c1)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1074,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, oc) | (~incident(c1, oc)) | (~point_equal(bc, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c1, oc)) | incident(bc, oc) | (~point_equal(bc, c1))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1073])).
% 1.53/1.70 tff(1075,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, oc) | (~incident(c1, oc)) | (~point_equal(bc, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, oc)) | incident(bc, oc) | (~point_equal(bc, c1)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[1074, 1072])).
% 1.53/1.70 tff(1076,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, oc) | (~incident(c1, oc)) | (~point_equal(bc, c1)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(1077,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, oc)) | incident(bc, oc) | (~point_equal(bc, c1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 1.53/1.70 tff(1078,plain,
% 1.53/1.70 (incident(bc, oc) | (~point_equal(bc, c1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1077, 224, 151])).
% 1.53/1.70 tff(1079,plain,
% 1.53/1.70 (incident(bc, oc)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1078, 1071])).
% 1.53/1.70 tff(1080,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(o, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | (~incident(o, b1c1)) | point_equal(o, bc) | line_equal(b1c1, oc))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(o, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | (~incident(o, b1c1)) | point_equal(o, bc) | line_equal(b1c1, oc))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1081,plain,
% 1.53/1.70 ((line_equal(b1c1, oc) | point_equal(o, bc) | (~incident(bc, b1c1)) | (~incident(o, b1c1)) | (~incident(o, oc)) | (~incident(bc, oc))) <=> ((~incident(o, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | (~incident(o, b1c1)) | point_equal(o, bc) | line_equal(b1c1, oc))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1082,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, oc) | point_equal(o, bc) | (~incident(bc, b1c1)) | (~incident(o, b1c1)) | (~incident(o, oc)) | (~incident(bc, oc)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(o, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | (~incident(o, b1c1)) | point_equal(o, bc) | line_equal(b1c1, oc)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1081])).
% 1.53/1.70 tff(1083,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, oc) | point_equal(o, bc) | (~incident(bc, b1c1)) | (~incident(o, b1c1)) | (~incident(o, oc)) | (~incident(bc, oc)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(o, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | (~incident(o, b1c1)) | point_equal(o, bc) | line_equal(b1c1, oc))),
% 1.53/1.70 inference(transitivity,[status(thm)],[1082, 1080])).
% 1.53/1.70 tff(1084,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, oc) | point_equal(o, bc) | (~incident(bc, b1c1)) | (~incident(o, b1c1)) | (~incident(o, oc)) | (~incident(bc, oc)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(1085,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(o, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | (~incident(o, b1c1)) | point_equal(o, bc) | line_equal(b1c1, oc)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 1.53/1.70 tff(1086,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1085, 240, 841, 46, 1079, 1048, 1009, 1000])).
% 1.53/1.70 tff(1087,plain,((~point_equal(b2, c1)) | incident(o, a2b2) | (~incident(b2, a1c1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(1088,plain,
% 1.53/1.70 (~incident(b2, a1c1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1087, 976, 933])).
% 1.53/1.70 tff(1089,plain,
% 1.53/1.70 (incident(a1, b2c2)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[685, 1088])).
% 1.53/1.70 tff(1090,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(b2c2, a1b1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(b2c2, a1b1))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1091,plain,
% 1.53/1.70 ((line_equal(b2c2, a1b1) | point_equal(c2, a1) | (~incident(a1, b2c2)) | (~incident(c2, b2c2)) | (~incident(c2, a1b1)) | (~incident(a1, a1b1))) <=> ((~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(b2c2, a1b1))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1092,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b2c2, a1b1) | point_equal(c2, a1) | (~incident(a1, b2c2)) | (~incident(c2, b2c2)) | (~incident(c2, a1b1)) | (~incident(a1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(b2c2, a1b1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1091])).
% 1.53/1.70 tff(1093,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b2c2, a1b1) | point_equal(c2, a1) | (~incident(a1, b2c2)) | (~incident(c2, b2c2)) | (~incident(c2, a1b1)) | (~incident(a1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(b2c2, a1b1))),
% 1.53/1.70 inference(transitivity,[status(thm)],[1092, 1090])).
% 1.53/1.70 tff(1094,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b2c2, a1b1) | point_equal(c2, a1) | (~incident(a1, b2c2)) | (~incident(c2, b2c2)) | (~incident(c2, a1b1)) | (~incident(a1, a1b1)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(1095,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, b2c2)) | (~incident(c2, a1b1)) | (~incident(c2, b2c2)) | (~incident(a1, a1b1)) | point_equal(c2, a1) | line_equal(b2c2, a1b1)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.53/1.70 tff(1096,plain,
% 1.53/1.70 ((~incident(a1, b2c2)) | (~incident(c2, a1b1)) | point_equal(c2, a1) | line_equal(b2c2, a1b1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1095, 108, 334, 46])).
% 1.53/1.70 tff(1097,plain,
% 1.53/1.70 (~incident(c2, a1b1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1096, 1089, 454, 900])).
% 1.53/1.70 tff(1098,assumption,(line_equal(a2c2, b1c1)), introduced(assumption)).
% 1.53/1.70 tff(1099,assumption,(~incident(c2, b1c1)), introduced(assumption)).
% 1.53/1.70 tff(1100,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, b1c1) | (~incident(c2, a2c2)) | (~line_equal(a2c2, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, b1c1) | (~incident(c2, a2c2)) | (~line_equal(a2c2, b1c1)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1101,plain,
% 1.53/1.70 ((incident(c2, b1c1) | (~line_equal(a2c2, b1c1)) | (~incident(c2, a2c2))) <=> (incident(c2, b1c1) | (~incident(c2, a2c2)) | (~line_equal(a2c2, b1c1)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1102,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, b1c1) | (~line_equal(a2c2, b1c1)) | (~incident(c2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, b1c1) | (~incident(c2, a2c2)) | (~line_equal(a2c2, b1c1))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1101])).
% 1.53/1.70 tff(1103,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, b1c1) | (~line_equal(a2c2, b1c1)) | (~incident(c2, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, b1c1) | (~incident(c2, a2c2)) | (~line_equal(a2c2, b1c1)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[1102, 1100])).
% 1.53/1.70 tff(1104,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, b1c1) | (~line_equal(a2c2, b1c1)) | (~incident(c2, a2c2)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(1105,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, b1c1) | (~incident(c2, a2c2)) | (~line_equal(a2c2, b1c1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 1.53/1.70 tff(1106,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1105, 177, 21, 1099, 1098])).
% 1.53/1.70 tff(1107,plain,(incident(c2, b1c1) | (~line_equal(a2c2, b1c1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(1108,plain,
% 1.53/1.70 (~line_equal(a2c2, b1c1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1107, 885])).
% 1.53/1.70 tff(1109,plain,
% 1.53/1.70 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(b1c1, a2c2)) | line_equal(a2c2, b1c1))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(b1c1, a2c2)) | line_equal(a2c2, b1c1))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1110,plain,
% 1.53/1.70 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(b1c1, a2c2)) | line_equal(a2c2, b1c1))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(1111,plain,
% 1.53/1.70 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(b1c1, a2c2)) | line_equal(a2c2, b1c1)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 1.53/1.70 tff(1112,plain,
% 1.53/1.70 (~line_equal(b1c1, a2c2)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1111, 464, 1108])).
% 1.53/1.70 tff(1113,plain,
% 1.53/1.70 (~incident(b1, a2c2)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[681, 1089, 1112, 575])).
% 1.53/1.70 tff(1114,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5, 1113, 1097])).
% 1.53/1.70 tff(1115,plain,(incident(b1, b2c2) | point_equal(b1, a2) | incident(a2, ob) | line_equal(a1b1, ob)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(1116,plain,
% 1.53/1.70 (incident(b1, b2c2)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1115, 400, 378, 360])).
% 1.53/1.70 tff(1117,plain,
% 1.53/1.70 (~incident(b2, a1b1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[452, 360])).
% 1.53/1.70 tff(1118,plain,
% 1.53/1.70 (~line_equal(b2c2, a1b1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[32, 1117])).
% 1.53/1.70 tff(1119,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, a1c1)) | incident(b1, a1c1) | (~point_equal(b1, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1c1)) | incident(b1, a1c1) | (~point_equal(b1, a1)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1120,plain,
% 1.53/1.70 ((incident(b1, a1c1) | (~incident(a1, a1c1)) | (~point_equal(b1, a1))) <=> ((~incident(a1, a1c1)) | incident(b1, a1c1) | (~point_equal(b1, a1)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1121,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a1c1) | (~incident(a1, a1c1)) | (~point_equal(b1, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, a1c1)) | incident(b1, a1c1) | (~point_equal(b1, a1))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1120])).
% 1.53/1.70 tff(1122,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a1c1) | (~incident(a1, a1c1)) | (~point_equal(b1, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1c1)) | incident(b1, a1c1) | (~point_equal(b1, a1)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[1121, 1119])).
% 1.53/1.70 tff(1123,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a1c1) | (~incident(a1, a1c1)) | (~point_equal(b1, a1)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(1124,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1c1)) | incident(b1, a1c1) | (~point_equal(b1, a1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 1.53/1.70 tff(1125,plain,
% 1.53/1.70 (~point_equal(b1, a1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1124, 230, 151, 994])).
% 1.53/1.70 tff(1126,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, b2c2)) | (~incident(b1, b2c2)) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | point_equal(b1, a1) | line_equal(b2c2, a1b1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, b2c2)) | (~incident(b1, b2c2)) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | point_equal(b1, a1) | line_equal(b2c2, a1b1))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1127,plain,
% 1.53/1.70 ((line_equal(b2c2, a1b1) | point_equal(b1, a1) | (~incident(a1, b2c2)) | (~incident(b1, b2c2)) | (~incident(b1, a1b1)) | (~incident(a1, a1b1))) <=> ((~incident(a1, b2c2)) | (~incident(b1, b2c2)) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | point_equal(b1, a1) | line_equal(b2c2, a1b1))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1128,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b2c2, a1b1) | point_equal(b1, a1) | (~incident(a1, b2c2)) | (~incident(b1, b2c2)) | (~incident(b1, a1b1)) | (~incident(a1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, b2c2)) | (~incident(b1, b2c2)) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | point_equal(b1, a1) | line_equal(b2c2, a1b1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1127])).
% 1.53/1.70 tff(1129,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b2c2, a1b1) | point_equal(b1, a1) | (~incident(a1, b2c2)) | (~incident(b1, b2c2)) | (~incident(b1, a1b1)) | (~incident(a1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, b2c2)) | (~incident(b1, b2c2)) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | point_equal(b1, a1) | line_equal(b2c2, a1b1))),
% 1.53/1.70 inference(transitivity,[status(thm)],[1128, 1126])).
% 1.53/1.70 tff(1130,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b2c2, a1b1) | point_equal(b1, a1) | (~incident(a1, b2c2)) | (~incident(b1, b2c2)) | (~incident(b1, a1b1)) | (~incident(a1, a1b1)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(1131,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, b2c2)) | (~incident(b1, b2c2)) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | point_equal(b1, a1) | line_equal(b2c2, a1b1)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 1.53/1.70 tff(1132,plain,
% 1.53/1.70 ((~incident(a1, b2c2)) | (~incident(b1, b2c2))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1131, 108, 64, 46, 1125, 1118])).
% 1.53/1.70 tff(1133,plain,
% 1.53/1.70 (~incident(a1, b2c2)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1132, 1116])).
% 1.53/1.70 tff(1134,plain,
% 1.53/1.70 (incident(b2, a1c1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[685, 1133])).
% 1.53/1.70 tff(1135,plain,
% 1.53/1.70 (~point_equal(a2, b1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[574, 430, 400])).
% 1.53/1.70 tff(1136,plain,
% 1.53/1.70 (~incident(b2, b1c1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1032, 1116])).
% 1.53/1.70 tff(1137,plain,
% 1.53/1.70 (~point_equal(b2, c1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[444, 1136])).
% 1.53/1.70 tff(1138,plain,
% 1.53/1.70 (~line_equal(ob, b1c1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[475, 1136])).
% 1.53/1.70 tff(1139,plain,
% 1.53/1.70 (~incident(c1, ob)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[493, 1138])).
% 1.53/1.70 tff(1140,plain,
% 1.53/1.70 (~point_equal(c1, o)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[501, 1139])).
% 1.53/1.70 tff(1141,plain,
% 1.53/1.70 (~incident(a2, a1c1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[553, 1140])).
% 1.53/1.70 tff(1142,plain,
% 1.53/1.70 (~line_equal(a2b2, a1c1)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[564, 1141])).
% 1.53/1.70 tff(1143,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a2b2, a1c1) | point_equal(b2, c1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a2b2, a1c1) | point_equal(b2, c1))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1144,plain,
% 1.53/1.70 ((line_equal(a2b2, a1c1) | point_equal(b2, c1) | (~incident(c1, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1))) <=> ((~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a2b2, a1c1) | point_equal(b2, c1))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(1145,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2b2, a1c1) | point_equal(b2, c1) | (~incident(c1, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a2b2, a1c1) | point_equal(b2, c1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[1144])).
% 1.53/1.70 tff(1146,plain,
% 1.53/1.70 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2b2, a1c1) | point_equal(b2, c1) | (~incident(c1, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a2b2, a1c1) | point_equal(b2, c1))),
% 1.53/1.70 inference(transitivity,[status(thm)],[1145, 1143])).
% 1.53/1.70 tff(1147,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2b2, a1c1) | point_equal(b2, c1) | (~incident(c1, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(1148,plain,
% 1.53/1.70 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a2b2, a1c1) | point_equal(b2, c1)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1147, 1146])).
% 1.53/1.71 tff(1149,plain,
% 1.53/1.71 ((~incident(c1, a2b2)) | (~incident(b2, a1c1)) | line_equal(a2b2, a1c1) | point_equal(b2, c1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1148, 297, 227, 46])).
% 1.53/1.71 tff(1150,plain,
% 1.53/1.71 (~incident(c1, a2b2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1149, 1142, 1137, 1134])).
% 1.53/1.71 tff(1151,plain,
% 1.53/1.71 (incident(a2, b1c1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[679, 1150])).
% 1.53/1.71 tff(1152,assumption,(incident(a2, b1c1)), introduced(assumption)).
% 1.53/1.71 tff(1153,plain,
% 1.53/1.71 (~incident(c2, a1b1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[735, 1152, 980])).
% 1.53/1.71 tff(1154,plain,
% 1.53/1.71 (~incident(b1, a2c2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[671, 1152, 663, 664])).
% 1.53/1.71 tff(1155,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5, 1154, 1153])).
% 1.53/1.71 tff(1156,plain,((~incident(a2, b1c1)) | point_equal(a2, b1) | line_equal(b1c1, a2c2) | (~incident(b2, a1c1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(1157,plain,
% 1.53/1.71 (line_equal(b1c1, a2c2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1156, 1151, 1135, 1134])).
% 1.53/1.71 tff(1158,plain,
% 1.53/1.71 (incident(c1, a2c2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[642, 1157])).
% 1.53/1.71 tff(1159,plain,
% 1.53/1.71 (~point_equal(a2, o)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[413, 75, 151, 378])).
% 1.53/1.71 tff(1160,plain,
% 1.53/1.71 (~incident(c2, a1b1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[735, 1151, 1134])).
% 1.53/1.71 tff(1161,plain,
% 1.53/1.71 (incident(b1, a2c2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5, 1160])).
% 1.53/1.71 tff(1162,plain,
% 1.53/1.71 (~line_equal(a2c2, oc)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[614, 1161, 1159])).
% 1.53/1.71 tff(1163,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[631, 1162, 1158])).
% 1.53/1.71 tff(1164,plain,(incident(ab, ob)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(1165,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(b1, ab))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(b1, ab))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1166,plain,
% 1.53/1.71 ((line_equal(ob, a1b1) | point_equal(b1, ab) | (~incident(ab, ob)) | (~incident(b1, ob)) | (~incident(b1, a1b1)) | (~incident(ab, a1b1))) <=> ((~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(b1, ab))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1167,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(b1, ab) | (~incident(ab, ob)) | (~incident(b1, ob)) | (~incident(b1, a1b1)) | (~incident(ab, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(b1, ab)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1166])).
% 1.53/1.71 tff(1168,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(b1, ab) | (~incident(ab, ob)) | (~incident(b1, ob)) | (~incident(b1, a1b1)) | (~incident(ab, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(b1, ab))),
% 1.53/1.71 inference(transitivity,[status(thm)],[1167, 1165])).
% 1.53/1.71 tff(1169,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(b1, ab) | (~incident(ab, ob)) | (~incident(b1, ob)) | (~incident(b1, a1b1)) | (~incident(ab, a1b1)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1170,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(b1, ab)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 1.53/1.71 tff(1171,plain,
% 1.53/1.71 ((~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(b1, ab)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1170, 64, 61, 115, 46])).
% 1.53/1.71 tff(1172,plain,
% 1.53/1.71 (line_equal(ob, a1b1) | point_equal(b1, ab)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1171, 1164])).
% 1.53/1.71 tff(1173,plain,
% 1.53/1.71 (point_equal(b1, ab)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1172, 349])).
% 1.53/1.71 tff(1174,plain,
% 1.53/1.71 (~line_equal(a1b1, b2c2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[467, 464, 320])).
% 1.53/1.71 tff(1175,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a2c2) | (~incident(c2, a2c2)) | (~point_equal(b1, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, a2c2) | (~incident(c2, a2c2)) | (~point_equal(b1, c2)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1176,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a2c2) | (~incident(c2, a2c2)) | (~point_equal(b1, c2)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1177,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, a2c2) | (~incident(c2, a2c2)) | (~point_equal(b1, c2))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 1.53/1.71 tff(1178,plain,
% 1.53/1.71 (~point_equal(b1, c2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1177, 2, 177, 151])).
% 1.53/1.71 tff(1179,plain,
% 1.53/1.71 (~point_equal(c2, b1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[433, 430, 1178])).
% 1.53/1.71 tff(1180,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(ob, a1b1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(ob, a1b1))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1181,plain,
% 1.53/1.71 ((line_equal(ob, a1b1) | point_equal(c2, b1) | (~incident(b1, ob)) | (~incident(c2, ob)) | (~incident(c2, a1b1)) | (~incident(b1, a1b1))) <=> ((~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(ob, a1b1))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1182,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(c2, b1) | (~incident(b1, ob)) | (~incident(c2, ob)) | (~incident(c2, a1b1)) | (~incident(b1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(ob, a1b1)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1181])).
% 1.53/1.71 tff(1183,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(c2, b1) | (~incident(b1, ob)) | (~incident(c2, ob)) | (~incident(c2, a1b1)) | (~incident(b1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(ob, a1b1))),
% 1.53/1.71 inference(transitivity,[status(thm)],[1182, 1180])).
% 1.53/1.71 tff(1184,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(c2, b1) | (~incident(b1, ob)) | (~incident(c2, ob)) | (~incident(c2, a1b1)) | (~incident(b1, a1b1)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1185,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c2, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(ob, a1b1)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 1.53/1.71 tff(1186,plain,
% 1.53/1.71 ((~incident(c2, a1b1)) | (~incident(c2, ob)) | point_equal(c2, b1) | line_equal(ob, a1b1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1185, 64, 61, 46])).
% 1.53/1.71 tff(1187,plain,
% 1.53/1.71 (~incident(c2, ob)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1186, 349, 6, 1179])).
% 1.53/1.71 tff(1188,plain,
% 1.53/1.71 (~point_equal(c2, o)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[786, 1187])).
% 1.53/1.71 tff(1189,plain,
% 1.53/1.71 (~point_equal(c2, a1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[899, 1188])).
% 1.53/1.71 tff(1190,plain,
% 1.53/1.71 (line_equal(a1c1, a2b2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[738, 1189, 1, 6, 1174])).
% 1.53/1.71 tff(1191,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a1, a1c1)) | incident(a1, a2b2) | (~line_equal(a1c1, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a1, a1c1)) | incident(a1, a2b2) | (~line_equal(a1c1, a2b2)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1192,plain,
% 1.53/1.71 ((incident(a1, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(a1, a1c1))) <=> ((~incident(a1, a1c1)) | incident(a1, a2b2) | (~line_equal(a1c1, a2b2)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1193,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(a1, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a1, a1c1)) | incident(a1, a2b2) | (~line_equal(a1c1, a2b2))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1192])).
% 1.53/1.71 tff(1194,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(a1, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a1, a1c1)) | incident(a1, a2b2) | (~line_equal(a1c1, a2b2)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[1193, 1191])).
% 1.53/1.71 tff(1195,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(a1, a1c1)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1196,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a1, a1c1)) | incident(a1, a2b2) | (~line_equal(a1c1, a2b2))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 1.53/1.71 tff(1197,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1196, 230, 21, 959, 918])).
% 1.53/1.71 tff(1198,plain,(incident(a1, a2b2) | (~line_equal(a1c1, a2b2))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(1199,plain,
% 1.53/1.71 (incident(a1, a2b2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1198, 1190])).
% 1.53/1.71 tff(1200,assumption,(~point_equal(ab, a1)), introduced(assumption)).
% 1.53/1.71 tff(1201,assumption,(incident(a1, a2b2)), introduced(assumption)).
% 1.53/1.71 tff(1202,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a1))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1203,plain,
% 1.53/1.71 ((line_equal(a1b1, a2b2) | point_equal(ab, a1) | (~incident(a1, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(a1, a2b2))) <=> (line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a1))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1204,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(ab, a1) | (~incident(a1, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(a1, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a1)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1203])).
% 1.53/1.71 tff(1205,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(ab, a1) | (~incident(a1, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(a1, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a1))),
% 1.53/1.71 inference(transitivity,[status(thm)],[1204, 1202])).
% 1.53/1.71 tff(1206,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(ab, a1) | (~incident(a1, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(a1, a2b2)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1207,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a1)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 1.53/1.71 tff(1208,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1207, 108, 115, 363, 294, 46, 1201, 1200])).
% 1.53/1.71 tff(1209,plain,(point_equal(ab, a1) | (~incident(a1, a2b2))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(1210,plain,
% 1.53/1.71 (point_equal(ab, a1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1209, 1199])).
% 1.53/1.71 tff(1211,assumption,(point_equal(ab, a1)), introduced(assumption)).
% 1.53/1.71 tff(1212,assumption,(~incident(ab, oa)), introduced(assumption)).
% 1.53/1.71 tff(1213,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, oa)) | incident(ab, oa) | (~point_equal(ab, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, oa)) | incident(ab, oa) | (~point_equal(ab, a1)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1214,plain,
% 1.53/1.71 ((incident(ab, oa) | (~incident(a1, oa)) | (~point_equal(ab, a1))) <=> ((~incident(a1, oa)) | incident(ab, oa) | (~point_equal(ab, a1)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1215,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, oa) | (~incident(a1, oa)) | (~point_equal(ab, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, oa)) | incident(ab, oa) | (~point_equal(ab, a1))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1214])).
% 1.53/1.71 tff(1216,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, oa) | (~incident(a1, oa)) | (~point_equal(ab, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, oa)) | incident(ab, oa) | (~point_equal(ab, a1)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[1215, 1213])).
% 1.53/1.71 tff(1217,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, oa) | (~incident(a1, oa)) | (~point_equal(ab, a1)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1218,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, oa)) | incident(ab, oa) | (~point_equal(ab, a1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 1.53/1.71 tff(1219,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1218, 250, 151, 1212, 1211])).
% 1.53/1.71 tff(1220,plain,(incident(ab, oa) | (~point_equal(ab, a1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(1221,plain,
% 1.53/1.71 (incident(ab, oa)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1220, 1210])).
% 1.53/1.71 tff(1222,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, oa) | (~incident(ab, oa)) | (~point_equal(b1, ab)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, oa) | (~incident(ab, oa)) | (~point_equal(b1, ab)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1223,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, oa) | (~incident(ab, oa)) | (~point_equal(b1, ab)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1224,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, oa) | (~incident(ab, oa)) | (~point_equal(b1, ab))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 1.53/1.71 tff(1225,plain,
% 1.53/1.71 (incident(b1, oa) | (~incident(ab, oa)) | (~point_equal(b1, ab))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1224, 151])).
% 1.53/1.71 tff(1226,plain,
% 1.53/1.71 (incident(b1, oa)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1225, 1221, 1173])).
% 1.53/1.71 tff(1227,plain,
% 1.53/1.71 (((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, oa)) | (~incident(b1, oa)) | (~incident(c1, oa)))) <=> ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, oa)) | (~incident(b1, oa)) | (~incident(c1, oa)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1228,plain,
% 1.53/1.71 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, oa)) | (~incident(b1, oa)) | (~incident(c1, oa)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1229,plain,
% 1.53/1.71 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, oa)) | (~incident(b1, oa)) | (~incident(c1, oa))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 1.53/1.71 tff(1230,plain,
% 1.53/1.71 ((~incident(b1, oa)) | (~incident(c1, oa))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1229, 49, 250, 210])).
% 1.53/1.71 tff(1231,plain,
% 1.53/1.71 (~incident(c1, oa)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1230, 1226])).
% 1.53/1.71 tff(1232,plain,
% 1.53/1.71 (~incident(a1, b2c2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1096, 1189, 6, 320])).
% 1.53/1.71 tff(1233,plain,
% 1.53/1.71 (incident(b2, a1c1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[685, 1232])).
% 1.53/1.71 tff(1234,plain,
% 1.53/1.71 (~incident(a2, b1c1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[735, 1233, 6])).
% 1.53/1.71 tff(1235,plain,
% 1.53/1.71 (incident(c1, a2b2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[679, 1234])).
% 1.53/1.71 tff(1236,plain,
% 1.53/1.71 (line_equal(a2b2, a1c1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1149, 1235, 1, 1233])).
% 1.53/1.71 tff(1237,plain,
% 1.53/1.71 (incident(a2, a1c1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[564, 1236])).
% 1.53/1.71 tff(1238,plain,
% 1.53/1.71 (point_equal(c1, o)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[553, 1237])).
% 1.53/1.71 tff(1239,assumption,(point_equal(c1, o)), introduced(assumption)).
% 1.53/1.71 tff(1240,assumption,(~incident(c1, oa)), introduced(assumption)).
% 1.53/1.71 tff(1241,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, oa)) | incident(c1, oa) | (~point_equal(c1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oa)) | incident(c1, oa) | (~point_equal(c1, o)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1242,plain,
% 1.53/1.71 ((incident(c1, oa) | (~incident(o, oa)) | (~point_equal(c1, o))) <=> ((~incident(o, oa)) | incident(c1, oa) | (~point_equal(c1, o)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1243,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, oa) | (~incident(o, oa)) | (~point_equal(c1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, oa)) | incident(c1, oa) | (~point_equal(c1, o))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1242])).
% 1.53/1.71 tff(1244,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, oa) | (~incident(o, oa)) | (~point_equal(c1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oa)) | incident(c1, oa) | (~point_equal(c1, o)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[1243, 1241])).
% 1.53/1.71 tff(1245,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, oa) | (~incident(o, oa)) | (~point_equal(c1, o)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1246,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oa)) | incident(c1, oa) | (~point_equal(c1, o))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 1.53/1.71 tff(1247,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1246, 253, 151, 1240, 1239])).
% 1.53/1.71 tff(1248,plain,(incident(c1, oa) | (~point_equal(c1, o))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(1249,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1248, 1238, 1231])).
% 1.53/1.71 tff(1250,plain,(incident(b1, a2c2) | point_equal(b2, c1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(1251,plain,
% 1.53/1.71 (incident(b1, a2c2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1250, 1])).
% 1.53/1.71 tff(1252,assumption,(point_equal(ab, b1)), introduced(assumption)).
% 1.53/1.71 tff(1253,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b1, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b1, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, b1)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1254,plain,
% 1.53/1.71 ((incident(ab, a2c2) | (~incident(b1, a2c2)) | (~point_equal(ab, b1))) <=> ((~incident(b1, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, b1)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1255,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, a2c2) | (~incident(b1, a2c2)) | (~point_equal(ab, b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b1, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, b1))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1254])).
% 1.53/1.71 tff(1256,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, a2c2) | (~incident(b1, a2c2)) | (~point_equal(ab, b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b1, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, b1)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[1255, 1253])).
% 1.53/1.71 tff(1257,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, a2c2) | (~incident(b1, a2c2)) | (~point_equal(ab, b1)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1258,plain,
% 1.53/1.71 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b1, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, b1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1257, 1256])).
% 1.53/1.71 tff(1259,plain,
% 1.53/1.71 ((~incident(b1, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, b1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1258, 151])).
% 1.53/1.71 tff(1260,plain,
% 1.53/1.71 (incident(ab, a2c2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1259, 1252, 576])).
% 1.53/1.71 tff(1261,plain,
% 1.53/1.71 (((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(a2, a2c2)) | line_equal(a2c2, a2c2))) <=> ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(a2, a2c2)) | line_equal(a2c2, a2c2))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1262,plain,
% 1.53/1.71 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(a2, a2c2)) | line_equal(a2c2, a2c2))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1263,plain,
% 1.53/1.71 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(a2, a2c2)) | line_equal(a2c2, a2c2)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 1.53/1.71 tff(1264,plain,
% 1.53/1.71 (line_equal(a2c2, a2c2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1263, 277, 105])).
% 1.53/1.71 tff(1265,plain,
% 1.53/1.71 (((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(a2c2, a2c2)) | (~incident(bc, a2c2)) | (~incident(ab, a2c2)) | (~incident(ac, a2c2)))) <=> ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~line_equal(a2c2, a2c2)) | (~incident(bc, a2c2)) | (~incident(ab, a2c2)) | (~incident(ac, a2c2)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1266,plain,
% 1.53/1.71 ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(a2c2, a2c2)) | (~incident(bc, a2c2)) | (~incident(ab, a2c2)) | (~incident(ac, a2c2)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1267,plain,
% 1.53/1.71 ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~line_equal(a2c2, a2c2)) | (~incident(bc, a2c2)) | (~incident(ab, a2c2)) | (~incident(ac, a2c2))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 1.53/1.71 tff(1268,plain,
% 1.53/1.71 ((~incident(bc, a2c2)) | (~incident(ab, a2c2))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1267, 128, 49, 171, 1264])).
% 1.53/1.71 tff(1269,plain,
% 1.53/1.71 (~incident(bc, a2c2)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1268, 1260])).
% 1.53/1.71 tff(1270,assumption,(~incident(bc, a2c2)), introduced(assumption)).
% 1.53/1.71 tff(1271,plain,
% 1.53/1.71 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(bc, b1c1)) | incident(bc, a2c2) | (~line_equal(b1c1, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(bc, b1c1)) | incident(bc, a2c2) | (~line_equal(b1c1, a2c2)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1272,plain,
% 1.53/1.71 ((incident(bc, a2c2) | (~line_equal(b1c1, a2c2)) | (~incident(bc, b1c1))) <=> ((~incident(bc, b1c1)) | incident(bc, a2c2) | (~line_equal(b1c1, a2c2)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1273,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(bc, a2c2) | (~line_equal(b1c1, a2c2)) | (~incident(bc, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(bc, b1c1)) | incident(bc, a2c2) | (~line_equal(b1c1, a2c2))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1272])).
% 1.53/1.72 tff(1274,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(bc, a2c2) | (~line_equal(b1c1, a2c2)) | (~incident(bc, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(bc, b1c1)) | incident(bc, a2c2) | (~line_equal(b1c1, a2c2)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1273, 1271])).
% 1.53/1.72 tff(1275,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(bc, a2c2) | (~line_equal(b1c1, a2c2)) | (~incident(bc, b1c1)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1276,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(bc, b1c1)) | incident(bc, a2c2) | (~line_equal(b1c1, a2c2))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1275, 1274])).
% 1.53/1.72 tff(1277,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1276, 841, 21, 1270, 633])).
% 1.53/1.72 tff(1278,plain,(incident(bc, a2c2) | (~line_equal(b1c1, a2c2))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(1279,plain,
% 1.53/1.72 (~line_equal(b1c1, a2c2)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1278, 1269])).
% 1.53/1.72 tff(1280,plain,
% 1.53/1.72 (point_equal(a2, b1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[671, 1279, 576, 1152])).
% 1.53/1.72 tff(1281,assumption,(point_equal(a2, b1)), introduced(assumption)).
% 1.53/1.72 tff(1282,assumption,(~incident(a2, a1b1)), introduced(assumption)).
% 1.53/1.72 tff(1283,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, a1b1) | (~incident(b1, a1b1)) | (~point_equal(a2, b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a2, a1b1) | (~incident(b1, a1b1)) | (~point_equal(a2, b1)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1284,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, a1b1) | (~incident(b1, a1b1)) | (~point_equal(a2, b1)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1285,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a2, a1b1) | (~incident(b1, a1b1)) | (~point_equal(a2, b1))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 1.53/1.72 tff(1286,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1285, 64, 151, 1282, 1281])).
% 1.53/1.72 tff(1287,plain,(incident(a2, a1b1) | (~point_equal(a2, b1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(1288,plain,
% 1.53/1.72 (incident(a2, a1b1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1287, 1280])).
% 1.53/1.72 tff(1289,assumption,(~point_equal(ab, a2)), introduced(assumption)).
% 1.53/1.72 tff(1290,assumption,(incident(a2, a1b1)), introduced(assumption)).
% 1.53/1.72 tff(1291,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a2))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1292,plain,
% 1.53/1.72 ((line_equal(a1b1, a2b2) | point_equal(ab, a2) | (~incident(a2, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(a2, a2b2))) <=> (line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a2))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1293,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(ab, a2) | (~incident(a2, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(a2, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a2)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1292])).
% 1.53/1.72 tff(1294,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(ab, a2) | (~incident(a2, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(a2, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a2))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1293, 1291])).
% 1.53/1.72 tff(1295,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(ab, a2) | (~incident(a2, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(a2, a2b2)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1296,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a2)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 1.53/1.72 tff(1297,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1296, 300, 115, 363, 294, 46, 1290, 1289])).
% 1.53/1.72 tff(1298,plain,(point_equal(ab, a2) | (~incident(a2, a1b1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(1299,plain,
% 1.53/1.72 (point_equal(ab, a2)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1298, 1288])).
% 1.53/1.72 tff(1300,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b1, b1c1)) | incident(ab, b1c1) | (~point_equal(ab, b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b1, b1c1)) | incident(ab, b1c1) | (~point_equal(ab, b1)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1301,plain,
% 1.53/1.72 ((incident(ab, b1c1) | (~incident(b1, b1c1)) | (~point_equal(ab, b1))) <=> ((~incident(b1, b1c1)) | incident(ab, b1c1) | (~point_equal(ab, b1)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1302,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, b1c1) | (~incident(b1, b1c1)) | (~point_equal(ab, b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b1, b1c1)) | incident(ab, b1c1) | (~point_equal(ab, b1))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1301])).
% 1.53/1.72 tff(1303,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, b1c1) | (~incident(b1, b1c1)) | (~point_equal(ab, b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b1, b1c1)) | incident(ab, b1c1) | (~point_equal(ab, b1)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1302, 1300])).
% 1.53/1.72 tff(1304,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, b1c1) | (~incident(b1, b1c1)) | (~point_equal(ab, b1)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1305,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b1, b1c1)) | incident(ab, b1c1) | (~point_equal(ab, b1))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 1.53/1.72 tff(1306,plain,
% 1.53/1.72 (incident(ab, b1c1) | (~point_equal(ab, b1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1305, 486, 151])).
% 1.53/1.72 tff(1307,plain,
% 1.53/1.72 (incident(ab, b1c1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1306, 1252])).
% 1.53/1.72 tff(1308,plain,
% 1.53/1.72 (((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(c1, b1c1)) | line_equal(b1c1, b1c1))) <=> ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(c1, b1c1)) | line_equal(b1c1, b1c1))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1309,plain,
% 1.53/1.72 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(c1, b1c1)) | line_equal(b1c1, b1c1))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1310,plain,
% 1.53/1.72 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(c1, b1c1)) | line_equal(b1c1, b1c1)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 1.53/1.72 tff(1311,plain,
% 1.53/1.72 (line_equal(b1c1, b1c1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1310, 439, 105])).
% 1.53/1.72 tff(1312,plain,
% 1.53/1.72 (((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ab, b1c1)) | (~incident(ac, b1c1)))) <=> ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ab, b1c1)) | (~incident(ac, b1c1)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1313,plain,
% 1.53/1.72 ((goal | (~line_equal(b1c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(ab, b1c1)) | (~incident(ac, b1c1))) <=> (goal | (~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ab, b1c1)) | (~incident(ac, b1c1)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1314,plain,
% 1.53/1.72 (((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(b1c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(ab, b1c1)) | (~incident(ac, b1c1)))) <=> ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ab, b1c1)) | (~incident(ac, b1c1))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1313])).
% 1.53/1.72 tff(1315,plain,
% 1.53/1.72 (((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(b1c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(ab, b1c1)) | (~incident(ac, b1c1)))) <=> ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ab, b1c1)) | (~incident(ac, b1c1)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1314, 1312])).
% 1.53/1.72 tff(1316,plain,
% 1.53/1.72 ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(b1c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(ab, b1c1)) | (~incident(ac, b1c1)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1317,plain,
% 1.53/1.72 ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ab, b1c1)) | (~incident(ac, b1c1))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 1.53/1.72 tff(1318,plain,
% 1.53/1.72 ((~incident(ab, b1c1)) | (~incident(ac, b1c1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1317, 128, 49, 841, 1311])).
% 1.53/1.72 tff(1319,plain,
% 1.53/1.72 (~incident(ac, b1c1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1318, 1307])).
% 1.53/1.72 tff(1320,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, b1c1) | (~incident(ac, a2c2)) | (~line_equal(a2c2, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ac, b1c1) | (~incident(ac, a2c2)) | (~line_equal(a2c2, b1c1)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1321,plain,
% 1.53/1.72 ((incident(ac, b1c1) | (~line_equal(a2c2, b1c1)) | (~incident(ac, a2c2))) <=> (incident(ac, b1c1) | (~incident(ac, a2c2)) | (~line_equal(a2c2, b1c1)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1322,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, b1c1) | (~line_equal(a2c2, b1c1)) | (~incident(ac, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, b1c1) | (~incident(ac, a2c2)) | (~line_equal(a2c2, b1c1))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1321])).
% 1.53/1.72 tff(1323,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, b1c1) | (~line_equal(a2c2, b1c1)) | (~incident(ac, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ac, b1c1) | (~incident(ac, a2c2)) | (~line_equal(a2c2, b1c1)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1322, 1320])).
% 1.53/1.72 tff(1324,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, b1c1) | (~line_equal(a2c2, b1c1)) | (~incident(ac, a2c2)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1325,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ac, b1c1) | (~incident(ac, a2c2)) | (~line_equal(a2c2, b1c1))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.53/1.72 tff(1326,plain,
% 1.53/1.72 (incident(ac, b1c1) | (~line_equal(a2c2, b1c1))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1325, 171, 21])).
% 1.53/1.72 tff(1327,plain,
% 1.53/1.72 (~line_equal(a2c2, b1c1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1326, 1319])).
% 1.53/1.72 tff(1328,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(a2c2, b1c1) | point_equal(b1, a2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(a2c2, b1c1) | point_equal(b1, a2))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1329,plain,
% 1.53/1.72 ((line_equal(a2c2, b1c1) | point_equal(b1, a2) | (~incident(a2, a2c2)) | (~incident(b1, a2c2)) | (~incident(b1, b1c1)) | (~incident(a2, b1c1))) <=> ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(a2c2, b1c1) | point_equal(b1, a2))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1330,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2c2, b1c1) | point_equal(b1, a2) | (~incident(a2, a2c2)) | (~incident(b1, a2c2)) | (~incident(b1, b1c1)) | (~incident(a2, b1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(a2c2, b1c1) | point_equal(b1, a2)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1329])).
% 1.53/1.72 tff(1331,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2c2, b1c1) | point_equal(b1, a2) | (~incident(a2, a2c2)) | (~incident(b1, a2c2)) | (~incident(b1, b1c1)) | (~incident(a2, b1c1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(a2c2, b1c1) | point_equal(b1, a2))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1330, 1328])).
% 1.53/1.72 tff(1332,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2c2, b1c1) | point_equal(b1, a2) | (~incident(a2, a2c2)) | (~incident(b1, a2c2)) | (~incident(b1, b1c1)) | (~incident(a2, b1c1)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1333,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(a2c2, b1c1) | point_equal(b1, a2)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 1.53/1.72 tff(1334,plain,
% 1.53/1.72 ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | line_equal(a2c2, b1c1) | point_equal(b1, a2)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1333, 277, 486, 46])).
% 1.53/1.72 tff(1335,plain,
% 1.53/1.72 (point_equal(b1, a2)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1334, 1327, 576, 1152])).
% 1.53/1.72 tff(1336,plain,
% 1.53/1.72 (incident(b1, a2b2)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[399, 1335])).
% 1.53/1.72 tff(1337,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | point_equal(b1, a1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | point_equal(b1, a1))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1338,plain,
% 1.53/1.72 ((line_equal(a1b1, a2b2) | point_equal(b1, a1) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | (~incident(a1, a2b2))) <=> (line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | point_equal(b1, a1))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1339,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(b1, a1) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | (~incident(a1, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | point_equal(b1, a1)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1338])).
% 1.53/1.72 tff(1340,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(b1, a1) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | (~incident(a1, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | point_equal(b1, a1))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1339, 1337])).
% 1.53/1.72 tff(1341,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1b1, a2b2) | point_equal(b1, a1) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | (~incident(a1, a2b2)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1342,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | point_equal(b1, a1)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 1.53/1.72 tff(1343,plain,
% 1.53/1.72 ((~incident(a1, a2b2)) | (~incident(b1, a2b2))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1342, 108, 64, 294, 46, 1125])).
% 1.53/1.72 tff(1344,plain,
% 1.53/1.72 (~incident(a1, a2b2)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1343, 1336])).
% 1.53/1.72 tff(1345,plain,
% 1.53/1.72 (~line_equal(oa, a2b2)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[967, 1344])).
% 1.53/1.72 tff(1346,plain,
% 1.53/1.72 (line_equal(a2b2, ob)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[388, 1336])).
% 1.53/1.72 tff(1347,plain,
% 1.53/1.72 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a2b2, ob)) | line_equal(ob, a2b2))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a2b2, ob)) | line_equal(ob, a2b2))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1348,plain,
% 1.53/1.72 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a2b2, ob)) | line_equal(ob, a2b2))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1349,plain,
% 1.53/1.72 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a2b2, ob)) | line_equal(ob, a2b2)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 1.53/1.72 tff(1350,plain,
% 1.53/1.72 (line_equal(ob, a2b2)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1349, 464, 1346])).
% 1.53/1.72 tff(1351,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, ob)) | incident(o, a2b2) | (~line_equal(ob, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | incident(o, a2b2) | (~line_equal(ob, a2b2)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1352,plain,
% 1.53/1.72 ((incident(o, a2b2) | (~line_equal(ob, a2b2)) | (~incident(o, ob))) <=> ((~incident(o, ob)) | incident(o, a2b2) | (~line_equal(ob, a2b2)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1353,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2b2) | (~line_equal(ob, a2b2)) | (~incident(o, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, ob)) | incident(o, a2b2) | (~line_equal(ob, a2b2))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1352])).
% 1.53/1.72 tff(1354,plain,
% 1.53/1.72 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2b2) | (~line_equal(ob, a2b2)) | (~incident(o, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | incident(o, a2b2) | (~line_equal(ob, a2b2)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1353, 1351])).
% 1.53/1.72 tff(1355,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2b2) | (~line_equal(ob, a2b2)) | (~incident(o, ob)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1356,plain,
% 1.53/1.72 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | incident(o, a2b2) | (~line_equal(ob, a2b2))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 1.53/1.72 tff(1357,plain,
% 1.53/1.72 (incident(o, a2b2) | (~line_equal(ob, a2b2))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1356, 75, 21])).
% 1.53/1.72 tff(1358,plain,
% 1.53/1.72 (incident(o, a2b2)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1357, 1350])).
% 1.53/1.72 tff(1359,plain,
% 1.53/1.72 (point_equal(a2, o)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[975, 1358, 1345])).
% 1.53/1.72 tff(1360,assumption,(point_equal(a2, o)), introduced(assumption)).
% 1.53/1.72 tff(1361,assumption,(~incident(a2, oc)), introduced(assumption)).
% 1.53/1.73 tff(1362,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, oc)) | incident(a2, oc) | (~point_equal(a2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oc)) | incident(a2, oc) | (~point_equal(a2, o)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1363,plain,
% 1.53/1.73 ((incident(a2, oc) | (~incident(o, oc)) | (~point_equal(a2, o))) <=> ((~incident(o, oc)) | incident(a2, oc) | (~point_equal(a2, o)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1364,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, oc) | (~incident(o, oc)) | (~point_equal(a2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, oc)) | incident(a2, oc) | (~point_equal(a2, o))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1363])).
% 1.53/1.73 tff(1365,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, oc) | (~incident(o, oc)) | (~point_equal(a2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oc)) | incident(a2, oc) | (~point_equal(a2, o)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1364, 1362])).
% 1.53/1.73 tff(1366,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, oc) | (~incident(o, oc)) | (~point_equal(a2, o)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1367,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oc)) | incident(a2, oc) | (~point_equal(a2, o))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 1.53/1.73 tff(1368,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1367, 240, 151, 1361, 1360])).
% 1.53/1.73 tff(1369,plain,(incident(a2, oc) | (~point_equal(a2, o))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(1370,plain,
% 1.53/1.73 (incident(a2, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1369, 1359])).
% 1.53/1.73 tff(1371,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oc)) | (~incident(c2, oc)) | point_equal(c2, a2) | line_equal(a2c2, oc))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oc)) | (~incident(c2, oc)) | point_equal(c2, a2) | line_equal(a2c2, oc))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1372,plain,
% 1.53/1.73 ((line_equal(a2c2, oc) | point_equal(c2, a2) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(c2, oc)) | (~incident(a2, oc))) <=> ((~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oc)) | (~incident(c2, oc)) | point_equal(c2, a2) | line_equal(a2c2, oc))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1373,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2c2, oc) | point_equal(c2, a2) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(c2, oc)) | (~incident(a2, oc)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oc)) | (~incident(c2, oc)) | point_equal(c2, a2) | line_equal(a2c2, oc)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1372])).
% 1.53/1.73 tff(1374,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2c2, oc) | point_equal(c2, a2) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(c2, oc)) | (~incident(a2, oc)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oc)) | (~incident(c2, oc)) | point_equal(c2, a2) | line_equal(a2c2, oc))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1373, 1371])).
% 1.53/1.73 tff(1375,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a2c2, oc) | point_equal(c2, a2) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(c2, oc)) | (~incident(a2, oc)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1376,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oc)) | (~incident(c2, oc)) | point_equal(c2, a2) | line_equal(a2c2, oc)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 1.53/1.73 tff(1377,plain,
% 1.53/1.73 ((~incident(a2, oc)) | line_equal(a2c2, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1376, 277, 177, 189, 46, 528])).
% 1.53/1.73 tff(1378,plain,
% 1.53/1.73 (line_equal(a2c2, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1377, 1370])).
% 1.53/1.73 tff(1379,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ac, a2c2)) | incident(ac, oc) | (~line_equal(a2c2, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ac, a2c2)) | incident(ac, oc) | (~line_equal(a2c2, oc)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1380,plain,
% 1.53/1.73 ((incident(ac, oc) | (~line_equal(a2c2, oc)) | (~incident(ac, a2c2))) <=> ((~incident(ac, a2c2)) | incident(ac, oc) | (~line_equal(a2c2, oc)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1381,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, oc) | (~line_equal(a2c2, oc)) | (~incident(ac, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ac, a2c2)) | incident(ac, oc) | (~line_equal(a2c2, oc))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1380])).
% 1.53/1.73 tff(1382,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, oc) | (~line_equal(a2c2, oc)) | (~incident(ac, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ac, a2c2)) | incident(ac, oc) | (~line_equal(a2c2, oc)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1381, 1379])).
% 1.53/1.73 tff(1383,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, oc) | (~line_equal(a2c2, oc)) | (~incident(ac, a2c2)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1384,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ac, a2c2)) | incident(ac, oc) | (~line_equal(a2c2, oc))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 1.53/1.73 tff(1385,plain,
% 1.53/1.73 (incident(ac, oc) | (~line_equal(a2c2, oc))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1384, 171, 21])).
% 1.53/1.73 tff(1386,plain,
% 1.53/1.73 (incident(ac, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1385, 1378])).
% 1.53/1.73 tff(1387,plain,
% 1.53/1.73 (incident(b1, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[600, 1378, 576])).
% 1.53/1.73 tff(1388,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a1c1) | (~incident(c1, a1c1)) | (~point_equal(b1, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, a1c1) | (~incident(c1, a1c1)) | (~point_equal(b1, c1)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1389,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a1c1) | (~incident(c1, a1c1)) | (~point_equal(b1, c1)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1390,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, a1c1) | (~incident(c1, a1c1)) | (~point_equal(b1, c1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 1.53/1.73 tff(1391,plain,
% 1.53/1.73 (~point_equal(b1, c1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1390, 227, 151, 994])).
% 1.53/1.73 tff(1392,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, oc)) | (~incident(c1, oc)) | point_equal(b1, c1) | line_equal(b1c1, oc))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, oc)) | (~incident(c1, oc)) | point_equal(b1, c1) | line_equal(b1c1, oc))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1393,plain,
% 1.53/1.73 ((line_equal(b1c1, oc) | point_equal(b1, c1) | (~incident(c1, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, oc)) | (~incident(c1, oc))) <=> ((~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, oc)) | (~incident(c1, oc)) | point_equal(b1, c1) | line_equal(b1c1, oc))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1394,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, oc) | point_equal(b1, c1) | (~incident(c1, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, oc)) | (~incident(c1, oc)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, oc)) | (~incident(c1, oc)) | point_equal(b1, c1) | line_equal(b1c1, oc)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1393])).
% 1.53/1.73 tff(1395,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, oc) | point_equal(b1, c1) | (~incident(c1, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, oc)) | (~incident(c1, oc)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, oc)) | (~incident(c1, oc)) | point_equal(b1, c1) | line_equal(b1c1, oc))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1394, 1392])).
% 1.53/1.73 tff(1396,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(b1c1, oc) | point_equal(b1, c1) | (~incident(c1, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, oc)) | (~incident(c1, oc)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1397,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, b1c1)) | (~incident(c1, b1c1)) | (~incident(b1, oc)) | (~incident(c1, oc)) | point_equal(b1, c1) | line_equal(b1c1, oc)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 1.53/1.73 tff(1398,plain,
% 1.53/1.73 ((~incident(b1, oc)) | line_equal(b1c1, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1397, 439, 486, 224, 46, 1391])).
% 1.53/1.73 tff(1399,plain,
% 1.53/1.73 (line_equal(b1c1, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1398, 1387])).
% 1.53/1.73 tff(1400,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(bc, b1c1)) | incident(bc, oc) | (~line_equal(b1c1, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(bc, b1c1)) | incident(bc, oc) | (~line_equal(b1c1, oc)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1401,plain,
% 1.53/1.73 ((incident(bc, oc) | (~line_equal(b1c1, oc)) | (~incident(bc, b1c1))) <=> ((~incident(bc, b1c1)) | incident(bc, oc) | (~line_equal(b1c1, oc)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1402,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(bc, oc) | (~line_equal(b1c1, oc)) | (~incident(bc, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(bc, b1c1)) | incident(bc, oc) | (~line_equal(b1c1, oc))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1401])).
% 1.53/1.73 tff(1403,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(bc, oc) | (~line_equal(b1c1, oc)) | (~incident(bc, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(bc, b1c1)) | incident(bc, oc) | (~line_equal(b1c1, oc)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1402, 1400])).
% 1.53/1.73 tff(1404,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(bc, oc) | (~line_equal(b1c1, oc)) | (~incident(bc, b1c1)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1405,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(bc, b1c1)) | incident(bc, oc) | (~line_equal(b1c1, oc))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 1.53/1.73 tff(1406,plain,
% 1.53/1.73 (incident(bc, oc) | (~line_equal(b1c1, oc))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1405, 841, 21])).
% 1.53/1.73 tff(1407,plain,
% 1.53/1.73 (incident(bc, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1406, 1399])).
% 1.53/1.73 tff(1408,plain,
% 1.53/1.73 (((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(o, oc)) | line_equal(oc, oc))) <=> ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(o, oc)) | line_equal(oc, oc))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1409,plain,
% 1.53/1.73 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(o, oc)) | line_equal(oc, oc))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1410,plain,
% 1.53/1.73 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(o, oc)) | line_equal(oc, oc)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 1.53/1.73 tff(1411,plain,
% 1.53/1.73 (line_equal(oc, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1410, 240, 105])).
% 1.53/1.73 tff(1412,plain,
% 1.53/1.73 (((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(oc, oc)) | (~incident(bc, oc)) | (~incident(ab, oc)) | (~incident(ac, oc)))) <=> ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~line_equal(oc, oc)) | (~incident(bc, oc)) | (~incident(ab, oc)) | (~incident(ac, oc)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1413,plain,
% 1.53/1.73 ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | (goal | (~line_equal(oc, oc)) | (~incident(bc, oc)) | (~incident(ab, oc)) | (~incident(ac, oc)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1414,plain,
% 1.53/1.73 ((~![A: $i] : (goal | (~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ab, A)) | (~incident(ac, A)))) | goal | (~line_equal(oc, oc)) | (~incident(bc, oc)) | (~incident(ab, oc)) | (~incident(ac, oc))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 1.53/1.73 tff(1415,plain,
% 1.53/1.73 ((~incident(bc, oc)) | (~incident(ab, oc)) | (~incident(ac, oc))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1414, 128, 49, 1411])).
% 1.53/1.73 tff(1416,plain,
% 1.53/1.73 (~incident(ab, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1415, 1407, 1386])).
% 1.53/1.73 tff(1417,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, oc)) | incident(ab, oc) | (~point_equal(ab, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, oc)) | incident(ab, oc) | (~point_equal(ab, a2)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1418,plain,
% 1.53/1.73 ((incident(ab, oc) | (~incident(a2, oc)) | (~point_equal(ab, a2))) <=> ((~incident(a2, oc)) | incident(ab, oc) | (~point_equal(ab, a2)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1419,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, oc) | (~incident(a2, oc)) | (~point_equal(ab, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, oc)) | incident(ab, oc) | (~point_equal(ab, a2))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1418])).
% 1.53/1.73 tff(1420,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, oc) | (~incident(a2, oc)) | (~point_equal(ab, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, oc)) | incident(ab, oc) | (~point_equal(ab, a2)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1419, 1417])).
% 1.53/1.73 tff(1421,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, oc) | (~incident(a2, oc)) | (~point_equal(ab, a2)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1422,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, oc)) | incident(ab, oc) | (~point_equal(ab, a2))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 1.53/1.73 tff(1423,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1422, 151, 1370, 1416, 1299])).
% 1.53/1.73 tff(1424,plain,((~point_equal(ab, b1)) | (~incident(b1, a2c2)) | (~incident(a2, b1c1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(1425,plain,
% 1.53/1.73 (~point_equal(ab, b1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1424, 1152, 576])).
% 1.53/1.73 tff(1426,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(ab, b1))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(ab, b1))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1427,plain,
% 1.53/1.73 ((line_equal(ob, a1b1) | point_equal(ab, b1) | (~incident(b1, ob)) | (~incident(ab, ob)) | (~incident(ab, a1b1)) | (~incident(b1, a1b1))) <=> ((~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(ab, b1))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1428,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(ab, b1) | (~incident(b1, ob)) | (~incident(ab, ob)) | (~incident(ab, a1b1)) | (~incident(b1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(ab, b1)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1427])).
% 1.53/1.73 tff(1429,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(ab, b1) | (~incident(b1, ob)) | (~incident(ab, ob)) | (~incident(ab, a1b1)) | (~incident(b1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(ab, b1))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1428, 1426])).
% 1.53/1.73 tff(1430,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a1b1) | point_equal(ab, b1) | (~incident(b1, ob)) | (~incident(ab, ob)) | (~incident(ab, a1b1)) | (~incident(b1, a1b1)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1431,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b1, a1b1)) | (~incident(b1, ob)) | (~incident(ab, a1b1)) | (~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(ab, b1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 1.53/1.73 tff(1432,plain,
% 1.53/1.73 ((~incident(ab, ob)) | line_equal(ob, a1b1) | point_equal(ab, b1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1431, 64, 61, 115, 46])).
% 1.53/1.73 tff(1433,plain,
% 1.53/1.73 (line_equal(ob, a1b1) | point_equal(ab, b1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1432, 1164])).
% 1.53/1.73 tff(1434,plain,
% 1.53/1.73 (line_equal(ob, a1b1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1433, 1425])).
% 1.53/1.73 tff(1435,plain,
% 1.53/1.73 (incident(o, a1b1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[82, 1434])).
% 1.53/1.73 tff(1436,plain,
% 1.53/1.73 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a2b2, a1b1)) | line_equal(a1b1, a2b2))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a2b2, a1b1)) | line_equal(a1b1, a2b2))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1437,plain,
% 1.53/1.73 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a2b2, a1b1)) | line_equal(a1b1, a2b2))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1438,plain,
% 1.53/1.73 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a2b2, a1b1)) | line_equal(a1b1, a2b2)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 1.53/1.73 tff(1439,plain,
% 1.53/1.73 (~line_equal(a2b2, a1b1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1438, 294, 464])).
% 1.53/1.73 tff(1440,plain,
% 1.53/1.73 (![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B))) <=> ![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1441,plain,
% 1.53/1.73 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((line_equal(A, B) & line_equal(B, C)) <=> (~((~line_equal(B, C)) | (~line_equal(A, B))))), ((~(line_equal(A, B) & line_equal(B, C))) <=> (~(~((~line_equal(B, C)) | (~line_equal(A, B))))))), rewrite((~(~((~line_equal(B, C)) | (~line_equal(A, B))))) <=> ((~line_equal(B, C)) | (~line_equal(A, B)))), ((~(line_equal(A, B) & line_equal(B, C))) <=> ((~line_equal(B, C)) | (~line_equal(A, B))))), (((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C)) <=> (((~line_equal(B, C)) | (~line_equal(A, B))) | line_equal(A, C)))), rewrite((((~line_equal(B, C)) | (~line_equal(A, B))) | line_equal(A, C)) <=> (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))), (((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C)) <=> (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(1442,plain,
% 1.53/1.73 (![A: $i, B: $i, C: $i] : ((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C)) <=> ![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[1441])).
% 1.53/1.73 tff(1443,plain,
% 1.53/1.73 (![A: $i, B: $i, C: $i] : ((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1444,plain,
% 1.53/1.73 (^[A: $i, B: $i, C: $i] : rewrite(((line_equal(A, B) & line_equal(B, C)) => line_equal(A, C)) <=> ((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C)))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(1445,plain,
% 1.53/1.73 (![A: $i, B: $i, C: $i] : ((line_equal(A, B) & line_equal(B, C)) => line_equal(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[1444])).
% 1.53/1.73 tff(1446,axiom,(![A: $i, B: $i, C: $i] : ((line_equal(A, B) & line_equal(B, C)) => line_equal(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity_of_line_equal')).
% 1.53/1.73 tff(1447,plain,
% 1.53/1.73 (![A: $i, B: $i, C: $i] : ((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 1.53/1.73 tff(1448,plain,
% 1.53/1.73 (![A: $i, B: $i, C: $i] : ((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1447, 1443])).
% 1.53/1.73 tff(1449,plain,(
% 1.53/1.73 ![A: $i, B: $i, C: $i] : ((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C))),
% 1.53/1.73 inference(skolemize,[status(sab)],[1448])).
% 1.53/1.73 tff(1450,plain,
% 1.53/1.73 (![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1449, 1442])).
% 1.53/1.73 tff(1451,plain,
% 1.53/1.73 (![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1450, 1440])).
% 1.53/1.73 tff(1452,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(a2b2, a1b1) | (~line_equal(ob, a1b1)) | (~line_equal(a2b2, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | line_equal(a2b2, a1b1) | (~line_equal(ob, a1b1)) | (~line_equal(a2b2, ob)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1453,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(a2b2, a1b1) | (~line_equal(ob, a1b1)) | (~line_equal(a2b2, ob)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1454,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | line_equal(a2b2, a1b1) | (~line_equal(ob, a1b1)) | (~line_equal(a2b2, ob))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 1.53/1.73 tff(1455,plain,
% 1.53/1.73 ((~line_equal(ob, a1b1)) | (~line_equal(a2b2, ob))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1454, 1451, 1439])).
% 1.53/1.73 tff(1456,plain,
% 1.53/1.73 (~line_equal(a2b2, ob)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1455, 1434])).
% 1.53/1.73 tff(1457,plain,
% 1.53/1.73 (~incident(b1, a2b2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[388, 1456])).
% 1.53/1.73 tff(1458,plain,
% 1.53/1.73 (~point_equal(b1, a2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[399, 1457])).
% 1.53/1.73 tff(1459,plain,
% 1.53/1.73 (line_equal(b1c1, a2c2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[693, 1458, 576, 1152])).
% 1.53/1.73 tff(1460,plain,
% 1.53/1.73 (incident(c1, a2c2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[642, 1459])).
% 1.53/1.73 tff(1461,plain,
% 1.53/1.73 (line_equal(a2c2, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[631, 1460])).
% 1.53/1.73 tff(1462,plain,
% 1.53/1.73 (point_equal(a2, o)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[614, 1461, 576])).
% 1.53/1.73 tff(1463,plain,
% 1.53/1.73 (incident(b2, a1b1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[348, 1434])).
% 1.53/1.73 tff(1464,plain,
% 1.53/1.73 (~incident(a2, a1b1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[307, 1463])).
% 1.53/1.73 tff(1465,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, a1b1) | (~incident(o, a1b1)) | (~point_equal(a2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a2, a1b1) | (~incident(o, a1b1)) | (~point_equal(a2, o)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1466,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, a1b1) | (~incident(o, a1b1)) | (~point_equal(a2, o)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1467,plain,
% 1.53/1.73 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a2, a1b1) | (~incident(o, a1b1)) | (~point_equal(a2, o))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 1.53/1.73 tff(1468,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1467, 151, 1464, 1462, 1435])).
% 1.53/1.73 tff(1469,plain,((~incident(a2, b1c1)) | (~incident(b1, a2c2))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(1470,plain,
% 1.53/1.73 (~incident(a2, b1c1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1469, 1251])).
% 1.53/1.73 tff(1471,plain,
% 1.53/1.73 (incident(c1, a2b2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[679, 1470])).
% 1.53/1.73 tff(1472,plain,
% 1.53/1.73 (~incident(a1, b2c2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[661, 1471, 1251])).
% 1.53/1.73 tff(1473,assumption,(incident(c1, a2b2)), introduced(assumption)).
% 1.53/1.73 tff(1474,plain,
% 1.53/1.73 (line_equal(a2b2, a1c1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1149, 1473, 1, 980])).
% 1.53/1.73 tff(1475,plain,
% 1.53/1.73 (incident(a2, a1c1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[564, 1474])).
% 1.53/1.73 tff(1476,plain,
% 1.53/1.73 (point_equal(c1, o)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[553, 1475])).
% 1.53/1.73 tff(1477,plain,
% 1.53/1.73 (incident(c1, ob)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[501, 1476])).
% 1.53/1.73 tff(1478,plain,
% 1.53/1.73 (line_equal(ob, b1c1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[493, 1477])).
% 1.53/1.73 tff(1479,plain,
% 1.53/1.73 (line_equal(a1c1, a2b2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[702, 1473, 1, 980])).
% 1.53/1.73 tff(1480,plain,
% 1.53/1.73 (incident(ac, a2b2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[927, 1479])).
% 1.53/1.73 tff(1481,plain,
% 1.53/1.73 (~incident(bc, a2b2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[916, 1480])).
% 1.53/1.73 tff(1482,plain,
% 1.53/1.73 (~point_equal(bc, b2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[907, 1481])).
% 1.53/1.73 tff(1483,plain,
% 1.53/1.73 (~incident(b2, b1c1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[849, 1482])).
% 1.53/1.73 tff(1484,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[475, 1483, 1478])).
% 1.53/1.73 tff(1485,plain,((~incident(c1, a2b2)) | point_equal(b2, c1) | (~incident(b2, a1c1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(1486,plain,
% 1.53/1.73 (~incident(b2, a1c1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1485, 1471, 1])).
% 1.53/1.73 tff(1487,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[685, 1486, 1472])).
% 1.53/1.73 tff(1488,plain,(point_equal(b2, c1)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(1489,plain,
% 1.53/1.73 (incident(b2, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1016, 1488])).
% 1.53/1.73 tff(1490,plain,
% 1.53/1.73 (((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (goal | (~incident(a2, oc)) | (~incident(b2, oc)) | (~incident(c2, oc)))) <=> ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | goal | (~incident(a2, oc)) | (~incident(b2, oc)) | (~incident(c2, oc)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1491,plain,
% 1.53/1.73 ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (goal | (~incident(a2, oc)) | (~incident(b2, oc)) | (~incident(c2, oc)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1492,plain,
% 1.53/1.73 ((~![A: $i] : (goal | (~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | goal | (~incident(a2, oc)) | (~incident(b2, oc)) | (~incident(c2, oc))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 1.53/1.73 tff(1493,plain,
% 1.53/1.73 ((~incident(a2, oc)) | (~incident(b2, oc))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1492, 49, 189, 274])).
% 1.53/1.73 tff(1494,plain,
% 1.53/1.73 (~incident(a2, oc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1493, 1489])).
% 1.53/1.73 tff(1495,plain,
% 1.53/1.73 (~point_equal(a2, o)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1369, 1494])).
% 1.53/1.73 tff(1496,plain,
% 1.53/1.73 (incident(b2, b1c1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[444, 1488])).
% 1.53/1.73 tff(1497,plain,
% 1.53/1.73 (~incident(b1, b2c2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1032, 1496])).
% 1.53/1.73 tff(1498,plain,
% 1.53/1.73 (~point_equal(b1, bc)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[405, 1497])).
% 1.53/1.73 tff(1499,plain,
% 1.53/1.73 (point_equal(bc, b2)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[849, 1496])).
% 1.53/1.73 tff(1500,plain,
% 1.53/1.73 (incident(bc, ob)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[860, 1499])).
% 1.53/1.73 tff(1501,plain,
% 1.53/1.73 (line_equal(b1c1, ob)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[940, 1500, 1498])).
% 1.53/1.73 tff(1502,plain,
% 1.53/1.73 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(c1, b1c1)) | incident(c1, ob) | (~line_equal(b1c1, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c1, b1c1)) | incident(c1, ob) | (~line_equal(b1c1, ob)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1503,plain,
% 1.53/1.74 ((incident(c1, ob) | (~line_equal(b1c1, ob)) | (~incident(c1, b1c1))) <=> ((~incident(c1, b1c1)) | incident(c1, ob) | (~line_equal(b1c1, ob)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1504,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, ob) | (~line_equal(b1c1, ob)) | (~incident(c1, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(c1, b1c1)) | incident(c1, ob) | (~line_equal(b1c1, ob))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1503])).
% 1.53/1.74 tff(1505,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, ob) | (~line_equal(b1c1, ob)) | (~incident(c1, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c1, b1c1)) | incident(c1, ob) | (~line_equal(b1c1, ob)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1504, 1502])).
% 1.53/1.74 tff(1506,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, ob) | (~line_equal(b1c1, ob)) | (~incident(c1, b1c1)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1507,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c1, b1c1)) | incident(c1, ob) | (~line_equal(b1c1, ob))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 1.53/1.74 tff(1508,plain,
% 1.53/1.74 (incident(c1, ob) | (~line_equal(b1c1, ob))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1507, 439, 21])).
% 1.53/1.74 tff(1509,plain,
% 1.53/1.74 (incident(c1, ob)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1508, 1501])).
% 1.53/1.74 tff(1510,plain,
% 1.53/1.74 (((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, ob)) | (~incident(b1, ob)) | (~incident(c1, ob)))) <=> ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, ob)) | (~incident(b1, ob)) | (~incident(c1, ob)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1511,plain,
% 1.53/1.74 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, ob)) | (~incident(b1, ob)) | (~incident(c1, ob)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1512,plain,
% 1.53/1.74 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, ob)) | (~incident(b1, ob)) | (~incident(c1, ob))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1511, 1510])).
% 1.53/1.74 tff(1513,plain,
% 1.53/1.74 ((~incident(a1, ob)) | (~incident(c1, ob))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1512, 49, 61, 210])).
% 1.53/1.74 tff(1514,plain,
% 1.53/1.74 (~incident(a1, ob)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1513, 1509])).
% 1.53/1.74 tff(1515,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a1, a1b1)) | incident(a1, ob) | (~line_equal(a1b1, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a1, a1b1)) | incident(a1, ob) | (~line_equal(a1b1, ob)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1516,plain,
% 1.53/1.74 ((incident(a1, ob) | (~line_equal(a1b1, ob)) | (~incident(a1, a1b1))) <=> ((~incident(a1, a1b1)) | incident(a1, ob) | (~line_equal(a1b1, ob)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1517,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, ob) | (~line_equal(a1b1, ob)) | (~incident(a1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a1, a1b1)) | incident(a1, ob) | (~line_equal(a1b1, ob))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1516])).
% 1.53/1.74 tff(1518,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, ob) | (~line_equal(a1b1, ob)) | (~incident(a1, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a1, a1b1)) | incident(a1, ob) | (~line_equal(a1b1, ob)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1517, 1515])).
% 1.53/1.74 tff(1519,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, ob) | (~line_equal(a1b1, ob)) | (~incident(a1, a1b1)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1520,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a1, a1b1)) | incident(a1, ob) | (~line_equal(a1b1, ob))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 1.53/1.74 tff(1521,plain,
% 1.53/1.74 (incident(a1, ob) | (~line_equal(a1b1, ob))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1520, 108, 21])).
% 1.53/1.74 tff(1522,plain,
% 1.53/1.74 (~line_equal(a1b1, ob)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1521, 1514])).
% 1.53/1.74 tff(1523,plain,
% 1.53/1.74 (~incident(b2, a1b1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[452, 1522])).
% 1.53/1.74 tff(1524,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, a1b1) | (~incident(ab, a1b1)) | (~point_equal(b2, ab)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b2, a1b1) | (~incident(ab, a1b1)) | (~point_equal(b2, ab)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1525,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, a1b1) | (~incident(ab, a1b1)) | (~point_equal(b2, ab)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1526,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b2, a1b1) | (~incident(ab, a1b1)) | (~point_equal(b2, ab))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1525, 1524])).
% 1.53/1.74 tff(1527,plain,
% 1.53/1.74 (~point_equal(b2, ab)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1526, 115, 151, 1523])).
% 1.53/1.74 tff(1528,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(ab, a2b2)) | (~incident(ab, ob)) | point_equal(b2, ab) | line_equal(ob, a2b2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(ab, a2b2)) | (~incident(ab, ob)) | point_equal(b2, ab) | line_equal(ob, a2b2))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1529,plain,
% 1.53/1.74 ((line_equal(ob, a2b2) | point_equal(b2, ab) | (~incident(ab, ob)) | (~incident(b2, ob)) | (~incident(b2, a2b2)) | (~incident(ab, a2b2))) <=> ((~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(ab, a2b2)) | (~incident(ab, ob)) | point_equal(b2, ab) | line_equal(ob, a2b2))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1530,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a2b2) | point_equal(b2, ab) | (~incident(ab, ob)) | (~incident(b2, ob)) | (~incident(b2, a2b2)) | (~incident(ab, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(ab, a2b2)) | (~incident(ab, ob)) | point_equal(b2, ab) | line_equal(ob, a2b2)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1529])).
% 1.53/1.74 tff(1531,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a2b2) | point_equal(b2, ab) | (~incident(ab, ob)) | (~incident(b2, ob)) | (~incident(b2, a2b2)) | (~incident(ab, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(ab, a2b2)) | (~incident(ab, ob)) | point_equal(b2, ab) | line_equal(ob, a2b2))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1530, 1528])).
% 1.53/1.74 tff(1532,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(ob, a2b2) | point_equal(b2, ab) | (~incident(ab, ob)) | (~incident(b2, ob)) | (~incident(b2, a2b2)) | (~incident(ab, a2b2)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1533,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(ab, a2b2)) | (~incident(ab, ob)) | point_equal(b2, ab) | line_equal(ob, a2b2)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 1.53/1.74 tff(1534,plain,
% 1.53/1.74 (point_equal(b2, ab) | line_equal(ob, a2b2)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1533, 297, 58, 363, 46, 1164])).
% 1.53/1.74 tff(1535,plain,
% 1.53/1.74 (line_equal(ob, a2b2)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1534, 1527])).
% 1.53/1.74 tff(1536,plain,
% 1.53/1.74 (incident(o, a2b2)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1357, 1535])).
% 1.53/1.74 tff(1537,plain,
% 1.53/1.74 (![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B))) <=> ![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1538,plain,
% 1.53/1.74 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((point_equal(A, B) & point_equal(B, C)) <=> (~((~point_equal(B, C)) | (~point_equal(A, B))))), ((~(point_equal(A, B) & point_equal(B, C))) <=> (~(~((~point_equal(B, C)) | (~point_equal(A, B))))))), rewrite((~(~((~point_equal(B, C)) | (~point_equal(A, B))))) <=> ((~point_equal(B, C)) | (~point_equal(A, B)))), ((~(point_equal(A, B) & point_equal(B, C))) <=> ((~point_equal(B, C)) | (~point_equal(A, B))))), (((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C)) <=> (((~point_equal(B, C)) | (~point_equal(A, B))) | point_equal(A, C)))), rewrite((((~point_equal(B, C)) | (~point_equal(A, B))) | point_equal(A, C)) <=> (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))), (((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C)) <=> (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(1539,plain,
% 1.53/1.74 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C)) <=> ![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[1538])).
% 1.53/1.74 tff(1540,plain,
% 1.53/1.74 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1541,plain,
% 1.53/1.74 (^[A: $i, B: $i, C: $i] : rewrite(((point_equal(A, B) & point_equal(B, C)) => point_equal(A, C)) <=> ((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C)))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(1542,plain,
% 1.53/1.74 (![A: $i, B: $i, C: $i] : ((point_equal(A, B) & point_equal(B, C)) => point_equal(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[1541])).
% 1.53/1.74 tff(1543,axiom,(![A: $i, B: $i, C: $i] : ((point_equal(A, B) & point_equal(B, C)) => point_equal(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity_of_point_equal')).
% 1.53/1.74 tff(1544,plain,
% 1.53/1.74 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 1.53/1.74 tff(1545,plain,
% 1.53/1.74 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1544, 1540])).
% 1.53/1.74 tff(1546,plain,(
% 1.53/1.74 ![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C))),
% 1.53/1.74 inference(skolemize,[status(sab)],[1545])).
% 1.53/1.74 tff(1547,plain,
% 1.53/1.74 (![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1546, 1539])).
% 1.53/1.74 tff(1548,plain,
% 1.53/1.74 (![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1547, 1537])).
% 1.53/1.74 tff(1549,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | ((~point_equal(b2, c1)) | (~point_equal(bc, b2)) | point_equal(bc, c1))) <=> ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (~point_equal(b2, c1)) | (~point_equal(bc, b2)) | point_equal(bc, c1))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1550,plain,
% 1.53/1.74 ((point_equal(bc, c1) | (~point_equal(b2, c1)) | (~point_equal(bc, b2))) <=> ((~point_equal(b2, c1)) | (~point_equal(bc, b2)) | point_equal(bc, c1))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1551,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (point_equal(bc, c1) | (~point_equal(b2, c1)) | (~point_equal(bc, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | ((~point_equal(b2, c1)) | (~point_equal(bc, b2)) | point_equal(bc, c1)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1550])).
% 1.53/1.74 tff(1552,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (point_equal(bc, c1) | (~point_equal(b2, c1)) | (~point_equal(bc, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (~point_equal(b2, c1)) | (~point_equal(bc, b2)) | point_equal(bc, c1))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1551, 1549])).
% 1.53/1.74 tff(1553,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (point_equal(bc, c1) | (~point_equal(b2, c1)) | (~point_equal(bc, b2)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1554,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (~point_equal(b2, c1)) | (~point_equal(bc, b2)) | point_equal(bc, c1)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1553, 1552])).
% 1.53/1.74 tff(1555,plain,
% 1.53/1.74 (point_equal(bc, c1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1554, 1548, 1488, 1499])).
% 1.53/1.74 tff(1556,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c1, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, c1)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1557,plain,
% 1.53/1.74 ((incident(bc, a1c1) | (~incident(c1, a1c1)) | (~point_equal(bc, c1))) <=> ((~incident(c1, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, c1)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1558,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, a1c1) | (~incident(c1, a1c1)) | (~point_equal(bc, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c1, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, c1))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1557])).
% 1.53/1.74 tff(1559,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, a1c1) | (~incident(c1, a1c1)) | (~point_equal(bc, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, c1)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1558, 1556])).
% 1.53/1.74 tff(1560,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, a1c1) | (~incident(c1, a1c1)) | (~point_equal(bc, c1)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1561,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, c1))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 1.53/1.74 tff(1562,plain,
% 1.53/1.74 (incident(bc, a1c1) | (~point_equal(bc, c1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1561, 227, 151])).
% 1.53/1.74 tff(1563,plain,
% 1.53/1.74 (incident(bc, a1c1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1562, 1555])).
% 1.53/1.74 tff(1564,plain,
% 1.53/1.74 (incident(bc, a2b2)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[907, 1499])).
% 1.53/1.74 tff(1565,plain,
% 1.53/1.74 (~incident(ac, a2b2)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[916, 1564])).
% 1.53/1.74 tff(1566,plain,
% 1.53/1.74 (~line_equal(a1c1, a2b2)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[927, 1565])).
% 1.53/1.74 tff(1567,plain,
% 1.53/1.74 (((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, b1c1)) | (~incident(b1, b1c1)) | (~incident(c1, b1c1)))) <=> ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, b1c1)) | (~incident(b1, b1c1)) | (~incident(c1, b1c1)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1568,plain,
% 1.53/1.74 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (goal | (~incident(a1, b1c1)) | (~incident(b1, b1c1)) | (~incident(c1, b1c1)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1569,plain,
% 1.53/1.74 ((~![A: $i] : (goal | (~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | goal | (~incident(a1, b1c1)) | (~incident(b1, b1c1)) | (~incident(c1, b1c1))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1568, 1567])).
% 1.53/1.74 tff(1570,plain,
% 1.53/1.74 (~incident(a1, b1c1)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1569, 49, 439, 486, 210])).
% 1.53/1.74 tff(1571,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a1, b1c1) | (~incident(bc, b1c1)) | (~point_equal(a1, bc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a1, b1c1) | (~incident(bc, b1c1)) | (~point_equal(a1, bc)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1572,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a1, b1c1) | (~incident(bc, b1c1)) | (~point_equal(a1, bc)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1573,plain,
% 1.53/1.74 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a1, b1c1) | (~incident(bc, b1c1)) | (~point_equal(a1, bc))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 1.53/1.74 tff(1574,plain,
% 1.53/1.74 (~point_equal(a1, bc)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1573, 841, 151, 1570])).
% 1.53/1.74 tff(1575,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, a1c1)) | (~incident(a1, a2b2)) | (~incident(bc, a1c1)) | (~incident(bc, a2b2)) | point_equal(a1, bc) | line_equal(a1c1, a2b2))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, a1c1)) | (~incident(a1, a2b2)) | (~incident(bc, a1c1)) | (~incident(bc, a2b2)) | point_equal(a1, bc) | line_equal(a1c1, a2b2))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1576,plain,
% 1.53/1.74 ((line_equal(a1c1, a2b2) | point_equal(a1, bc) | (~incident(bc, a1c1)) | (~incident(a1, a1c1)) | (~incident(a1, a2b2)) | (~incident(bc, a2b2))) <=> ((~incident(a1, a1c1)) | (~incident(a1, a2b2)) | (~incident(bc, a1c1)) | (~incident(bc, a2b2)) | point_equal(a1, bc) | line_equal(a1c1, a2b2))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1577,plain,
% 1.53/1.74 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2b2) | point_equal(a1, bc) | (~incident(bc, a1c1)) | (~incident(a1, a1c1)) | (~incident(a1, a2b2)) | (~incident(bc, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | ((~incident(a1, a1c1)) | (~incident(a1, a2b2)) | (~incident(bc, a1c1)) | (~incident(bc, a2b2)) | point_equal(a1, bc) | line_equal(a1c1, a2b2)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[1576])).
% 1.53/1.75 tff(1578,plain,
% 1.53/1.75 (((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2b2) | point_equal(a1, bc) | (~incident(bc, a1c1)) | (~incident(a1, a1c1)) | (~incident(a1, a2b2)) | (~incident(bc, a2b2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, a1c1)) | (~incident(a1, a2b2)) | (~incident(bc, a1c1)) | (~incident(bc, a2b2)) | point_equal(a1, bc) | line_equal(a1c1, a2b2))),
% 1.53/1.75 inference(transitivity,[status(thm)],[1577, 1575])).
% 1.53/1.75 tff(1579,plain,
% 1.53/1.75 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (line_equal(a1c1, a2b2) | point_equal(a1, bc) | (~incident(bc, a1c1)) | (~incident(a1, a1c1)) | (~incident(a1, a2b2)) | (~incident(bc, a2b2)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(1580,plain,
% 1.53/1.75 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(a1, a1c1)) | (~incident(a1, a2b2)) | (~incident(bc, a1c1)) | (~incident(bc, a2b2)) | point_equal(a1, bc) | line_equal(a1c1, a2b2)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 1.53/1.75 tff(1581,plain,
% 1.53/1.75 ((~incident(a1, a2b2)) | (~incident(bc, a1c1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1580, 230, 46, 1564, 1574, 1566])).
% 1.53/1.75 tff(1582,plain,
% 1.53/1.75 (~incident(a1, a2b2)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1581, 1563])).
% 1.53/1.75 tff(1583,plain,
% 1.53/1.75 (~line_equal(oa, a2b2)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[967, 1582])).
% 1.53/1.75 tff(1584,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[975, 1583, 1536, 1495])).
% 1.53/1.75 % SZS output end Proof
% 1.53/1.75 % E exiting
%------------------------------------------------------------------------------