TSTP Solution File: GEO169+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO169+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:35:12 EDT 2022
% Result : Theorem 1.56s 1.26s
% Output : Proof 1.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO169+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.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 : Wed Aug 31 06:39:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.56/1.26 % SZS status Theorem
% 1.56/1.26 % SZS output start Proof
% 1.56/1.26 tff(line_equal_type, type, (
% 1.56/1.26 line_equal: ( $i * $i ) > $o)).
% 1.56/1.26 tff(a2c2_type, type, (
% 1.56/1.26 a2c2: $i)).
% 1.56/1.26 tff(oc_type, type, (
% 1.56/1.26 oc: $i)).
% 1.56/1.26 tff(b1c1_type, type, (
% 1.56/1.26 b1c1: $i)).
% 1.56/1.26 tff(point_equal_type, type, (
% 1.56/1.26 point_equal: ( $i * $i ) > $o)).
% 1.56/1.26 tff(bc_type, type, (
% 1.56/1.26 bc: $i)).
% 1.56/1.26 tff(c1_type, type, (
% 1.56/1.26 c1: $i)).
% 1.56/1.26 tff(incident_type, type, (
% 1.56/1.26 incident: ( $i * $i ) > $o)).
% 1.56/1.26 tff(b2c2_type, type, (
% 1.56/1.26 b2c2: $i)).
% 1.56/1.26 tff(c2_type, type, (
% 1.56/1.26 c2: $i)).
% 1.56/1.26 tff(a1b1_type, type, (
% 1.56/1.26 a1b1: $i)).
% 1.56/1.26 tff(ob_type, type, (
% 1.56/1.26 ob: $i)).
% 1.56/1.26 tff(b2_type, type, (
% 1.56/1.26 b2: $i)).
% 1.56/1.26 tff(b1_type, type, (
% 1.56/1.26 b1: $i)).
% 1.56/1.26 tff(goal_type, type, (
% 1.56/1.26 goal: $o)).
% 1.56/1.26 tff(o_type, type, (
% 1.56/1.26 o: $i)).
% 1.56/1.26 tff(oa_type, type, (
% 1.56/1.26 oa: $i)).
% 1.56/1.26 tff(a1_type, type, (
% 1.56/1.26 a1: $i)).
% 1.56/1.26 tff(ac_type, type, (
% 1.56/1.26 ac: $i)).
% 1.56/1.26 tff(ab_type, type, (
% 1.56/1.26 ab: $i)).
% 1.56/1.26 tff(a1c1_type, type, (
% 1.56/1.26 a1c1: $i)).
% 1.56/1.26 tff(a2_type, type, (
% 1.56/1.26 a2: $i)).
% 1.56/1.26 tff(a2b2_type, type, (
% 1.56/1.26 a2b2: $i)).
% 1.56/1.26 tff(1,assumption,(line_equal(b2c2, a1b1)), introduced(assumption)).
% 1.56/1.26 tff(2,assumption,(~incident(b2, a1b1)), introduced(assumption)).
% 1.56/1.26 tff(3,plain,
% 1.56/1.26 (^[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))))),
% 1.56/1.26 inference(bind,[status(th)],[])).
% 1.56/1.26 tff(4,plain,
% 1.56/1.26 (![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)))),
% 1.56/1.26 inference(quant_intro,[status(thm)],[3])).
% 1.56/1.26 tff(5,plain,
% 1.56/1.26 (^[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)))))),
% 1.56/1.26 inference(bind,[status(th)],[])).
% 1.56/1.26 tff(6,plain,
% 1.56/1.26 (![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)))),
% 1.56/1.26 inference(quant_intro,[status(thm)],[5])).
% 1.56/1.26 tff(7,plain,
% 1.56/1.26 (![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))),
% 1.56/1.26 inference(rewrite,[status(thm)],[])).
% 1.56/1.26 tff(8,plain,
% 1.56/1.26 (^[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)))),
% 1.56/1.26 inference(bind,[status(th)],[])).
% 1.56/1.26 tff(9,plain,
% 1.56/1.26 (![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))),
% 1.56/1.26 inference(quant_intro,[status(thm)],[8])).
% 1.56/1.26 tff(10,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')).
% 1.56/1.26 tff(11,plain,
% 1.56/1.26 (![A: $i, B: $i, C: $i] : ((~(incident(A, B) & line_equal(B, C))) | incident(A, C))),
% 1.56/1.26 inference(modus_ponens,[status(thm)],[10, 9])).
% 1.56/1.26 tff(12,plain,
% 1.56/1.26 (![A: $i, B: $i, C: $i] : ((~(incident(A, B) & line_equal(B, C))) | incident(A, C))),
% 1.56/1.26 inference(modus_ponens,[status(thm)],[11, 7])).
% 1.56/1.26 tff(13,plain,(
% 1.56/1.26 ![A: $i, B: $i, C: $i] : ((~(incident(A, B) & line_equal(B, C))) | incident(A, C))),
% 1.56/1.26 inference(skolemize,[status(sab)],[12])).
% 1.56/1.26 tff(14,plain,
% 1.56/1.26 (![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))),
% 1.56/1.26 inference(modus_ponens,[status(thm)],[13, 6])).
% 1.56/1.26 tff(15,plain,
% 1.56/1.26 (![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))),
% 1.56/1.26 inference(modus_ponens,[status(thm)],[14, 4])).
% 1.56/1.26 tff(16,plain,
% 1.56/1.26 (incident(b2, b2c2) <=> incident(b2, b2c2)),
% 1.56/1.26 inference(rewrite,[status(thm)],[])).
% 1.56/1.26 tff(17,axiom,(incident(b2, b2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib2c2')).
% 1.56/1.26 tff(18,plain,
% 1.56/1.26 (incident(b2, b2c2)),
% 1.56/1.26 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.56/1.26 tff(19,plain,
% 1.56/1.26 (((~![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)))),
% 1.56/1.26 inference(rewrite,[status(thm)],[])).
% 1.56/1.26 tff(20,plain,
% 1.56/1.26 ((incident(b2, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(b2, b2c2))) <=> ((~incident(b2, b2c2)) | incident(b2, a1b1) | (~line_equal(b2c2, a1b1)))),
% 1.56/1.26 inference(rewrite,[status(thm)],[])).
% 1.56/1.26 tff(21,plain,
% 1.56/1.26 (((~![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))))),
% 1.56/1.26 inference(monotonicity,[status(thm)],[20])).
% 1.56/1.26 tff(22,plain,
% 1.56/1.26 (((~![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)))),
% 1.56/1.26 inference(transitivity,[status(thm)],[21, 19])).
% 1.56/1.26 tff(23,plain,
% 1.56/1.26 ((~![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)))),
% 1.56/1.26 inference(quant_inst,[status(thm)],[])).
% 1.56/1.26 tff(24,plain,
% 1.56/1.26 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(b2, b2c2)) | incident(b2, a1b1) | (~line_equal(b2c2, a1b1))),
% 1.56/1.26 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.56/1.26 tff(25,plain,
% 1.56/1.26 ($false),
% 1.56/1.26 inference(unit_resolution,[status(thm)],[24, 18, 15, 2, 1])).
% 1.56/1.26 tff(26,plain,(incident(b2, a1b1) | (~line_equal(b2c2, a1b1))), inference(lemma,lemma(discharge,[]))).
% 1.56/1.26 tff(27,plain,
% 1.56/1.26 (incident(b2, a1b1)),
% 1.56/1.26 inference(unit_resolution,[status(thm)],[26, 1])).
% 1.56/1.26 tff(28,plain,
% 1.56/1.26 (^[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))))),
% 1.56/1.26 inference(bind,[status(th)],[])).
% 1.56/1.26 tff(29,plain,
% 1.56/1.26 (![A: $i, B: $i, 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)))),
% 1.56/1.26 inference(quant_intro,[status(thm)],[28])).
% 1.56/1.26 tff(30,plain,
% 1.56/1.26 (^[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)))))),
% 1.56/1.26 inference(bind,[status(th)],[])).
% 1.56/1.26 tff(31,plain,
% 1.56/1.26 (![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)))),
% 1.56/1.26 inference(quant_intro,[status(thm)],[30])).
% 1.56/1.26 tff(32,plain,
% 1.56/1.26 (![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))))),
% 1.56/1.26 inference(rewrite,[status(thm)],[])).
% 1.56/1.26 tff(33,plain,
% 1.56/1.26 (^[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))))))),
% 1.56/1.26 inference(bind,[status(th)],[])).
% 1.56/1.26 tff(34,plain,
% 1.56/1.26 (![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))))),
% 1.56/1.26 inference(quant_intro,[status(thm)],[33])).
% 1.56/1.26 tff(35,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')).
% 1.56/1.26 tff(36,plain,
% 1.56/1.26 (![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))))),
% 1.56/1.26 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.56/1.26 tff(37,plain,
% 1.56/1.26 (![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))))),
% 1.56/1.26 inference(modus_ponens,[status(thm)],[36, 32])).
% 1.56/1.26 tff(38,plain,(
% 1.56/1.26 ![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))))),
% 1.56/1.27 inference(skolemize,[status(sab)],[37])).
% 1.56/1.27 tff(39,plain,
% 1.56/1.27 (![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[38, 31])).
% 1.56/1.27 tff(40,plain,
% 1.56/1.27 (![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[39, 29])).
% 1.56/1.27 tff(41,plain,
% 1.56/1.27 ((~point_equal(b2, b1)) <=> (~point_equal(b2, b1))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(42,plain,
% 1.56/1.27 (($false | (~point_equal(b2, b1))) <=> (~point_equal(b2, b1))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(43,axiom,(~goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goal_to_be_proved')).
% 1.56/1.27 tff(44,plain,
% 1.56/1.27 (goal <=> $false),
% 1.56/1.27 inference(iff_false,[status(thm)],[43])).
% 1.56/1.27 tff(45,plain,
% 1.56/1.27 ((goal | (~point_equal(b2, b1))) <=> ($false | (~point_equal(b2, b1)))),
% 1.56/1.27 inference(monotonicity,[status(thm)],[44])).
% 1.56/1.27 tff(46,plain,
% 1.56/1.27 ((goal | (~point_equal(b2, b1))) <=> (~point_equal(b2, b1))),
% 1.56/1.27 inference(transitivity,[status(thm)],[45, 42])).
% 1.56/1.27 tff(47,plain,
% 1.56/1.27 ((point_equal(b2, b1) => goal) <=> (goal | (~point_equal(b2, b1)))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(48,axiom,(point_equal(b2, b1) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notbb')).
% 1.56/1.27 tff(49,plain,
% 1.56/1.27 (goal | (~point_equal(b2, b1))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.56/1.27 tff(50,plain,
% 1.56/1.27 (~point_equal(b2, b1)),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[49, 46])).
% 1.56/1.27 tff(51,plain,
% 1.56/1.27 (~point_equal(b2, b1)),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[50, 41])).
% 1.56/1.27 tff(52,plain,
% 1.56/1.27 (incident(b2, ob) <=> incident(b2, ob)),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(53,axiom,(incident(b2, ob)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib2ob')).
% 1.56/1.27 tff(54,plain,
% 1.56/1.27 (incident(b2, ob)),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.56/1.27 tff(55,plain,
% 1.56/1.27 (incident(b1, ob) <=> incident(b1, ob)),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(56,axiom,(incident(b1, ob)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib1ob')).
% 1.56/1.27 tff(57,plain,
% 1.56/1.27 (incident(b1, ob)),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.56/1.27 tff(58,plain,
% 1.56/1.27 (incident(b1, a1b1) <=> incident(b1, a1b1)),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(59,axiom,(incident(b1, a1b1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib1a1')).
% 1.56/1.27 tff(60,plain,
% 1.56/1.27 (incident(b1, a1b1)),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.56/1.27 tff(61,plain,
% 1.56/1.27 (((~![A: $i, B: $i, 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))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(62,plain,
% 1.56/1.27 ((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))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(63,plain,
% 1.56/1.27 (((~![A: $i, B: $i, 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)))),
% 1.56/1.27 inference(monotonicity,[status(thm)],[62])).
% 1.56/1.27 tff(64,plain,
% 1.56/1.27 (((~![A: $i, B: $i, 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))),
% 1.56/1.27 inference(transitivity,[status(thm)],[63, 61])).
% 1.56/1.27 tff(65,plain,
% 1.56/1.27 ((~![A: $i, B: $i, 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)))),
% 1.56/1.27 inference(quant_inst,[status(thm)],[])).
% 1.56/1.27 tff(66,plain,
% 1.56/1.27 ((~![A: $i, B: $i, 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)),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.56/1.27 tff(67,plain,
% 1.56/1.27 ((~incident(b2, a1b1)) | line_equal(a1b1, ob)),
% 1.56/1.27 inference(unit_resolution,[status(thm)],[66, 60, 57, 54, 51, 40])).
% 1.56/1.27 tff(68,plain,
% 1.56/1.27 (line_equal(a1b1, ob)),
% 1.56/1.27 inference(unit_resolution,[status(thm)],[67, 27])).
% 1.56/1.27 tff(69,plain,
% 1.56/1.27 (![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)))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(70,plain,
% 1.56/1.27 (^[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)))))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(71,plain,
% 1.56/1.27 (![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)))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[70])).
% 1.56/1.27 tff(72,plain,
% 1.56/1.27 (![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))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(73,plain,
% 1.56/1.27 (^[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)))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(74,plain,
% 1.56/1.27 (![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))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[73])).
% 1.56/1.27 tff(75,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')).
% 1.56/1.27 tff(76,plain,
% 1.56/1.27 (![A: $i, B: $i, C: $i] : ((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.56/1.27 tff(77,plain,
% 1.56/1.27 (![A: $i, B: $i, C: $i] : ((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[76, 72])).
% 1.56/1.27 tff(78,plain,(
% 1.56/1.27 ![A: $i, B: $i, C: $i] : ((~(line_equal(A, B) & line_equal(B, C))) | line_equal(A, C))),
% 1.56/1.27 inference(skolemize,[status(sab)],[77])).
% 1.56/1.27 tff(79,plain,
% 1.56/1.27 (![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[78, 71])).
% 1.56/1.27 tff(80,plain,
% 1.56/1.27 (![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[79, 69])).
% 1.56/1.27 tff(81,plain,
% 1.56/1.27 (((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(b2c2, ob) | (~line_equal(b2c2, a1b1)) | (~line_equal(a1b1, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | line_equal(b2c2, ob) | (~line_equal(b2c2, a1b1)) | (~line_equal(a1b1, ob)))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(82,plain,
% 1.56/1.27 ((line_equal(b2c2, ob) | (~line_equal(a1b1, ob)) | (~line_equal(b2c2, a1b1))) <=> (line_equal(b2c2, ob) | (~line_equal(b2c2, a1b1)) | (~line_equal(a1b1, ob)))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(83,plain,
% 1.56/1.27 (((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(b2c2, ob) | (~line_equal(a1b1, ob)) | (~line_equal(b2c2, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(b2c2, ob) | (~line_equal(b2c2, a1b1)) | (~line_equal(a1b1, ob))))),
% 1.56/1.27 inference(monotonicity,[status(thm)],[82])).
% 1.56/1.27 tff(84,plain,
% 1.56/1.27 (((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(b2c2, ob) | (~line_equal(a1b1, ob)) | (~line_equal(b2c2, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | line_equal(b2c2, ob) | (~line_equal(b2c2, a1b1)) | (~line_equal(a1b1, ob)))),
% 1.56/1.27 inference(transitivity,[status(thm)],[83, 81])).
% 1.56/1.27 tff(85,plain,
% 1.56/1.27 ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(b2c2, ob) | (~line_equal(a1b1, ob)) | (~line_equal(b2c2, a1b1)))),
% 1.56/1.27 inference(quant_inst,[status(thm)],[])).
% 1.56/1.27 tff(86,plain,
% 1.56/1.27 ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | line_equal(b2c2, ob) | (~line_equal(b2c2, a1b1)) | (~line_equal(a1b1, ob))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.56/1.27 tff(87,plain,
% 1.56/1.27 (line_equal(b2c2, ob)),
% 1.56/1.27 inference(unit_resolution,[status(thm)],[86, 80, 1, 68])).
% 1.56/1.27 tff(88,plain,
% 1.56/1.27 (^[A: $i, B: $i] : refl(((~line_equal(A, B)) | line_equal(B, A)) <=> ((~line_equal(A, B)) | line_equal(B, A)))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(89,plain,
% 1.56/1.27 (![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A)) <=> ![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[88])).
% 1.56/1.27 tff(90,plain,
% 1.56/1.27 (![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A)) <=> ![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(91,plain,
% 1.56/1.27 (^[A: $i, B: $i] : rewrite((line_equal(A, B) => line_equal(B, A)) <=> ((~line_equal(A, B)) | line_equal(B, A)))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(92,plain,
% 1.56/1.27 (![A: $i, B: $i] : (line_equal(A, B) => line_equal(B, A)) <=> ![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[91])).
% 1.56/1.27 tff(93,axiom,(![A: $i, B: $i] : (line_equal(A, B) => line_equal(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_of_line_equal')).
% 1.56/1.27 tff(94,plain,
% 1.56/1.27 (![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.56/1.27 tff(95,plain,
% 1.56/1.27 (![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[94, 90])).
% 1.56/1.27 tff(96,plain,(
% 1.56/1.27 ![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.56/1.27 inference(skolemize,[status(sab)],[95])).
% 1.56/1.27 tff(97,plain,
% 1.56/1.27 (![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[96, 89])).
% 1.56/1.27 tff(98,plain,
% 1.56/1.27 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(b2c2, ob)) | line_equal(ob, b2c2))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(b2c2, ob)) | line_equal(ob, b2c2))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(99,plain,
% 1.56/1.27 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(b2c2, ob)) | line_equal(ob, b2c2))),
% 1.56/1.27 inference(quant_inst,[status(thm)],[])).
% 1.56/1.27 tff(100,plain,
% 1.56/1.27 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(b2c2, ob)) | line_equal(ob, b2c2)),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.56/1.27 tff(101,plain,
% 1.56/1.27 (line_equal(ob, b2c2)),
% 1.56/1.27 inference(unit_resolution,[status(thm)],[100, 97, 87])).
% 1.56/1.27 tff(102,assumption,(~incident(bc, a1b1)), introduced(assumption)).
% 1.56/1.27 tff(103,plain,
% 1.56/1.27 (incident(bc, b2c2) <=> incident(bc, b2c2)),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(104,axiom,(incident(bc, b2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ibc2')).
% 1.56/1.27 tff(105,plain,
% 1.56/1.27 (incident(bc, b2c2)),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.56/1.27 tff(106,plain,
% 1.56/1.27 (((~![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)))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(107,plain,
% 1.56/1.27 ((incident(bc, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(bc, b2c2))) <=> ((~incident(bc, b2c2)) | incident(bc, a1b1) | (~line_equal(b2c2, a1b1)))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(108,plain,
% 1.56/1.27 (((~![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))))),
% 1.56/1.27 inference(monotonicity,[status(thm)],[107])).
% 1.56/1.27 tff(109,plain,
% 1.56/1.27 (((~![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)))),
% 1.56/1.27 inference(transitivity,[status(thm)],[108, 106])).
% 1.56/1.27 tff(110,plain,
% 1.56/1.27 ((~![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)))),
% 1.56/1.27 inference(quant_inst,[status(thm)],[])).
% 1.56/1.27 tff(111,plain,
% 1.56/1.27 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(bc, b2c2)) | incident(bc, a1b1) | (~line_equal(b2c2, a1b1))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.56/1.27 tff(112,plain,
% 1.56/1.27 ($false),
% 1.56/1.27 inference(unit_resolution,[status(thm)],[111, 105, 15, 102, 1])).
% 1.56/1.27 tff(113,plain,(incident(bc, a1b1) | (~line_equal(b2c2, a1b1))), inference(lemma,lemma(discharge,[]))).
% 1.56/1.27 tff(114,plain,
% 1.56/1.27 (incident(bc, a1b1)),
% 1.56/1.27 inference(unit_resolution,[status(thm)],[113, 1])).
% 1.56/1.27 tff(115,plain,
% 1.56/1.27 (^[A: $i, B: $i] : refl(((~incident(A, B)) | line_equal(B, B)) <=> ((~incident(A, B)) | line_equal(B, B)))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(116,plain,
% 1.56/1.27 (![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B)) <=> ![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[115])).
% 1.56/1.27 tff(117,plain,
% 1.56/1.27 (![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B)) <=> ![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(118,plain,
% 1.56/1.27 (^[A: $i, B: $i] : rewrite((incident(A, B) => line_equal(B, B)) <=> ((~incident(A, B)) | line_equal(B, B)))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(119,plain,
% 1.56/1.27 (![A: $i, B: $i] : (incident(A, B) => line_equal(B, B)) <=> ![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[118])).
% 1.56/1.27 tff(120,axiom,(![A: $i, B: $i] : (incident(A, B) => line_equal(B, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_of_line_equal')).
% 1.56/1.27 tff(121,plain,
% 1.56/1.27 (![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.56/1.27 tff(122,plain,
% 1.56/1.27 (![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[121, 117])).
% 1.56/1.27 tff(123,plain,(
% 1.56/1.27 ![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.56/1.27 inference(skolemize,[status(sab)],[122])).
% 1.56/1.27 tff(124,plain,
% 1.56/1.27 (![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[123, 116])).
% 1.56/1.27 tff(125,plain,
% 1.56/1.27 (incident(a1, a1b1) <=> incident(a1, a1b1)),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(126,axiom,(incident(a1, a1b1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia1b1')).
% 1.56/1.27 tff(127,plain,
% 1.56/1.27 (incident(a1, a1b1)),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.56/1.27 tff(128,plain,
% 1.56/1.27 (((~![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))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(129,plain,
% 1.56/1.27 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(a1, a1b1)) | line_equal(a1b1, a1b1))),
% 1.56/1.27 inference(quant_inst,[status(thm)],[])).
% 1.56/1.27 tff(130,plain,
% 1.56/1.27 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(a1, a1b1)) | line_equal(a1b1, a1b1)),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.56/1.27 tff(131,plain,
% 1.56/1.27 (line_equal(a1b1, a1b1)),
% 1.56/1.27 inference(unit_resolution,[status(thm)],[130, 127, 124])).
% 1.56/1.27 tff(132,plain,
% 1.56/1.27 (incident(ab, a1b1) <=> incident(ab, a1b1)),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(133,axiom,(incident(ab, a1b1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iab1')).
% 1.56/1.27 tff(134,plain,
% 1.56/1.27 (incident(ab, a1b1)),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.56/1.27 tff(135,plain,
% 1.56/1.27 (^[A: $i] : refl(((~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))))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(136,plain,
% 1.56/1.27 (![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A))) <=> ![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[135])).
% 1.56/1.27 tff(137,plain,
% 1.56/1.27 (^[A: $i] : trans(monotonicity(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))))))), 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)))))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(138,plain,
% 1.56/1.27 (![A: $i] : (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))) <=> ![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[137])).
% 1.56/1.27 tff(139,plain,
% 1.56/1.27 (![A: $i] : (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))) <=> ![A: $i] : (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(140,plain,
% 1.56/1.27 (^[A: $i] : trans(monotonicity(iff_false(asserted(~goal), (goal <=> $false)), ((goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))) <=> ($false | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))))), rewrite(($false | (~(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)))) <=> (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(141,plain,
% 1.56/1.27 (![A: $i] : (goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))) <=> ![A: $i] : (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[140])).
% 1.56/1.27 tff(142,plain,
% 1.56/1.27 (^[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))))))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(143,plain,
% 1.56/1.27 (![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))))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[142])).
% 1.56/1.27 tff(144,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')).
% 1.56/1.27 tff(145,plain,
% 1.56/1.27 (![A: $i] : (goal | (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A))))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.56/1.27 tff(146,plain,
% 1.56/1.27 (![A: $i] : (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[145, 141])).
% 1.56/1.27 tff(147,plain,
% 1.56/1.27 (![A: $i] : (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[146, 139])).
% 1.56/1.27 tff(148,plain,(
% 1.56/1.27 ![A: $i] : (~(line_equal(A, A) & incident(bc, A) & incident(ac, A) & incident(ab, A)))),
% 1.56/1.27 inference(skolemize,[status(sab)],[147])).
% 1.56/1.27 tff(149,plain,
% 1.56/1.27 (![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[148, 138])).
% 1.56/1.27 tff(150,plain,
% 1.56/1.27 (![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[149, 136])).
% 1.56/1.27 tff(151,plain,
% 1.56/1.27 (((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)))) <=> ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(152,plain,
% 1.56/1.27 (((~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)) | (~incident(ab, a1b1))) <=> ((~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)))),
% 1.56/1.27 inference(rewrite,[status(thm)],[])).
% 1.56/1.27 tff(153,plain,
% 1.56/1.27 (((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)) | (~incident(ab, a1b1)))) <=> ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1))))),
% 1.56/1.27 inference(monotonicity,[status(thm)],[152])).
% 1.56/1.27 tff(154,plain,
% 1.56/1.27 (((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)) | (~incident(ab, a1b1)))) <=> ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)))),
% 1.56/1.27 inference(transitivity,[status(thm)],[153, 151])).
% 1.56/1.27 tff(155,plain,
% 1.56/1.27 ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1)) | (~incident(ab, a1b1)))),
% 1.56/1.27 inference(quant_inst,[status(thm)],[])).
% 1.56/1.27 tff(156,plain,
% 1.56/1.27 ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~incident(ab, a1b1)) | (~line_equal(a1b1, a1b1)) | (~incident(bc, a1b1)) | (~incident(ac, a1b1))),
% 1.56/1.27 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.56/1.27 tff(157,plain,
% 1.56/1.27 ((~incident(bc, a1b1)) | (~incident(ac, a1b1))),
% 1.56/1.27 inference(unit_resolution,[status(thm)],[156, 150, 134, 131])).
% 1.56/1.27 tff(158,plain,
% 1.56/1.27 (~incident(ac, a1b1)),
% 1.56/1.27 inference(unit_resolution,[status(thm)],[157, 114])).
% 1.56/1.27 tff(159,plain,
% 1.56/1.27 (^[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))))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(160,plain,
% 1.56/1.27 (![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)))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[159])).
% 1.56/1.27 tff(161,plain,
% 1.56/1.27 (^[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)))))),
% 1.56/1.27 inference(bind,[status(th)],[])).
% 1.56/1.27 tff(162,plain,
% 1.56/1.27 (![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)))),
% 1.56/1.27 inference(quant_intro,[status(thm)],[161])).
% 1.56/1.27 tff(163,plain,
% 1.56/1.27 (![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))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(164,plain,
% 1.56/1.28 (^[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)))),
% 1.56/1.28 inference(bind,[status(th)],[])).
% 1.56/1.28 tff(165,plain,
% 1.56/1.28 (![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))),
% 1.56/1.28 inference(quant_intro,[status(thm)],[164])).
% 1.56/1.28 tff(166,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')).
% 1.56/1.28 tff(167,plain,
% 1.56/1.28 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & incident(B, C))) | incident(A, C))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.56/1.28 tff(168,plain,
% 1.56/1.28 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & incident(B, C))) | incident(A, C))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[167, 163])).
% 1.56/1.28 tff(169,plain,(
% 1.56/1.28 ![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & incident(B, C))) | incident(A, C))),
% 1.56/1.28 inference(skolemize,[status(sab)],[168])).
% 1.56/1.28 tff(170,plain,
% 1.56/1.28 (![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[169, 162])).
% 1.56/1.28 tff(171,plain,
% 1.56/1.28 (![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[170, 160])).
% 1.56/1.28 tff(172,plain,
% 1.56/1.28 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, a1)))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(173,plain,
% 1.56/1.28 ((incident(ac, a1b1) | (~incident(a1, a1b1)) | (~point_equal(ac, a1))) <=> ((~incident(a1, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, a1)))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(174,plain,
% 1.56/1.28 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, a1b1) | (~incident(a1, a1b1)) | (~point_equal(ac, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a1, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, a1))))),
% 1.56/1.28 inference(monotonicity,[status(thm)],[173])).
% 1.56/1.28 tff(175,plain,
% 1.56/1.28 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, a1b1) | (~incident(a1, a1b1)) | (~point_equal(ac, a1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, a1)))),
% 1.56/1.28 inference(transitivity,[status(thm)],[174, 172])).
% 1.56/1.28 tff(176,plain,
% 1.56/1.28 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, a1b1) | (~incident(a1, a1b1)) | (~point_equal(ac, a1)))),
% 1.56/1.28 inference(quant_inst,[status(thm)],[])).
% 1.56/1.28 tff(177,plain,
% 1.56/1.28 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1b1)) | incident(ac, a1b1) | (~point_equal(ac, a1))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.56/1.28 tff(178,plain,
% 1.56/1.28 (incident(ac, a1b1) | (~point_equal(ac, a1))),
% 1.56/1.28 inference(unit_resolution,[status(thm)],[177, 127, 171])).
% 1.56/1.28 tff(179,plain,
% 1.56/1.28 (~point_equal(ac, a1)),
% 1.56/1.28 inference(unit_resolution,[status(thm)],[178, 158])).
% 1.56/1.28 tff(180,plain,
% 1.56/1.28 ((~line_equal(a1c1, a2c2)) <=> (~line_equal(a1c1, a2c2))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(181,plain,
% 1.56/1.28 (($false | (~line_equal(a1c1, a2c2))) <=> (~line_equal(a1c1, a2c2))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(182,plain,
% 1.56/1.28 ((goal | (~line_equal(a1c1, a2c2))) <=> ($false | (~line_equal(a1c1, a2c2)))),
% 1.56/1.28 inference(monotonicity,[status(thm)],[44])).
% 1.56/1.28 tff(183,plain,
% 1.56/1.28 ((goal | (~line_equal(a1c1, a2c2))) <=> (~line_equal(a1c1, a2c2))),
% 1.56/1.28 inference(transitivity,[status(thm)],[182, 181])).
% 1.56/1.28 tff(184,plain,
% 1.56/1.28 ((line_equal(a1c1, a2c2) => goal) <=> (goal | (~line_equal(a1c1, a2c2)))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(185,axiom,(line_equal(a1c1, a2c2) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notac')).
% 1.56/1.28 tff(186,plain,
% 1.56/1.28 (goal | (~line_equal(a1c1, a2c2))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.56/1.28 tff(187,plain,
% 1.56/1.28 (~line_equal(a1c1, a2c2)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[186, 183])).
% 1.56/1.28 tff(188,plain,
% 1.56/1.28 (~line_equal(a1c1, a2c2)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[187, 180])).
% 1.56/1.28 tff(189,plain,
% 1.56/1.28 (incident(ac, a2c2) <=> incident(ac, a2c2)),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(190,axiom,(incident(ac, a2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iac2')).
% 1.56/1.28 tff(191,plain,
% 1.56/1.28 (incident(ac, a2c2)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[190, 189])).
% 1.56/1.28 tff(192,plain,
% 1.56/1.28 (incident(ac, a1c1) <=> incident(ac, a1c1)),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(193,axiom,(incident(ac, a1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iac1')).
% 1.56/1.28 tff(194,plain,
% 1.56/1.28 (incident(ac, a1c1)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.56/1.28 tff(195,plain,
% 1.56/1.28 (incident(a1, a1c1) <=> incident(a1, a1c1)),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(196,axiom,(incident(a1, a1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia1c1')).
% 1.56/1.28 tff(197,plain,
% 1.56/1.28 (incident(a1, a1c1)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[196, 195])).
% 1.56/1.28 tff(198,plain,
% 1.56/1.28 (((~![A: $i, B: $i, 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(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, 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(a1c1, a2c2) | (~incident(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, a1))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(199,plain,
% 1.56/1.28 ((line_equal(a1c1, a2c2) | point_equal(ac, a1) | (~incident(a1, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | (~incident(a1, a2c2))) <=> (line_equal(a1c1, a2c2) | (~incident(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, a1))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(200,plain,
% 1.56/1.28 (((~![A: $i, B: $i, 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, a1) | (~incident(a1, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | (~incident(a1, 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(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, a1)))),
% 1.56/1.28 inference(monotonicity,[status(thm)],[199])).
% 1.56/1.28 tff(201,plain,
% 1.56/1.28 (((~![A: $i, B: $i, 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, a1) | (~incident(a1, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | (~incident(a1, 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(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, a1))),
% 1.56/1.28 inference(transitivity,[status(thm)],[200, 198])).
% 1.56/1.28 tff(202,plain,
% 1.56/1.28 ((~![A: $i, B: $i, 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, a1) | (~incident(a1, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | (~incident(a1, a2c2)))),
% 1.56/1.28 inference(quant_inst,[status(thm)],[])).
% 1.56/1.28 tff(203,plain,
% 1.56/1.28 ((~![A: $i, B: $i, 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(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, a1)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[202, 201])).
% 1.56/1.28 tff(204,plain,
% 1.56/1.28 (~incident(a1, a2c2)),
% 1.56/1.28 inference(unit_resolution,[status(thm)],[203, 197, 194, 191, 188, 40, 179])).
% 1.56/1.28 tff(205,plain,
% 1.56/1.28 (incident(a1, oa) <=> incident(a1, oa)),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(206,axiom,(incident(a1, oa)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia1oa')).
% 1.56/1.28 tff(207,plain,
% 1.56/1.28 (incident(a1, oa)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[206, 205])).
% 1.56/1.28 tff(208,plain,
% 1.56/1.28 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2c2) | (~incident(a1, oa)) | (~line_equal(oa, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a1, a2c2) | (~incident(a1, oa)) | (~line_equal(oa, a2c2)))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(209,plain,
% 1.56/1.28 ((incident(a1, a2c2) | (~line_equal(oa, a2c2)) | (~incident(a1, oa))) <=> (incident(a1, a2c2) | (~incident(a1, oa)) | (~line_equal(oa, a2c2)))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(210,plain,
% 1.56/1.28 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2c2) | (~line_equal(oa, a2c2)) | (~incident(a1, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2c2) | (~incident(a1, oa)) | (~line_equal(oa, a2c2))))),
% 1.56/1.28 inference(monotonicity,[status(thm)],[209])).
% 1.56/1.28 tff(211,plain,
% 1.56/1.28 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2c2) | (~line_equal(oa, a2c2)) | (~incident(a1, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a1, a2c2) | (~incident(a1, oa)) | (~line_equal(oa, a2c2)))),
% 1.56/1.28 inference(transitivity,[status(thm)],[210, 208])).
% 1.56/1.28 tff(212,plain,
% 1.56/1.28 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a1, a2c2) | (~line_equal(oa, a2c2)) | (~incident(a1, oa)))),
% 1.56/1.28 inference(quant_inst,[status(thm)],[])).
% 1.56/1.28 tff(213,plain,
% 1.56/1.28 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a1, a2c2) | (~incident(a1, oa)) | (~line_equal(oa, a2c2))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.56/1.28 tff(214,plain,
% 1.56/1.28 (incident(a1, a2c2) | (~line_equal(oa, a2c2))),
% 1.56/1.28 inference(unit_resolution,[status(thm)],[213, 207, 15])).
% 1.56/1.28 tff(215,plain,
% 1.56/1.28 (~line_equal(oa, a2c2)),
% 1.56/1.28 inference(unit_resolution,[status(thm)],[214, 204])).
% 1.56/1.28 tff(216,plain,
% 1.56/1.28 (^[A: $i] : refl(((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A))) <=> ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A))))),
% 1.56/1.28 inference(bind,[status(th)],[])).
% 1.56/1.28 tff(217,plain,
% 1.56/1.28 (![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A))) <=> ![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))),
% 1.56/1.28 inference(quant_intro,[status(thm)],[216])).
% 1.56/1.28 tff(218,plain,
% 1.56/1.28 (^[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))) <=> (~(~((~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)))))),
% 1.56/1.28 inference(bind,[status(th)],[])).
% 1.56/1.28 tff(219,plain,
% 1.56/1.28 (![A: $i] : (~(incident(a2, A) & incident(b2, A) & incident(c2, A))) <=> ![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))),
% 1.56/1.28 inference(quant_intro,[status(thm)],[218])).
% 1.56/1.28 tff(220,plain,
% 1.56/1.28 (![A: $i] : (~(incident(a2, A) & incident(b2, A) & incident(c2, A))) <=> ![A: $i] : (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(221,plain,
% 1.56/1.28 (^[A: $i] : trans(monotonicity(iff_false(asserted(~goal), (goal <=> $false)), ((goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))) <=> ($false | (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))))), rewrite(($false | (~(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)))) <=> (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))))),
% 1.56/1.28 inference(bind,[status(th)],[])).
% 1.56/1.28 tff(222,plain,
% 1.56/1.28 (![A: $i] : (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))) <=> ![A: $i] : (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))),
% 1.56/1.28 inference(quant_intro,[status(thm)],[221])).
% 1.56/1.28 tff(223,plain,
% 1.56/1.28 (^[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))))))),
% 1.56/1.28 inference(bind,[status(th)],[])).
% 1.56/1.28 tff(224,plain,
% 1.56/1.28 (![A: $i] : (((incident(a2, A) & incident(b2, A)) & incident(c2, A)) => goal) <=> ![A: $i] : (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A))))),
% 1.56/1.28 inference(quant_intro,[status(thm)],[223])).
% 1.56/1.28 tff(225,axiom,(![A: $i] : (((incident(a2, A) & incident(b2, A)) & incident(c2, A)) => goal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','triangle2')).
% 1.56/1.28 tff(226,plain,
% 1.56/1.28 (![A: $i] : (goal | (~(incident(a2, A) & incident(b2, A) & incident(c2, A))))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[225, 224])).
% 1.56/1.28 tff(227,plain,
% 1.56/1.28 (![A: $i] : (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[226, 222])).
% 1.56/1.28 tff(228,plain,
% 1.56/1.28 (![A: $i] : (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[227, 220])).
% 1.56/1.28 tff(229,plain,(
% 1.56/1.28 ![A: $i] : (~(incident(a2, A) & incident(b2, A) & incident(c2, A)))),
% 1.56/1.28 inference(skolemize,[status(sab)],[228])).
% 1.56/1.28 tff(230,plain,
% 1.56/1.28 (![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[229, 219])).
% 1.56/1.28 tff(231,plain,
% 1.56/1.28 (![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[230, 217])).
% 1.56/1.28 tff(232,plain,
% 1.56/1.28 (incident(b2, a2b2) <=> incident(b2, a2b2)),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(233,axiom,(incident(b2, a2b2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib2a2')).
% 1.56/1.28 tff(234,plain,
% 1.56/1.28 (incident(b2, a2b2)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.56/1.28 tff(235,plain,
% 1.56/1.28 (incident(a2, a2b2) <=> incident(a2, a2b2)),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(236,axiom,(incident(a2, a2b2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia2b2')).
% 1.56/1.28 tff(237,plain,
% 1.56/1.28 (incident(a2, a2b2)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.56/1.28 tff(238,plain,
% 1.56/1.28 (((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | ((~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(c2, a2b2)))) <=> ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(c2, a2b2)))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(239,plain,
% 1.56/1.28 ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | ((~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(c2, a2b2)))),
% 1.56/1.28 inference(quant_inst,[status(thm)],[])).
% 1.56/1.28 tff(240,plain,
% 1.56/1.28 ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(c2, a2b2))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.56/1.28 tff(241,plain,
% 1.56/1.28 (~incident(c2, a2b2)),
% 1.56/1.28 inference(unit_resolution,[status(thm)],[240, 237, 234, 231])).
% 1.56/1.28 tff(242,plain,
% 1.56/1.28 (((~![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)))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(243,plain,
% 1.56/1.28 ((incident(c2, a2b2) | (~incident(a2, a2b2)) | (~point_equal(c2, a2))) <=> ((~incident(a2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, a2)))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(244,plain,
% 1.56/1.28 (((~![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))))),
% 1.56/1.28 inference(monotonicity,[status(thm)],[243])).
% 1.56/1.28 tff(245,plain,
% 1.56/1.28 (((~![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)))),
% 1.56/1.28 inference(transitivity,[status(thm)],[244, 242])).
% 1.56/1.28 tff(246,plain,
% 1.56/1.28 ((~![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)))),
% 1.56/1.28 inference(quant_inst,[status(thm)],[])).
% 1.56/1.28 tff(247,plain,
% 1.56/1.28 ((~![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))),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[246, 245])).
% 1.56/1.28 tff(248,plain,
% 1.56/1.28 (~point_equal(c2, a2)),
% 1.56/1.28 inference(unit_resolution,[status(thm)],[247, 237, 171, 241])).
% 1.56/1.28 tff(249,plain,
% 1.56/1.28 (incident(a2, oa) <=> incident(a2, oa)),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(250,axiom,(incident(a2, oa)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia2oa')).
% 1.56/1.28 tff(251,plain,
% 1.56/1.28 (incident(a2, oa)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[250, 249])).
% 1.56/1.28 tff(252,plain,
% 1.56/1.28 (incident(c2, a2c2) <=> incident(c2, a2c2)),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(253,axiom,(incident(c2, a2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic2a2')).
% 1.56/1.28 tff(254,plain,
% 1.56/1.28 (incident(c2, a2c2)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[253, 252])).
% 1.56/1.28 tff(255,plain,
% 1.56/1.28 (incident(a2, a2c2) <=> incident(a2, a2c2)),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(256,axiom,(incident(a2, a2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ia2c2')).
% 1.56/1.28 tff(257,plain,
% 1.56/1.28 (incident(a2, a2c2)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[256, 255])).
% 1.56/1.28 tff(258,plain,
% 1.56/1.28 (((~![A: $i, B: $i, 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(c2, a2) | 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(c2, a2) | line_equal(oa, a2c2))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(259,plain,
% 1.56/1.28 ((line_equal(oa, a2c2) | point_equal(c2, a2) | (~incident(a2, oa)) | (~incident(c2, oa)) | (~incident(c2, a2c2)) | (~incident(a2, a2c2))) <=> ((~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oa)) | (~incident(c2, oa)) | point_equal(c2, a2) | line_equal(oa, a2c2))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(260,plain,
% 1.56/1.28 (((~![A: $i, B: $i, 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(c2, a2) | (~incident(a2, oa)) | (~incident(c2, oa)) | (~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)))) | ((~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oa)) | (~incident(c2, oa)) | point_equal(c2, a2) | line_equal(oa, a2c2)))),
% 1.56/1.28 inference(monotonicity,[status(thm)],[259])).
% 1.56/1.28 tff(261,plain,
% 1.56/1.28 (((~![A: $i, B: $i, 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(c2, a2) | (~incident(a2, oa)) | (~incident(c2, oa)) | (~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)))) | (~incident(a2, a2c2)) | (~incident(c2, a2c2)) | (~incident(a2, oa)) | (~incident(c2, oa)) | point_equal(c2, a2) | line_equal(oa, a2c2))),
% 1.56/1.28 inference(transitivity,[status(thm)],[260, 258])).
% 1.56/1.28 tff(262,plain,
% 1.56/1.28 ((~![A: $i, B: $i, 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(c2, a2) | (~incident(a2, oa)) | (~incident(c2, oa)) | (~incident(c2, a2c2)) | (~incident(a2, a2c2)))),
% 1.56/1.28 inference(quant_inst,[status(thm)],[])).
% 1.56/1.28 tff(263,plain,
% 1.56/1.28 ((~![A: $i, B: $i, 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(c2, a2) | line_equal(oa, a2c2)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.56/1.28 tff(264,plain,
% 1.56/1.28 ((~incident(c2, oa)) | line_equal(oa, a2c2)),
% 1.56/1.28 inference(unit_resolution,[status(thm)],[263, 257, 254, 251, 40, 248])).
% 1.56/1.28 tff(265,plain,
% 1.56/1.28 (~incident(c2, oa)),
% 1.56/1.28 inference(unit_resolution,[status(thm)],[264, 215])).
% 1.56/1.28 tff(266,plain,
% 1.56/1.28 (incident(o, oa) <=> incident(o, oa)),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(267,axiom,(incident(o, oa)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iooa')).
% 1.56/1.28 tff(268,plain,
% 1.56/1.28 (incident(o, oa)),
% 1.56/1.28 inference(modus_ponens,[status(thm)],[267, 266])).
% 1.56/1.28 tff(269,plain,
% 1.56/1.28 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, oa)) | incident(c2, oa) | (~point_equal(c2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oa)) | incident(c2, oa) | (~point_equal(c2, o)))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(270,plain,
% 1.56/1.28 ((incident(c2, oa) | (~incident(o, oa)) | (~point_equal(c2, o))) <=> ((~incident(o, oa)) | incident(c2, oa) | (~point_equal(c2, o)))),
% 1.56/1.28 inference(rewrite,[status(thm)],[])).
% 1.56/1.28 tff(271,plain,
% 1.56/1.28 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, oa) | (~incident(o, oa)) | (~point_equal(c2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, oa)) | incident(c2, oa) | (~point_equal(c2, o))))),
% 1.56/1.28 inference(monotonicity,[status(thm)],[270])).
% 1.56/1.28 tff(272,plain,
% 1.56/1.28 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, oa) | (~incident(o, oa)) | (~point_equal(c2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oa)) | incident(c2, oa) | (~point_equal(c2, o)))),
% 1.56/1.29 inference(transitivity,[status(thm)],[271, 269])).
% 1.56/1.29 tff(273,plain,
% 1.56/1.29 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c2, oa) | (~incident(o, oa)) | (~point_equal(c2, o)))),
% 1.56/1.29 inference(quant_inst,[status(thm)],[])).
% 1.56/1.29 tff(274,plain,
% 1.56/1.29 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oa)) | incident(c2, oa) | (~point_equal(c2, o))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[273, 272])).
% 1.56/1.29 tff(275,plain,
% 1.56/1.29 (incident(c2, oa) | (~point_equal(c2, o))),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[274, 268, 171])).
% 1.56/1.29 tff(276,plain,
% 1.56/1.29 (~point_equal(c2, o)),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[275, 265])).
% 1.56/1.29 tff(277,plain,
% 1.56/1.29 (^[A: $i] : refl(((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A))) <=> ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A))))),
% 1.56/1.29 inference(bind,[status(th)],[])).
% 1.56/1.29 tff(278,plain,
% 1.56/1.29 (![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A))) <=> ![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))),
% 1.56/1.29 inference(quant_intro,[status(thm)],[277])).
% 1.56/1.29 tff(279,plain,
% 1.56/1.29 (^[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))) <=> (~(~((~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)))))),
% 1.56/1.29 inference(bind,[status(th)],[])).
% 1.56/1.29 tff(280,plain,
% 1.56/1.29 (![A: $i] : (~(incident(a1, A) & incident(b1, A) & incident(c1, A))) <=> ![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))),
% 1.56/1.29 inference(quant_intro,[status(thm)],[279])).
% 1.56/1.29 tff(281,plain,
% 1.56/1.29 (![A: $i] : (~(incident(a1, A) & incident(b1, A) & incident(c1, A))) <=> ![A: $i] : (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(282,plain,
% 1.56/1.29 (^[A: $i] : trans(monotonicity(iff_false(asserted(~goal), (goal <=> $false)), ((goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))) <=> ($false | (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))))), rewrite(($false | (~(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)))) <=> (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))))),
% 1.56/1.29 inference(bind,[status(th)],[])).
% 1.56/1.29 tff(283,plain,
% 1.56/1.29 (![A: $i] : (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))) <=> ![A: $i] : (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))),
% 1.56/1.29 inference(quant_intro,[status(thm)],[282])).
% 1.56/1.29 tff(284,plain,
% 1.56/1.29 (^[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))))))),
% 1.56/1.29 inference(bind,[status(th)],[])).
% 1.56/1.29 tff(285,plain,
% 1.56/1.29 (![A: $i] : (((incident(a1, A) & incident(b1, A)) & incident(c1, A)) => goal) <=> ![A: $i] : (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A))))),
% 1.56/1.29 inference(quant_intro,[status(thm)],[284])).
% 1.56/1.29 tff(286,axiom,(![A: $i] : (((incident(a1, A) & incident(b1, A)) & incident(c1, A)) => goal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','triangle1')).
% 1.56/1.29 tff(287,plain,
% 1.56/1.29 (![A: $i] : (goal | (~(incident(a1, A) & incident(b1, A) & incident(c1, A))))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[286, 285])).
% 1.56/1.29 tff(288,plain,
% 1.56/1.29 (![A: $i] : (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[287, 283])).
% 1.56/1.29 tff(289,plain,
% 1.56/1.29 (![A: $i] : (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[288, 281])).
% 1.56/1.29 tff(290,plain,(
% 1.56/1.29 ![A: $i] : (~(incident(a1, A) & incident(b1, A) & incident(c1, A)))),
% 1.56/1.29 inference(skolemize,[status(sab)],[289])).
% 1.56/1.29 tff(291,plain,
% 1.56/1.29 (![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[290, 280])).
% 1.56/1.29 tff(292,plain,
% 1.56/1.29 (![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[291, 278])).
% 1.56/1.29 tff(293,plain,
% 1.56/1.29 (((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | ((~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(c1, a1b1)))) <=> ((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(c1, a1b1)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(294,plain,
% 1.56/1.29 ((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | ((~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(c1, a1b1)))),
% 1.56/1.29 inference(quant_inst,[status(thm)],[])).
% 1.56/1.29 tff(295,plain,
% 1.56/1.29 ((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (~incident(a1, a1b1)) | (~incident(b1, a1b1)) | (~incident(c1, a1b1))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.56/1.29 tff(296,plain,
% 1.56/1.29 (~incident(c1, a1b1)),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[295, 127, 60, 292])).
% 1.56/1.29 tff(297,plain,
% 1.56/1.29 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(c1, b2c2)) | incident(c1, a1b1) | (~line_equal(b2c2, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c1, b2c2)) | incident(c1, a1b1) | (~line_equal(b2c2, a1b1)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(298,plain,
% 1.56/1.29 ((incident(c1, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(c1, b2c2))) <=> ((~incident(c1, b2c2)) | incident(c1, a1b1) | (~line_equal(b2c2, a1b1)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(299,plain,
% 1.56/1.29 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(c1, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(c1, b2c2)) | incident(c1, a1b1) | (~line_equal(b2c2, a1b1))))),
% 1.56/1.29 inference(monotonicity,[status(thm)],[298])).
% 1.56/1.29 tff(300,plain,
% 1.56/1.29 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(c1, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c1, b2c2)) | incident(c1, a1b1) | (~line_equal(b2c2, a1b1)))),
% 1.56/1.29 inference(transitivity,[status(thm)],[299, 297])).
% 1.56/1.29 tff(301,plain,
% 1.56/1.29 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, a1b1) | (~line_equal(b2c2, a1b1)) | (~incident(c1, b2c2)))),
% 1.56/1.29 inference(quant_inst,[status(thm)],[])).
% 1.56/1.29 tff(302,plain,
% 1.56/1.29 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c1, b2c2)) | incident(c1, a1b1) | (~line_equal(b2c2, a1b1))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[301, 300])).
% 1.56/1.29 tff(303,plain,
% 1.56/1.29 (~incident(c1, b2c2)),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[302, 15, 296, 1])).
% 1.56/1.29 tff(304,plain,
% 1.56/1.29 (incident(c1, oc) <=> incident(c1, oc)),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(305,axiom,(incident(c1, oc)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic1oc')).
% 1.56/1.29 tff(306,plain,
% 1.56/1.29 (incident(c1, oc)),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.56/1.29 tff(307,plain,
% 1.56/1.29 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, b2c2) | (~incident(c1, oc)) | (~line_equal(oc, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c1, b2c2) | (~incident(c1, oc)) | (~line_equal(oc, b2c2)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(308,plain,
% 1.56/1.29 ((incident(c1, b2c2) | (~line_equal(oc, b2c2)) | (~incident(c1, oc))) <=> (incident(c1, b2c2) | (~incident(c1, oc)) | (~line_equal(oc, b2c2)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(309,plain,
% 1.56/1.29 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, b2c2) | (~line_equal(oc, b2c2)) | (~incident(c1, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, b2c2) | (~incident(c1, oc)) | (~line_equal(oc, b2c2))))),
% 1.56/1.29 inference(monotonicity,[status(thm)],[308])).
% 1.56/1.29 tff(310,plain,
% 1.56/1.29 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, b2c2) | (~line_equal(oc, b2c2)) | (~incident(c1, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c1, b2c2) | (~incident(c1, oc)) | (~line_equal(oc, b2c2)))),
% 1.56/1.29 inference(transitivity,[status(thm)],[309, 307])).
% 1.56/1.29 tff(311,plain,
% 1.56/1.29 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c1, b2c2) | (~line_equal(oc, b2c2)) | (~incident(c1, oc)))),
% 1.56/1.29 inference(quant_inst,[status(thm)],[])).
% 1.56/1.29 tff(312,plain,
% 1.56/1.29 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c1, b2c2) | (~incident(c1, oc)) | (~line_equal(oc, b2c2))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[311, 310])).
% 1.56/1.29 tff(313,plain,
% 1.56/1.29 (incident(c1, b2c2) | (~line_equal(oc, b2c2))),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[312, 306, 15])).
% 1.56/1.29 tff(314,plain,
% 1.56/1.29 (~line_equal(oc, b2c2)),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[313, 303])).
% 1.56/1.29 tff(315,plain,
% 1.56/1.29 (incident(c2, oc) <=> incident(c2, oc)),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(316,axiom,(incident(c2, oc)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic2oc')).
% 1.56/1.29 tff(317,plain,
% 1.56/1.29 (incident(c2, oc)),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[316, 315])).
% 1.56/1.29 tff(318,plain,
% 1.56/1.29 (incident(o, oc) <=> incident(o, oc)),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(319,axiom,(incident(o, oc)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iooc')).
% 1.56/1.29 tff(320,plain,
% 1.56/1.29 (incident(o, oc)),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[319, 318])).
% 1.56/1.29 tff(321,plain,
% 1.56/1.29 (incident(c2, b2c2) <=> incident(c2, b2c2)),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(322,axiom,(incident(c2, b2c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic2b2')).
% 1.56/1.29 tff(323,plain,
% 1.56/1.29 (incident(c2, b2c2)),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[322, 321])).
% 1.56/1.29 tff(324,plain,
% 1.56/1.29 (((~![A: $i, B: $i, 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, b2c2)) | (~incident(o, oc)) | (~incident(c2, oc)) | (~incident(o, b2c2)) | line_equal(oc, b2c2) | 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)))) | (~incident(c2, b2c2)) | (~incident(o, oc)) | (~incident(c2, oc)) | (~incident(o, b2c2)) | line_equal(oc, b2c2) | point_equal(c2, o))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(325,plain,
% 1.56/1.29 ((line_equal(oc, b2c2) | point_equal(c2, o) | (~incident(o, oc)) | (~incident(c2, oc)) | (~incident(c2, b2c2)) | (~incident(o, b2c2))) <=> ((~incident(c2, b2c2)) | (~incident(o, oc)) | (~incident(c2, oc)) | (~incident(o, b2c2)) | line_equal(oc, b2c2) | point_equal(c2, o))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(326,plain,
% 1.56/1.29 (((~![A: $i, B: $i, 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, o) | (~incident(o, oc)) | (~incident(c2, oc)) | (~incident(c2, b2c2)) | (~incident(o, 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(c2, b2c2)) | (~incident(o, oc)) | (~incident(c2, oc)) | (~incident(o, b2c2)) | line_equal(oc, b2c2) | point_equal(c2, o)))),
% 1.56/1.29 inference(monotonicity,[status(thm)],[325])).
% 1.56/1.29 tff(327,plain,
% 1.56/1.29 (((~![A: $i, B: $i, 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, o) | (~incident(o, oc)) | (~incident(c2, oc)) | (~incident(c2, b2c2)) | (~incident(o, 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(c2, b2c2)) | (~incident(o, oc)) | (~incident(c2, oc)) | (~incident(o, b2c2)) | line_equal(oc, b2c2) | point_equal(c2, o))),
% 1.56/1.29 inference(transitivity,[status(thm)],[326, 324])).
% 1.56/1.29 tff(328,plain,
% 1.56/1.29 ((~![A: $i, B: $i, 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, o) | (~incident(o, oc)) | (~incident(c2, oc)) | (~incident(c2, b2c2)) | (~incident(o, b2c2)))),
% 1.56/1.29 inference(quant_inst,[status(thm)],[])).
% 1.56/1.29 tff(329,plain,
% 1.56/1.29 ((~![A: $i, B: $i, 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, b2c2)) | (~incident(o, oc)) | (~incident(c2, oc)) | (~incident(o, b2c2)) | line_equal(oc, b2c2) | point_equal(c2, o)),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[328, 327])).
% 1.56/1.29 tff(330,plain,
% 1.56/1.29 (~incident(o, b2c2)),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[329, 323, 320, 317, 40, 314, 276])).
% 1.56/1.29 tff(331,plain,
% 1.56/1.29 (incident(o, ob) <=> incident(o, ob)),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(332,axiom,(incident(o, ob)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ioob')).
% 1.56/1.29 tff(333,plain,
% 1.56/1.29 (incident(o, ob)),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[332, 331])).
% 1.56/1.29 tff(334,plain,
% 1.56/1.29 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, ob)) | incident(o, b2c2) | (~line_equal(ob, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | incident(o, b2c2) | (~line_equal(ob, b2c2)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(335,plain,
% 1.56/1.29 ((incident(o, b2c2) | (~line_equal(ob, b2c2)) | (~incident(o, ob))) <=> ((~incident(o, ob)) | incident(o, b2c2) | (~line_equal(ob, b2c2)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(336,plain,
% 1.56/1.29 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, b2c2) | (~line_equal(ob, b2c2)) | (~incident(o, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, ob)) | incident(o, b2c2) | (~line_equal(ob, b2c2))))),
% 1.56/1.29 inference(monotonicity,[status(thm)],[335])).
% 1.56/1.29 tff(337,plain,
% 1.56/1.29 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, b2c2) | (~line_equal(ob, b2c2)) | (~incident(o, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | incident(o, b2c2) | (~line_equal(ob, b2c2)))),
% 1.56/1.29 inference(transitivity,[status(thm)],[336, 334])).
% 1.56/1.29 tff(338,plain,
% 1.56/1.29 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, b2c2) | (~line_equal(ob, b2c2)) | (~incident(o, ob)))),
% 1.56/1.29 inference(quant_inst,[status(thm)],[])).
% 1.56/1.29 tff(339,plain,
% 1.56/1.29 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | incident(o, b2c2) | (~line_equal(ob, b2c2))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[338, 337])).
% 1.56/1.29 tff(340,plain,
% 1.56/1.29 ($false),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[339, 333, 15, 330, 101])).
% 1.56/1.29 tff(341,plain,(~line_equal(b2c2, a1b1)), inference(lemma,lemma(discharge,[]))).
% 1.56/1.29 tff(342,assumption,(~line_equal(b2c2, a1b1)), introduced(assumption)).
% 1.56/1.29 tff(343,assumption,(~line_equal(a2c2, b1c1)), introduced(assumption)).
% 1.56/1.29 tff(344,assumption,(point_equal(c2, a1)), introduced(assumption)).
% 1.56/1.29 tff(345,assumption,(~incident(c2, a1c1)), introduced(assumption)).
% 1.56/1.29 tff(346,plain,
% 1.56/1.29 (((~![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)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(347,plain,
% 1.56/1.29 ((incident(c2, a1c1) | (~incident(a1, a1c1)) | (~point_equal(c2, a1))) <=> ((~incident(a1, a1c1)) | incident(c2, a1c1) | (~point_equal(c2, a1)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(348,plain,
% 1.56/1.29 (((~![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))))),
% 1.56/1.29 inference(monotonicity,[status(thm)],[347])).
% 1.56/1.29 tff(349,plain,
% 1.56/1.29 (((~![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)))),
% 1.56/1.29 inference(transitivity,[status(thm)],[348, 346])).
% 1.56/1.29 tff(350,plain,
% 1.56/1.29 ((~![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)))),
% 1.56/1.29 inference(quant_inst,[status(thm)],[])).
% 1.56/1.29 tff(351,plain,
% 1.56/1.29 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1c1)) | incident(c2, a1c1) | (~point_equal(c2, a1))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[350, 349])).
% 1.56/1.29 tff(352,plain,
% 1.56/1.29 ($false),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[351, 197, 171, 345, 344])).
% 1.56/1.29 tff(353,plain,(incident(c2, a1c1) | (~point_equal(c2, a1))), inference(lemma,lemma(discharge,[]))).
% 1.56/1.29 tff(354,plain,
% 1.56/1.29 (incident(c2, a1c1)),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[353, 344])).
% 1.56/1.29 tff(355,assumption,(~incident(c2, oa)), introduced(assumption)).
% 1.56/1.29 tff(356,plain,
% 1.56/1.29 (((~![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)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(357,plain,
% 1.56/1.29 ((incident(c2, oa) | (~incident(a1, oa)) | (~point_equal(c2, a1))) <=> ((~incident(a1, oa)) | incident(c2, oa) | (~point_equal(c2, a1)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(358,plain,
% 1.56/1.29 (((~![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))))),
% 1.56/1.29 inference(monotonicity,[status(thm)],[357])).
% 1.56/1.29 tff(359,plain,
% 1.56/1.29 (((~![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)))),
% 1.56/1.29 inference(transitivity,[status(thm)],[358, 356])).
% 1.56/1.29 tff(360,plain,
% 1.56/1.29 ((~![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)))),
% 1.56/1.29 inference(quant_inst,[status(thm)],[])).
% 1.56/1.29 tff(361,plain,
% 1.56/1.29 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, oa)) | incident(c2, oa) | (~point_equal(c2, a1))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[360, 359])).
% 1.56/1.29 tff(362,plain,
% 1.56/1.29 ($false),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[361, 207, 171, 355, 344])).
% 1.56/1.29 tff(363,plain,(incident(c2, oa) | (~point_equal(c2, a1))), inference(lemma,lemma(discharge,[]))).
% 1.56/1.29 tff(364,plain,
% 1.56/1.29 (incident(c2, oa)),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[363, 344])).
% 1.56/1.29 tff(365,plain,
% 1.56/1.29 (line_equal(oa, a2c2)),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[264, 364])).
% 1.56/1.29 tff(366,plain,
% 1.56/1.29 (((~![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)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(367,plain,
% 1.56/1.29 ((incident(o, a2c2) | (~line_equal(oa, a2c2)) | (~incident(o, oa))) <=> ((~incident(o, oa)) | incident(o, a2c2) | (~line_equal(oa, a2c2)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(368,plain,
% 1.56/1.29 (((~![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))))),
% 1.56/1.29 inference(monotonicity,[status(thm)],[367])).
% 1.56/1.29 tff(369,plain,
% 1.56/1.29 (((~![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)))),
% 1.56/1.29 inference(transitivity,[status(thm)],[368, 366])).
% 1.56/1.29 tff(370,plain,
% 1.56/1.29 ((~![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)))),
% 1.56/1.29 inference(quant_inst,[status(thm)],[])).
% 1.56/1.29 tff(371,plain,
% 1.56/1.29 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a2c2) | (~line_equal(oa, a2c2))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[370, 369])).
% 1.56/1.29 tff(372,plain,
% 1.56/1.29 (incident(o, a2c2) | (~line_equal(oa, a2c2))),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[371, 268, 15])).
% 1.56/1.29 tff(373,plain,
% 1.56/1.29 (incident(o, a2c2)),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[372, 365])).
% 1.56/1.29 tff(374,assumption,(incident(c2, a1c1)), introduced(assumption)).
% 1.56/1.29 tff(375,plain,
% 1.56/1.29 ((~point_equal(c2, c1)) <=> (~point_equal(c2, c1))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(376,plain,
% 1.56/1.29 (($false | (~point_equal(c2, c1))) <=> (~point_equal(c2, c1))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(377,plain,
% 1.56/1.29 ((goal | (~point_equal(c2, c1))) <=> ($false | (~point_equal(c2, c1)))),
% 1.56/1.29 inference(monotonicity,[status(thm)],[44])).
% 1.56/1.29 tff(378,plain,
% 1.56/1.29 ((goal | (~point_equal(c2, c1))) <=> (~point_equal(c2, c1))),
% 1.56/1.29 inference(transitivity,[status(thm)],[377, 376])).
% 1.56/1.29 tff(379,plain,
% 1.56/1.29 ((point_equal(c2, c1) => goal) <=> (goal | (~point_equal(c2, c1)))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(380,axiom,(point_equal(c2, c1) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notcc')).
% 1.56/1.29 tff(381,plain,
% 1.56/1.29 (goal | (~point_equal(c2, c1))),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[380, 379])).
% 1.56/1.29 tff(382,plain,
% 1.56/1.29 (~point_equal(c2, c1)),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[381, 378])).
% 1.56/1.29 tff(383,plain,
% 1.56/1.29 (~point_equal(c2, c1)),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[382, 375])).
% 1.56/1.29 tff(384,plain,
% 1.56/1.29 (incident(c1, a1c1) <=> incident(c1, a1c1)),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(385,axiom,(incident(c1, a1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic1a1')).
% 1.56/1.29 tff(386,plain,
% 1.56/1.29 (incident(c1, a1c1)),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[385, 384])).
% 1.56/1.29 tff(387,plain,
% 1.56/1.29 (((~![A: $i, B: $i, 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(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a1c1, 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(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a1c1, oc))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(388,plain,
% 1.56/1.29 ((line_equal(a1c1, oc) | point_equal(c2, c1) | (~incident(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c2, oc)) | (~incident(c1, oc))) <=> (point_equal(c2, c1) | (~incident(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a1c1, oc))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(389,plain,
% 1.56/1.29 (((~![A: $i, B: $i, 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, oc) | point_equal(c2, c1) | (~incident(c1, a1c1)) | (~incident(c2, a1c1)) | (~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(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a1c1, oc)))),
% 1.56/1.29 inference(monotonicity,[status(thm)],[388])).
% 1.56/1.29 tff(390,plain,
% 1.56/1.29 (((~![A: $i, B: $i, 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, oc) | point_equal(c2, c1) | (~incident(c1, a1c1)) | (~incident(c2, a1c1)) | (~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(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a1c1, oc))),
% 1.56/1.29 inference(transitivity,[status(thm)],[389, 387])).
% 1.56/1.29 tff(391,plain,
% 1.56/1.29 ((~![A: $i, B: $i, 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, oc) | point_equal(c2, c1) | (~incident(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c2, oc)) | (~incident(c1, oc)))),
% 1.56/1.29 inference(quant_inst,[status(thm)],[])).
% 1.56/1.29 tff(392,plain,
% 1.56/1.29 ((~![A: $i, B: $i, 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(c1, a1c1)) | (~incident(c2, a1c1)) | (~incident(c1, oc)) | (~incident(c2, oc)) | line_equal(a1c1, oc)),
% 1.56/1.29 inference(modus_ponens,[status(thm)],[391, 390])).
% 1.56/1.29 tff(393,plain,
% 1.56/1.29 ((~incident(c2, a1c1)) | line_equal(a1c1, oc)),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[392, 386, 306, 317, 383, 40])).
% 1.56/1.29 tff(394,plain,
% 1.56/1.29 (line_equal(a1c1, oc)),
% 1.56/1.29 inference(unit_resolution,[status(thm)],[393, 374])).
% 1.56/1.29 tff(395,plain,
% 1.56/1.29 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a1c1, oc)) | line_equal(oc, a1c1))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a1c1, oc)) | line_equal(oc, a1c1))),
% 1.56/1.29 inference(rewrite,[status(thm)],[])).
% 1.56/1.29 tff(396,plain,
% 1.56/1.29 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a1c1, oc)) | line_equal(oc, a1c1))),
% 1.56/1.30 inference(quant_inst,[status(thm)],[])).
% 1.56/1.30 tff(397,plain,
% 1.56/1.30 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a1c1, oc)) | line_equal(oc, a1c1)),
% 1.56/1.30 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.56/1.30 tff(398,plain,
% 1.56/1.30 (line_equal(oc, a1c1)),
% 1.56/1.30 inference(unit_resolution,[status(thm)],[397, 97, 394])).
% 1.56/1.30 tff(399,plain,
% 1.56/1.30 (((~![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)))),
% 1.56/1.30 inference(rewrite,[status(thm)],[])).
% 1.56/1.30 tff(400,plain,
% 1.56/1.30 ((incident(o, a1c1) | (~line_equal(oc, a1c1)) | (~incident(o, oc))) <=> ((~incident(o, oc)) | incident(o, a1c1) | (~line_equal(oc, a1c1)))),
% 1.56/1.30 inference(rewrite,[status(thm)],[])).
% 1.56/1.30 tff(401,plain,
% 1.56/1.30 (((~![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))))),
% 1.56/1.30 inference(monotonicity,[status(thm)],[400])).
% 1.56/1.30 tff(402,plain,
% 1.56/1.30 (((~![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)))),
% 1.56/1.30 inference(transitivity,[status(thm)],[401, 399])).
% 1.56/1.30 tff(403,plain,
% 1.56/1.30 ((~![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)))),
% 1.56/1.30 inference(quant_inst,[status(thm)],[])).
% 1.56/1.30 tff(404,plain,
% 1.56/1.30 ((~![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))),
% 1.56/1.30 inference(modus_ponens,[status(thm)],[403, 402])).
% 1.56/1.30 tff(405,plain,
% 1.56/1.30 (incident(o, a1c1) | (~line_equal(oc, a1c1))),
% 1.56/1.30 inference(unit_resolution,[status(thm)],[404, 320, 15])).
% 1.56/1.30 tff(406,plain,
% 1.56/1.30 (incident(o, a1c1)),
% 1.56/1.30 inference(unit_resolution,[status(thm)],[405, 398])).
% 1.56/1.30 tff(407,assumption,(~point_equal(c2, o)), introduced(assumption)).
% 1.56/1.30 tff(408,assumption,(incident(o, a2c2)), introduced(assumption)).
% 1.56/1.30 tff(409,plain,
% 1.56/1.30 (((~![A: $i, B: $i, 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))),
% 1.56/1.30 inference(rewrite,[status(thm)],[])).
% 1.56/1.30 tff(410,plain,
% 1.56/1.30 ((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))),
% 1.56/1.30 inference(rewrite,[status(thm)],[])).
% 1.56/1.30 tff(411,plain,
% 1.56/1.30 (((~![A: $i, B: $i, 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)))),
% 1.56/1.30 inference(monotonicity,[status(thm)],[410])).
% 1.56/1.30 tff(412,plain,
% 1.56/1.30 (((~![A: $i, B: $i, 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))),
% 1.56/1.30 inference(transitivity,[status(thm)],[411, 409])).
% 1.56/1.30 tff(413,plain,
% 1.56/1.30 ((~![A: $i, B: $i, 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)))),
% 1.56/1.30 inference(quant_inst,[status(thm)],[])).
% 1.56/1.30 tff(414,plain,
% 1.56/1.30 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(o, a1c1)) | (~incident(o, a2c2)) | point_equal(c2, o)),
% 1.56/1.30 inference(modus_ponens,[status(thm)],[413, 412])).
% 1.56/1.30 tff(415,plain,
% 1.56/1.30 ($false),
% 1.56/1.30 inference(unit_resolution,[status(thm)],[414, 254, 188, 40, 374, 408, 407, 406])).
% 1.56/1.30 tff(416,plain,(point_equal(c2, o) | (~incident(c2, a1c1)) | (~incident(o, a2c2))), inference(lemma,lemma(discharge,[]))).
% 1.56/1.30 tff(417,plain,
% 1.56/1.30 (point_equal(c2, o)),
% 1.56/1.30 inference(unit_resolution,[status(thm)],[416, 373, 354])).
% 1.56/1.30 tff(418,plain,
% 1.56/1.30 (((~![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)))),
% 1.56/1.30 inference(rewrite,[status(thm)],[])).
% 1.56/1.30 tff(419,plain,
% 1.56/1.30 ((incident(c2, ob) | (~incident(o, ob)) | (~point_equal(c2, o))) <=> ((~incident(o, ob)) | incident(c2, ob) | (~point_equal(c2, o)))),
% 1.56/1.30 inference(rewrite,[status(thm)],[])).
% 1.56/1.30 tff(420,plain,
% 1.56/1.30 (((~![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))))),
% 1.56/1.30 inference(monotonicity,[status(thm)],[419])).
% 1.56/1.30 tff(421,plain,
% 1.56/1.30 (((~![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)))),
% 1.56/1.30 inference(transitivity,[status(thm)],[420, 418])).
% 1.56/1.30 tff(422,plain,
% 1.56/1.30 ((~![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)))),
% 1.56/1.30 inference(quant_inst,[status(thm)],[])).
% 1.56/1.30 tff(423,plain,
% 1.56/1.30 ((~![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))),
% 1.56/1.30 inference(modus_ponens,[status(thm)],[422, 421])).
% 1.56/1.30 tff(424,plain,
% 1.56/1.30 (incident(c2, ob) | (~point_equal(c2, o))),
% 1.56/1.30 inference(unit_resolution,[status(thm)],[423, 333, 171])).
% 1.56/1.30 tff(425,plain,
% 1.56/1.30 (incident(c2, ob)),
% 1.56/1.30 inference(unit_resolution,[status(thm)],[424, 417])).
% 1.56/1.30 tff(426,plain,
% 1.56/1.30 (((~![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)))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(427,plain,
% 1.65/1.30 ((incident(c2, a2b2) | (~incident(b2, a2b2)) | (~point_equal(c2, b2))) <=> ((~incident(b2, a2b2)) | incident(c2, a2b2) | (~point_equal(c2, b2)))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(428,plain,
% 1.65/1.30 (((~![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))))),
% 1.65/1.30 inference(monotonicity,[status(thm)],[427])).
% 1.65/1.30 tff(429,plain,
% 1.65/1.30 (((~![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)))),
% 1.65/1.30 inference(transitivity,[status(thm)],[428, 426])).
% 1.65/1.30 tff(430,plain,
% 1.65/1.30 ((~![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)))),
% 1.65/1.30 inference(quant_inst,[status(thm)],[])).
% 1.65/1.30 tff(431,plain,
% 1.65/1.30 ((~![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))),
% 1.65/1.30 inference(modus_ponens,[status(thm)],[430, 429])).
% 1.65/1.30 tff(432,plain,
% 1.65/1.30 (~point_equal(c2, b2)),
% 1.65/1.30 inference(unit_resolution,[status(thm)],[431, 234, 171, 241])).
% 1.65/1.30 tff(433,plain,
% 1.65/1.30 (((~![A: $i, B: $i, 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, ob)) | (~incident(c2, ob)) | point_equal(c2, b2) | line_equal(ob, 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, ob)) | (~incident(c2, ob)) | point_equal(c2, b2) | line_equal(ob, b2c2))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(434,plain,
% 1.65/1.30 ((line_equal(ob, b2c2) | point_equal(c2, b2) | (~incident(b2, ob)) | (~incident(c2, ob)) | (~incident(c2, b2c2)) | (~incident(b2, b2c2))) <=> ((~incident(b2, b2c2)) | (~incident(c2, b2c2)) | (~incident(b2, ob)) | (~incident(c2, ob)) | point_equal(c2, b2) | line_equal(ob, b2c2))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(435,plain,
% 1.65/1.30 (((~![A: $i, B: $i, 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, b2c2) | point_equal(c2, b2) | (~incident(b2, ob)) | (~incident(c2, ob)) | (~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, ob)) | (~incident(c2, ob)) | point_equal(c2, b2) | line_equal(ob, b2c2)))),
% 1.65/1.30 inference(monotonicity,[status(thm)],[434])).
% 1.65/1.30 tff(436,plain,
% 1.65/1.30 (((~![A: $i, B: $i, 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, b2c2) | point_equal(c2, b2) | (~incident(b2, ob)) | (~incident(c2, ob)) | (~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, ob)) | (~incident(c2, ob)) | point_equal(c2, b2) | line_equal(ob, b2c2))),
% 1.65/1.30 inference(transitivity,[status(thm)],[435, 433])).
% 1.65/1.30 tff(437,plain,
% 1.65/1.30 ((~![A: $i, B: $i, 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, b2c2) | point_equal(c2, b2) | (~incident(b2, ob)) | (~incident(c2, ob)) | (~incident(c2, b2c2)) | (~incident(b2, b2c2)))),
% 1.65/1.30 inference(quant_inst,[status(thm)],[])).
% 1.65/1.30 tff(438,plain,
% 1.65/1.30 ((~![A: $i, B: $i, 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, ob)) | (~incident(c2, ob)) | point_equal(c2, b2) | line_equal(ob, b2c2)),
% 1.65/1.30 inference(modus_ponens,[status(thm)],[437, 436])).
% 1.65/1.30 tff(439,plain,
% 1.65/1.30 ((~incident(c2, ob)) | line_equal(ob, b2c2)),
% 1.65/1.30 inference(unit_resolution,[status(thm)],[438, 323, 18, 54, 40, 432])).
% 1.65/1.30 tff(440,plain,
% 1.65/1.30 (line_equal(ob, b2c2)),
% 1.65/1.30 inference(unit_resolution,[status(thm)],[439, 425])).
% 1.65/1.30 tff(441,assumption,(~point_equal(ac, c2)), introduced(assumption)).
% 1.65/1.30 tff(442,plain,
% 1.65/1.30 (((~![A: $i, B: $i, 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))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(443,plain,
% 1.65/1.30 ((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))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(444,plain,
% 1.65/1.30 (((~![A: $i, B: $i, 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)))),
% 1.65/1.30 inference(monotonicity,[status(thm)],[443])).
% 1.65/1.30 tff(445,plain,
% 1.65/1.30 (((~![A: $i, B: $i, 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))),
% 1.65/1.30 inference(transitivity,[status(thm)],[444, 442])).
% 1.65/1.30 tff(446,plain,
% 1.65/1.30 ((~![A: $i, B: $i, 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)))),
% 1.65/1.30 inference(quant_inst,[status(thm)],[])).
% 1.65/1.30 tff(447,plain,
% 1.65/1.30 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(c2, a1c1)) | (~incident(c2, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, c2)),
% 1.65/1.30 inference(modus_ponens,[status(thm)],[446, 445])).
% 1.65/1.30 tff(448,plain,
% 1.65/1.30 ($false),
% 1.65/1.30 inference(unit_resolution,[status(thm)],[447, 254, 194, 191, 188, 40, 374, 441])).
% 1.65/1.30 tff(449,plain,(point_equal(ac, c2) | (~incident(c2, a1c1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.30 tff(450,plain,
% 1.65/1.30 (point_equal(ac, c2)),
% 1.65/1.30 inference(unit_resolution,[status(thm)],[449, 354])).
% 1.65/1.30 tff(451,plain,
% 1.65/1.30 (![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)))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(452,plain,
% 1.65/1.30 (^[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)))))),
% 1.65/1.30 inference(bind,[status(th)],[])).
% 1.65/1.30 tff(453,plain,
% 1.65/1.30 (![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)))),
% 1.65/1.30 inference(quant_intro,[status(thm)],[452])).
% 1.65/1.30 tff(454,plain,
% 1.65/1.30 (![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))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(455,plain,
% 1.65/1.30 (^[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)))),
% 1.65/1.30 inference(bind,[status(th)],[])).
% 1.65/1.30 tff(456,plain,
% 1.65/1.30 (![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))),
% 1.65/1.30 inference(quant_intro,[status(thm)],[455])).
% 1.65/1.30 tff(457,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')).
% 1.65/1.30 tff(458,plain,
% 1.65/1.30 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C))),
% 1.65/1.30 inference(modus_ponens,[status(thm)],[457, 456])).
% 1.65/1.30 tff(459,plain,
% 1.65/1.30 (![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C))),
% 1.65/1.30 inference(modus_ponens,[status(thm)],[458, 454])).
% 1.65/1.30 tff(460,plain,(
% 1.65/1.30 ![A: $i, B: $i, C: $i] : ((~(point_equal(A, B) & point_equal(B, C))) | point_equal(A, C))),
% 1.65/1.30 inference(skolemize,[status(sab)],[459])).
% 1.65/1.30 tff(461,plain,
% 1.65/1.30 (![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))),
% 1.65/1.30 inference(modus_ponens,[status(thm)],[460, 453])).
% 1.65/1.30 tff(462,plain,
% 1.65/1.30 (![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))),
% 1.65/1.30 inference(modus_ponens,[status(thm)],[461, 451])).
% 1.65/1.30 tff(463,plain,
% 1.65/1.30 (((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | ((~point_equal(c2, a1)) | (~point_equal(ac, c2)) | point_equal(ac, a1))) <=> ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (~point_equal(c2, a1)) | (~point_equal(ac, c2)) | point_equal(ac, a1))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(464,plain,
% 1.65/1.30 ((point_equal(ac, a1) | (~point_equal(c2, a1)) | (~point_equal(ac, c2))) <=> ((~point_equal(c2, a1)) | (~point_equal(ac, c2)) | point_equal(ac, a1))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(465,plain,
% 1.65/1.30 (((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (point_equal(ac, a1) | (~point_equal(c2, a1)) | (~point_equal(ac, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | ((~point_equal(c2, a1)) | (~point_equal(ac, c2)) | point_equal(ac, a1)))),
% 1.65/1.30 inference(monotonicity,[status(thm)],[464])).
% 1.65/1.30 tff(466,plain,
% 1.65/1.30 (((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (point_equal(ac, a1) | (~point_equal(c2, a1)) | (~point_equal(ac, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (~point_equal(c2, a1)) | (~point_equal(ac, c2)) | point_equal(ac, a1))),
% 1.65/1.30 inference(transitivity,[status(thm)],[465, 463])).
% 1.65/1.30 tff(467,plain,
% 1.65/1.30 ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (point_equal(ac, a1) | (~point_equal(c2, a1)) | (~point_equal(ac, c2)))),
% 1.65/1.30 inference(quant_inst,[status(thm)],[])).
% 1.65/1.30 tff(468,plain,
% 1.65/1.30 ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (~point_equal(c2, a1)) | (~point_equal(ac, c2)) | point_equal(ac, a1)),
% 1.65/1.30 inference(modus_ponens,[status(thm)],[467, 466])).
% 1.65/1.30 tff(469,plain,
% 1.65/1.30 (point_equal(ac, a1)),
% 1.65/1.30 inference(unit_resolution,[status(thm)],[468, 462, 344, 450])).
% 1.65/1.30 tff(470,plain,
% 1.65/1.30 (incident(ac, a1b1)),
% 1.65/1.30 inference(unit_resolution,[status(thm)],[178, 469])).
% 1.65/1.30 tff(471,assumption,(point_equal(ac, c2)), introduced(assumption)).
% 1.65/1.30 tff(472,assumption,(~incident(ac, b2c2)), introduced(assumption)).
% 1.65/1.30 tff(473,plain,
% 1.65/1.30 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c2, b2c2)) | incident(ac, b2c2) | (~point_equal(ac, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c2, b2c2)) | incident(ac, b2c2) | (~point_equal(ac, c2)))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(474,plain,
% 1.65/1.30 ((incident(ac, b2c2) | (~incident(c2, b2c2)) | (~point_equal(ac, c2))) <=> ((~incident(c2, b2c2)) | incident(ac, b2c2) | (~point_equal(ac, c2)))),
% 1.65/1.30 inference(rewrite,[status(thm)],[])).
% 1.65/1.30 tff(475,plain,
% 1.65/1.30 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, b2c2) | (~incident(c2, b2c2)) | (~point_equal(ac, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c2, b2c2)) | incident(ac, b2c2) | (~point_equal(ac, c2))))),
% 1.65/1.30 inference(monotonicity,[status(thm)],[474])).
% 1.65/1.30 tff(476,plain,
% 1.65/1.30 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, b2c2) | (~incident(c2, b2c2)) | (~point_equal(ac, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c2, b2c2)) | incident(ac, b2c2) | (~point_equal(ac, c2)))),
% 1.65/1.30 inference(transitivity,[status(thm)],[475, 473])).
% 1.65/1.30 tff(477,plain,
% 1.65/1.30 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, b2c2) | (~incident(c2, b2c2)) | (~point_equal(ac, c2)))),
% 1.65/1.30 inference(quant_inst,[status(thm)],[])).
% 1.65/1.30 tff(478,plain,
% 1.65/1.30 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c2, b2c2)) | incident(ac, b2c2) | (~point_equal(ac, c2))),
% 1.65/1.30 inference(modus_ponens,[status(thm)],[477, 476])).
% 1.65/1.30 tff(479,plain,
% 1.65/1.30 ($false),
% 1.65/1.30 inference(unit_resolution,[status(thm)],[478, 323, 171, 472, 471])).
% 1.65/1.30 tff(480,plain,(incident(ac, b2c2) | (~point_equal(ac, c2))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.30 tff(481,plain,
% 1.65/1.30 (incident(ac, b2c2)),
% 1.65/1.30 inference(unit_resolution,[status(thm)],[480, 450])).
% 1.65/1.30 tff(482,plain,
% 1.65/1.30 (((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(c2, b2c2)) | line_equal(b2c2, b2c2))) <=> ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(c2, b2c2)) | line_equal(b2c2, b2c2))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(483,plain,
% 1.65/1.31 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(c2, b2c2)) | line_equal(b2c2, b2c2))),
% 1.65/1.31 inference(quant_inst,[status(thm)],[])).
% 1.65/1.31 tff(484,plain,
% 1.65/1.31 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(c2, b2c2)) | line_equal(b2c2, b2c2)),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[483, 482])).
% 1.65/1.31 tff(485,plain,
% 1.65/1.31 (line_equal(b2c2, b2c2)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[484, 323, 124])).
% 1.65/1.31 tff(486,plain,
% 1.65/1.31 (((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(b2c2, b2c2)) | (~incident(bc, b2c2)) | (~incident(ac, b2c2)) | (~incident(ab, b2c2)))) <=> ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~line_equal(b2c2, b2c2)) | (~incident(bc, b2c2)) | (~incident(ac, b2c2)) | (~incident(ab, b2c2)))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(487,plain,
% 1.65/1.31 ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(b2c2, b2c2)) | (~incident(bc, b2c2)) | (~incident(ac, b2c2)) | (~incident(ab, b2c2)))),
% 1.65/1.31 inference(quant_inst,[status(thm)],[])).
% 1.65/1.31 tff(488,plain,
% 1.65/1.31 ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~line_equal(b2c2, b2c2)) | (~incident(bc, b2c2)) | (~incident(ac, b2c2)) | (~incident(ab, b2c2))),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[487, 486])).
% 1.65/1.31 tff(489,plain,
% 1.65/1.31 ((~incident(ac, b2c2)) | (~incident(ab, b2c2))),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[488, 150, 105, 485])).
% 1.65/1.31 tff(490,plain,
% 1.65/1.31 (~incident(ab, b2c2)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[489, 481])).
% 1.65/1.31 tff(491,plain,
% 1.65/1.31 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, b2c2) | (~incident(ab, a1b1)) | (~line_equal(a1b1, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ab, b2c2) | (~incident(ab, a1b1)) | (~line_equal(a1b1, b2c2)))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(492,plain,
% 1.65/1.31 ((incident(ab, b2c2) | (~line_equal(a1b1, b2c2)) | (~incident(ab, a1b1))) <=> (incident(ab, b2c2) | (~incident(ab, a1b1)) | (~line_equal(a1b1, b2c2)))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(493,plain,
% 1.65/1.31 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, b2c2) | (~line_equal(a1b1, b2c2)) | (~incident(ab, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, b2c2) | (~incident(ab, a1b1)) | (~line_equal(a1b1, b2c2))))),
% 1.65/1.31 inference(monotonicity,[status(thm)],[492])).
% 1.65/1.31 tff(494,plain,
% 1.65/1.31 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, b2c2) | (~line_equal(a1b1, b2c2)) | (~incident(ab, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ab, b2c2) | (~incident(ab, a1b1)) | (~line_equal(a1b1, b2c2)))),
% 1.65/1.31 inference(transitivity,[status(thm)],[493, 491])).
% 1.65/1.31 tff(495,plain,
% 1.65/1.31 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, b2c2) | (~line_equal(a1b1, b2c2)) | (~incident(ab, a1b1)))),
% 1.65/1.31 inference(quant_inst,[status(thm)],[])).
% 1.65/1.31 tff(496,plain,
% 1.65/1.31 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ab, b2c2) | (~incident(ab, a1b1)) | (~line_equal(a1b1, b2c2))),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[495, 494])).
% 1.65/1.31 tff(497,plain,
% 1.65/1.31 (incident(ab, b2c2) | (~line_equal(a1b1, b2c2))),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[496, 134, 15])).
% 1.65/1.31 tff(498,plain,
% 1.65/1.31 (~line_equal(a1b1, b2c2)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[497, 490])).
% 1.65/1.31 tff(499,plain,
% 1.65/1.31 (((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | ((~incident(a1, a1c1)) | (~incident(b1, a1c1)) | (~incident(c1, a1c1)))) <=> ((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (~incident(a1, a1c1)) | (~incident(b1, a1c1)) | (~incident(c1, a1c1)))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(500,plain,
% 1.65/1.31 ((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | ((~incident(a1, a1c1)) | (~incident(b1, a1c1)) | (~incident(c1, a1c1)))),
% 1.65/1.31 inference(quant_inst,[status(thm)],[])).
% 1.65/1.31 tff(501,plain,
% 1.65/1.31 ((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (~incident(a1, a1c1)) | (~incident(b1, a1c1)) | (~incident(c1, a1c1))),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[500, 499])).
% 1.65/1.31 tff(502,plain,
% 1.65/1.31 (~incident(b1, a1c1)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[501, 197, 386, 292])).
% 1.65/1.31 tff(503,plain,
% 1.65/1.31 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a1c1) | (~incident(ac, a1c1)) | (~point_equal(b1, ac)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, a1c1) | (~incident(ac, a1c1)) | (~point_equal(b1, ac)))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(504,plain,
% 1.65/1.31 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b1, a1c1) | (~incident(ac, a1c1)) | (~point_equal(b1, ac)))),
% 1.65/1.31 inference(quant_inst,[status(thm)],[])).
% 1.65/1.31 tff(505,plain,
% 1.65/1.31 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b1, a1c1) | (~incident(ac, a1c1)) | (~point_equal(b1, ac))),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[504, 503])).
% 1.65/1.31 tff(506,plain,
% 1.65/1.31 (~point_equal(b1, ac)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[505, 194, 171, 502])).
% 1.65/1.31 tff(507,plain,
% 1.65/1.31 (((~![A: $i, B: $i, 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, b2c2)) | (~incident(b1, a1b1)) | (~incident(ac, b2c2)) | (~incident(ac, a1b1)) | point_equal(b1, ac) | 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(b1, b2c2)) | (~incident(b1, a1b1)) | (~incident(ac, b2c2)) | (~incident(ac, a1b1)) | point_equal(b1, ac) | line_equal(a1b1, b2c2))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(508,plain,
% 1.65/1.31 ((line_equal(a1b1, b2c2) | point_equal(b1, ac) | (~incident(ac, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, b2c2)) | (~incident(ac, b2c2))) <=> ((~incident(b1, b2c2)) | (~incident(b1, a1b1)) | (~incident(ac, b2c2)) | (~incident(ac, a1b1)) | point_equal(b1, ac) | line_equal(a1b1, b2c2))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(509,plain,
% 1.65/1.31 (((~![A: $i, B: $i, 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(b1, ac) | (~incident(ac, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, b2c2)) | (~incident(ac, 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(b1, b2c2)) | (~incident(b1, a1b1)) | (~incident(ac, b2c2)) | (~incident(ac, a1b1)) | point_equal(b1, ac) | line_equal(a1b1, b2c2)))),
% 1.65/1.31 inference(monotonicity,[status(thm)],[508])).
% 1.65/1.31 tff(510,plain,
% 1.65/1.31 (((~![A: $i, B: $i, 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(b1, ac) | (~incident(ac, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, b2c2)) | (~incident(ac, 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(b1, b2c2)) | (~incident(b1, a1b1)) | (~incident(ac, b2c2)) | (~incident(ac, a1b1)) | point_equal(b1, ac) | line_equal(a1b1, b2c2))),
% 1.65/1.31 inference(transitivity,[status(thm)],[509, 507])).
% 1.65/1.31 tff(511,plain,
% 1.65/1.31 ((~![A: $i, B: $i, 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(b1, ac) | (~incident(ac, a1b1)) | (~incident(b1, a1b1)) | (~incident(b1, b2c2)) | (~incident(ac, b2c2)))),
% 1.65/1.31 inference(quant_inst,[status(thm)],[])).
% 1.65/1.31 tff(512,plain,
% 1.65/1.31 ((~![A: $i, B: $i, 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, b2c2)) | (~incident(b1, a1b1)) | (~incident(ac, b2c2)) | (~incident(ac, a1b1)) | point_equal(b1, ac) | line_equal(a1b1, b2c2)),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[511, 510])).
% 1.65/1.31 tff(513,plain,
% 1.65/1.31 ((~incident(b1, b2c2)) | (~incident(ac, a1b1))),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[512, 60, 40, 481, 506, 498])).
% 1.65/1.31 tff(514,plain,
% 1.65/1.31 (~incident(b1, b2c2)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[513, 470])).
% 1.65/1.31 tff(515,plain,
% 1.65/1.31 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, b2c2) | (~incident(b1, ob)) | (~line_equal(ob, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b1, b2c2) | (~incident(b1, ob)) | (~line_equal(ob, b2c2)))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(516,plain,
% 1.65/1.31 ((incident(b1, b2c2) | (~line_equal(ob, b2c2)) | (~incident(b1, ob))) <=> (incident(b1, b2c2) | (~incident(b1, ob)) | (~line_equal(ob, b2c2)))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(517,plain,
% 1.65/1.31 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, b2c2) | (~line_equal(ob, b2c2)) | (~incident(b1, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, b2c2) | (~incident(b1, ob)) | (~line_equal(ob, b2c2))))),
% 1.65/1.31 inference(monotonicity,[status(thm)],[516])).
% 1.65/1.31 tff(518,plain,
% 1.65/1.31 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, b2c2) | (~line_equal(ob, b2c2)) | (~incident(b1, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b1, b2c2) | (~incident(b1, ob)) | (~line_equal(ob, b2c2)))),
% 1.65/1.31 inference(transitivity,[status(thm)],[517, 515])).
% 1.65/1.31 tff(519,plain,
% 1.65/1.31 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, b2c2) | (~line_equal(ob, b2c2)) | (~incident(b1, ob)))),
% 1.65/1.31 inference(quant_inst,[status(thm)],[])).
% 1.65/1.31 tff(520,plain,
% 1.65/1.31 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b1, b2c2) | (~incident(b1, ob)) | (~line_equal(ob, b2c2))),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[519, 518])).
% 1.65/1.31 tff(521,plain,
% 1.65/1.31 ($false),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[520, 57, 15, 514, 440])).
% 1.65/1.31 tff(522,plain,(~point_equal(c2, a1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.31 tff(523,assumption,(~point_equal(a2, b1)), introduced(assumption)).
% 1.65/1.31 tff(524,assumption,(~point_equal(c2, a1)), introduced(assumption)).
% 1.65/1.31 tff(525,assumption,(~point_equal(c1, b2)), introduced(assumption)).
% 1.65/1.31 tff(526,assumption,(~line_equal(a1c1, oc)), introduced(assumption)).
% 1.65/1.31 tff(527,assumption,(~incident(a2, a1b1)), introduced(assumption)).
% 1.65/1.31 tff(528,assumption,(point_equal(a2, b1)), introduced(assumption)).
% 1.65/1.31 tff(529,plain,
% 1.65/1.31 (((~![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)))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(530,plain,
% 1.65/1.31 ((~![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)))),
% 1.65/1.31 inference(quant_inst,[status(thm)],[])).
% 1.65/1.31 tff(531,plain,
% 1.65/1.31 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a2, a1b1) | (~incident(b1, a1b1)) | (~point_equal(a2, b1))),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[530, 529])).
% 1.65/1.31 tff(532,plain,
% 1.65/1.31 ($false),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[531, 60, 171, 527, 528])).
% 1.65/1.31 tff(533,plain,(incident(a2, a1b1) | (~point_equal(a2, b1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.31 tff(534,plain,
% 1.65/1.31 (~point_equal(a2, b1)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[533, 527])).
% 1.65/1.31 tff(535,assumption,(incident(a1, b2c2)), introduced(assumption)).
% 1.65/1.31 tff(536,plain,
% 1.65/1.31 (((~![A: $i, B: $i, 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))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(537,plain,
% 1.65/1.31 ((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))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(538,plain,
% 1.65/1.31 (((~![A: $i, B: $i, 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)))),
% 1.65/1.31 inference(monotonicity,[status(thm)],[537])).
% 1.65/1.31 tff(539,plain,
% 1.65/1.31 (((~![A: $i, B: $i, 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))),
% 1.65/1.31 inference(transitivity,[status(thm)],[538, 536])).
% 1.65/1.31 tff(540,plain,
% 1.65/1.31 ((~![A: $i, B: $i, 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)))),
% 1.65/1.31 inference(quant_inst,[status(thm)],[])).
% 1.65/1.31 tff(541,plain,
% 1.65/1.31 ((~![A: $i, B: $i, 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)),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[540, 539])).
% 1.65/1.31 tff(542,plain,
% 1.65/1.31 ((~incident(a1, b2c2)) | (~incident(c2, a1b1)) | point_equal(c2, a1) | line_equal(b2c2, a1b1)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[541, 127, 323, 40])).
% 1.65/1.31 tff(543,plain,
% 1.65/1.31 (~incident(c2, a1b1)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[542, 535, 342, 524])).
% 1.65/1.31 tff(544,plain,
% 1.65/1.31 ((incident(b1, a2c2) | incident(c2, a1b1)) <=> (incident(b1, a2c2) | incident(c2, a1b1))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(545,axiom,(incident(b1, a2c2) | incident(c2, a1b1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gap_b')).
% 1.65/1.31 tff(546,plain,
% 1.65/1.31 (incident(b1, a2c2) | incident(c2, a1b1)),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[545, 544])).
% 1.65/1.31 tff(547,plain,
% 1.65/1.31 (incident(b1, a2c2)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[546, 543])).
% 1.65/1.31 tff(548,plain,
% 1.65/1.31 ((~(~((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2))))) <=> ((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2)))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(549,plain,
% 1.65/1.31 ((incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)) <=> (~((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2))))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(550,plain,
% 1.65/1.31 ((~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))) <=> (~(~((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2)))))),
% 1.65/1.31 inference(monotonicity,[status(thm)],[549])).
% 1.65/1.31 tff(551,plain,
% 1.65/1.31 ((~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))) <=> ((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2)))),
% 1.65/1.31 inference(transitivity,[status(thm)],[550, 548])).
% 1.65/1.31 tff(552,plain,
% 1.65/1.31 ((~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))) <=> (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(553,plain,
% 1.65/1.31 (($false | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))) <=> (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(554,plain,
% 1.65/1.31 ((goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))) <=> ($false | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))))),
% 1.65/1.31 inference(monotonicity,[status(thm)],[44])).
% 1.65/1.31 tff(555,plain,
% 1.65/1.31 ((goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))) <=> (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))),
% 1.65/1.31 inference(transitivity,[status(thm)],[554, 553])).
% 1.65/1.31 tff(556,plain,
% 1.65/1.31 (((incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)) => goal) <=> (goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(557,plain,
% 1.65/1.31 (((incident(a1, b2c2) & incident(b1, a2c2)) & incident(c1, a2b2)) <=> (incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(558,plain,
% 1.65/1.31 ((((incident(a1, b2c2) & incident(b1, a2c2)) & incident(c1, a2b2)) => goal) <=> ((incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)) => goal)),
% 1.65/1.31 inference(monotonicity,[status(thm)],[557])).
% 1.65/1.31 tff(559,plain,
% 1.65/1.31 ((((incident(a1, b2c2) & incident(b1, a2c2)) & incident(c1, a2b2)) => goal) <=> (goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))))),
% 1.65/1.31 inference(transitivity,[status(thm)],[558, 556])).
% 1.65/1.31 tff(560,axiom,(((incident(a1, b2c2) & incident(b1, a2c2)) & incident(c1, a2b2)) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1in2')).
% 1.65/1.31 tff(561,plain,
% 1.65/1.31 (goal | (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2)))),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[560, 559])).
% 1.65/1.31 tff(562,plain,
% 1.65/1.31 (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[561, 555])).
% 1.65/1.31 tff(563,plain,
% 1.65/1.31 (~(incident(a1, b2c2) & incident(b1, a2c2) & incident(c1, a2b2))),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[562, 552])).
% 1.65/1.31 tff(564,plain,
% 1.65/1.31 ((~incident(a1, b2c2)) | (~incident(b1, a2c2)) | (~incident(c1, a2b2))),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[563, 551])).
% 1.65/1.31 tff(565,plain,
% 1.65/1.31 (~incident(c1, a2b2)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[564, 547, 535])).
% 1.65/1.31 tff(566,plain,
% 1.65/1.31 (incident(b1, b1c1) <=> incident(b1, b1c1)),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(567,axiom,(incident(b1, b1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ib1c1')).
% 1.65/1.31 tff(568,plain,
% 1.65/1.31 (incident(b1, b1c1)),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[567, 566])).
% 1.65/1.31 tff(569,plain,
% 1.65/1.31 (((~![A: $i, B: $i, 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(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(a2c2, b1c1) | point_equal(a2, b1))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(570,plain,
% 1.65/1.31 ((line_equal(a2c2, b1c1) | point_equal(a2, b1) | (~incident(b1, a2c2)) | (~incident(a2, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1))) <=> ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(a2c2, b1c1) | point_equal(a2, b1))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(571,plain,
% 1.65/1.31 (((~![A: $i, B: $i, 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(a2, b1) | (~incident(b1, a2c2)) | (~incident(a2, a2c2)) | (~incident(a2, 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, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(a2c2, b1c1) | point_equal(a2, b1)))),
% 1.65/1.31 inference(monotonicity,[status(thm)],[570])).
% 1.65/1.31 tff(572,plain,
% 1.65/1.31 (((~![A: $i, B: $i, 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(a2, b1) | (~incident(b1, a2c2)) | (~incident(a2, a2c2)) | (~incident(a2, 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, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)) | (~incident(a2, a2c2)) | line_equal(a2c2, b1c1) | point_equal(a2, b1))),
% 1.65/1.31 inference(transitivity,[status(thm)],[571, 569])).
% 1.65/1.31 tff(573,plain,
% 1.65/1.31 ((~![A: $i, B: $i, 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(a2, b1) | (~incident(b1, a2c2)) | (~incident(a2, a2c2)) | (~incident(a2, b1c1)) | (~incident(b1, b1c1)))),
% 1.65/1.31 inference(quant_inst,[status(thm)],[])).
% 1.65/1.31 tff(574,plain,
% 1.65/1.31 ((~![A: $i, B: $i, 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(a2, b1)),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[573, 572])).
% 1.65/1.31 tff(575,plain,
% 1.65/1.31 ((~incident(b1, a2c2)) | (~incident(a2, b1c1)) | line_equal(a2c2, b1c1) | point_equal(a2, b1)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[574, 257, 568, 40])).
% 1.65/1.31 tff(576,plain,
% 1.65/1.31 (~incident(a2, b1c1)),
% 1.65/1.31 inference(unit_resolution,[status(thm)],[575, 547, 523, 343])).
% 1.65/1.31 tff(577,plain,
% 1.65/1.31 ((incident(c1, a2b2) | incident(a2, b1c1)) <=> (incident(c1, a2b2) | incident(a2, b1c1))),
% 1.65/1.31 inference(rewrite,[status(thm)],[])).
% 1.65/1.31 tff(578,axiom,(incident(c1, a2b2) | incident(a2, b1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gap_c')).
% 1.65/1.31 tff(579,plain,
% 1.65/1.31 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[578, 577])).
% 1.65/1.31 tff(580,plain,
% 1.65/1.31 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[579, 577])).
% 1.65/1.31 tff(581,plain,
% 1.65/1.31 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.65/1.31 inference(modus_ponens,[status(thm)],[580, 577])).
% 1.65/1.32 tff(582,plain,
% 1.65/1.32 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[581, 577])).
% 1.65/1.32 tff(583,plain,
% 1.65/1.32 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[582, 577])).
% 1.65/1.32 tff(584,plain,
% 1.65/1.32 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[583, 577])).
% 1.65/1.32 tff(585,plain,
% 1.65/1.32 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[584, 577])).
% 1.65/1.32 tff(586,plain,
% 1.65/1.32 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[585, 577])).
% 1.65/1.32 tff(587,plain,
% 1.65/1.32 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[586, 577])).
% 1.65/1.32 tff(588,plain,
% 1.65/1.32 (incident(c1, a2b2) | incident(a2, b1c1)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[587, 577])).
% 1.65/1.32 tff(589,plain,
% 1.65/1.32 ($false),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[588, 576, 565])).
% 1.65/1.32 tff(590,plain,((~incident(a1, b2c2)) | point_equal(a2, b1) | line_equal(a2c2, b1c1) | line_equal(b2c2, a1b1) | point_equal(c2, a1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.32 tff(591,plain,
% 1.65/1.32 (~incident(a1, b2c2)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[590, 534, 343, 342, 524])).
% 1.65/1.32 tff(592,plain,
% 1.65/1.32 ((incident(a1, b2c2) | incident(b2, a1c1)) <=> (incident(a1, b2c2) | incident(b2, a1c1))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(593,axiom,(incident(a1, b2c2) | incident(b2, a1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','gap_a')).
% 1.65/1.32 tff(594,plain,
% 1.65/1.32 (incident(a1, b2c2) | incident(b2, a1c1)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[593, 592])).
% 1.65/1.32 tff(595,plain,
% 1.65/1.32 (incident(b2, a1c1)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[594, 591])).
% 1.65/1.32 tff(596,assumption,(incident(b2, a1c1)), introduced(assumption)).
% 1.65/1.32 tff(597,assumption,(~line_equal(a1c1, a2b2)), introduced(assumption)).
% 1.65/1.32 tff(598,plain,
% 1.65/1.32 (((~![A: $i, B: $i, 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(c1, 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)))) | (~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a1c1, a2b2) | point_equal(c1, b2))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(599,plain,
% 1.65/1.32 ((line_equal(a1c1, a2b2) | point_equal(c1, b2) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2b2)) | (~incident(b2, a2b2))) <=> ((~incident(c1, a2b2)) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(b2, a2b2)) | line_equal(a1c1, a2b2) | point_equal(c1, b2))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(600,plain,
% 1.65/1.32 (((~![A: $i, B: $i, 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, b2) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2b2)) | (~incident(b2, 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(c1, b2)))),
% 1.65/1.32 inference(monotonicity,[status(thm)],[599])).
% 1.65/1.32 tff(601,plain,
% 1.65/1.32 (((~![A: $i, B: $i, 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, b2) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2b2)) | (~incident(b2, 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(c1, b2))),
% 1.65/1.32 inference(transitivity,[status(thm)],[600, 598])).
% 1.65/1.32 tff(602,plain,
% 1.65/1.32 ((~![A: $i, B: $i, 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, b2) | (~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2b2)) | (~incident(b2, a2b2)))),
% 1.65/1.32 inference(quant_inst,[status(thm)],[])).
% 1.65/1.32 tff(603,plain,
% 1.65/1.32 ((~![A: $i, B: $i, 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(c1, b2)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[602, 601])).
% 1.65/1.32 tff(604,plain,
% 1.65/1.32 ((~incident(c1, a2b2)) | (~incident(b2, a1c1)) | line_equal(a1c1, a2b2) | point_equal(c1, b2)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[603, 234, 386, 40])).
% 1.65/1.32 tff(605,plain,
% 1.65/1.32 (~incident(c1, a2b2)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[604, 596, 597, 525])).
% 1.65/1.32 tff(606,plain,
% 1.65/1.32 (incident(a2, b1c1)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[588, 605])).
% 1.65/1.32 tff(607,plain,
% 1.65/1.32 ((~(~((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1))))) <=> ((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1)))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(608,plain,
% 1.65/1.32 ((incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)) <=> (~((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1))))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(609,plain,
% 1.65/1.32 ((~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))) <=> (~(~((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1)))))),
% 1.65/1.32 inference(monotonicity,[status(thm)],[608])).
% 1.65/1.32 tff(610,plain,
% 1.65/1.32 ((~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))) <=> ((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1)))),
% 1.65/1.32 inference(transitivity,[status(thm)],[609, 607])).
% 1.65/1.32 tff(611,plain,
% 1.65/1.32 ((~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))) <=> (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(612,plain,
% 1.65/1.32 (($false | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))) <=> (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(613,plain,
% 1.65/1.32 ((goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))) <=> ($false | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))))),
% 1.65/1.32 inference(monotonicity,[status(thm)],[44])).
% 1.65/1.32 tff(614,plain,
% 1.65/1.32 ((goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))) <=> (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))),
% 1.65/1.32 inference(transitivity,[status(thm)],[613, 612])).
% 1.65/1.32 tff(615,plain,
% 1.65/1.32 (((incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)) => goal) <=> (goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(616,plain,
% 1.65/1.32 (((incident(a2, b1c1) & incident(b2, a1c1)) & incident(c2, a1b1)) <=> (incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(617,plain,
% 1.65/1.32 ((((incident(a2, b1c1) & incident(b2, a1c1)) & incident(c2, a1b1)) => goal) <=> ((incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)) => goal)),
% 1.65/1.32 inference(monotonicity,[status(thm)],[616])).
% 1.65/1.32 tff(618,plain,
% 1.65/1.32 ((((incident(a2, b1c1) & incident(b2, a1c1)) & incident(c2, a1b1)) => goal) <=> (goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))))),
% 1.65/1.32 inference(transitivity,[status(thm)],[617, 615])).
% 1.65/1.32 tff(619,axiom,(((incident(a2, b1c1) & incident(b2, a1c1)) & incident(c2, a1b1)) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2in1')).
% 1.65/1.32 tff(620,plain,
% 1.65/1.32 (goal | (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1)))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[619, 618])).
% 1.65/1.32 tff(621,plain,
% 1.65/1.32 (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[620, 614])).
% 1.65/1.32 tff(622,plain,
% 1.65/1.32 (~(incident(a2, b1c1) & incident(b2, a1c1) & incident(c2, a1b1))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[621, 611])).
% 1.65/1.32 tff(623,plain,
% 1.65/1.32 ((~incident(a2, b1c1)) | (~incident(b2, a1c1)) | (~incident(c2, a1b1))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[622, 610])).
% 1.65/1.32 tff(624,plain,
% 1.65/1.32 (~incident(c2, a1b1)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[623, 606, 596])).
% 1.65/1.32 tff(625,plain,
% 1.65/1.32 (~incident(b1, a2c2)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[575, 606, 523, 343])).
% 1.65/1.32 tff(626,plain,
% 1.65/1.32 ($false),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[546, 625, 624])).
% 1.65/1.32 tff(627,plain,((~incident(b2, a1c1)) | point_equal(a2, b1) | line_equal(a2c2, b1c1) | line_equal(a1c1, a2b2) | point_equal(c1, b2)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.32 tff(628,plain,
% 1.65/1.32 (line_equal(a1c1, a2b2)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[627, 595, 343, 534, 525])).
% 1.65/1.32 tff(629,assumption,(line_equal(a1c1, a2b2)), introduced(assumption)).
% 1.65/1.32 tff(630,assumption,(~incident(ac, a2b2)), introduced(assumption)).
% 1.65/1.32 tff(631,plain,
% 1.65/1.32 (((~![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)))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(632,plain,
% 1.65/1.32 ((incident(ac, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(ac, a1c1))) <=> ((~incident(ac, a1c1)) | incident(ac, a2b2) | (~line_equal(a1c1, a2b2)))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(633,plain,
% 1.65/1.32 (((~![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))))),
% 1.65/1.32 inference(monotonicity,[status(thm)],[632])).
% 1.65/1.32 tff(634,plain,
% 1.65/1.32 (((~![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)))),
% 1.65/1.32 inference(transitivity,[status(thm)],[633, 631])).
% 1.65/1.32 tff(635,plain,
% 1.65/1.32 ((~![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)))),
% 1.65/1.32 inference(quant_inst,[status(thm)],[])).
% 1.65/1.32 tff(636,plain,
% 1.65/1.32 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ac, a1c1)) | incident(ac, a2b2) | (~line_equal(a1c1, a2b2))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[635, 634])).
% 1.65/1.32 tff(637,plain,
% 1.65/1.32 ($false),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[636, 194, 15, 630, 629])).
% 1.65/1.32 tff(638,plain,(incident(ac, a2b2) | (~line_equal(a1c1, a2b2))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.32 tff(639,plain,
% 1.65/1.32 (incident(ac, a2b2)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[638, 628])).
% 1.65/1.32 tff(640,plain,
% 1.65/1.32 (((~![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))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(641,plain,
% 1.65/1.32 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(a2, a2b2)) | line_equal(a2b2, a2b2))),
% 1.65/1.32 inference(quant_inst,[status(thm)],[])).
% 1.65/1.32 tff(642,plain,
% 1.65/1.32 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(a2, a2b2)) | line_equal(a2b2, a2b2)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[641, 640])).
% 1.65/1.32 tff(643,plain,
% 1.65/1.32 (line_equal(a2b2, a2b2)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[642, 237, 124])).
% 1.65/1.32 tff(644,plain,
% 1.65/1.32 (incident(ab, a2b2) <=> incident(ab, a2b2)),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(645,axiom,(incident(ab, a2b2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','iab2')).
% 1.65/1.32 tff(646,plain,
% 1.65/1.32 (incident(ab, a2b2)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[645, 644])).
% 1.65/1.32 tff(647,plain,
% 1.65/1.32 (((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(a2b2, a2b2)) | (~incident(bc, a2b2)) | (~incident(ac, a2b2)) | (~incident(ab, a2b2)))) <=> ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~line_equal(a2b2, a2b2)) | (~incident(bc, a2b2)) | (~incident(ac, a2b2)) | (~incident(ab, a2b2)))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(648,plain,
% 1.65/1.32 ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(a2b2, a2b2)) | (~incident(bc, a2b2)) | (~incident(ac, a2b2)) | (~incident(ab, a2b2)))),
% 1.65/1.32 inference(quant_inst,[status(thm)],[])).
% 1.65/1.32 tff(649,plain,
% 1.65/1.32 ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~line_equal(a2b2, a2b2)) | (~incident(bc, a2b2)) | (~incident(ac, a2b2)) | (~incident(ab, a2b2))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[648, 647])).
% 1.65/1.32 tff(650,plain,
% 1.65/1.32 ((~incident(bc, a2b2)) | (~incident(ac, a2b2))),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[649, 150, 646, 643])).
% 1.65/1.32 tff(651,plain,
% 1.65/1.32 (~incident(bc, a2b2)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[650, 639])).
% 1.65/1.32 tff(652,plain,
% 1.65/1.32 (((~![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)))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(653,plain,
% 1.65/1.32 ((incident(bc, a2b2) | (~incident(b2, a2b2)) | (~point_equal(bc, b2))) <=> ((~incident(b2, a2b2)) | incident(bc, a2b2) | (~point_equal(bc, b2)))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(654,plain,
% 1.65/1.32 (((~![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))))),
% 1.65/1.32 inference(monotonicity,[status(thm)],[653])).
% 1.65/1.32 tff(655,plain,
% 1.65/1.32 (((~![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)))),
% 1.65/1.32 inference(transitivity,[status(thm)],[654, 652])).
% 1.65/1.32 tff(656,plain,
% 1.65/1.32 ((~![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)))),
% 1.65/1.32 inference(quant_inst,[status(thm)],[])).
% 1.65/1.32 tff(657,plain,
% 1.65/1.32 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a2b2)) | incident(bc, a2b2) | (~point_equal(bc, b2))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[656, 655])).
% 1.65/1.32 tff(658,plain,
% 1.65/1.32 (~point_equal(bc, b2)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[657, 234, 171, 651])).
% 1.65/1.32 tff(659,assumption,(~point_equal(bc, b2)), introduced(assumption)).
% 1.65/1.32 tff(660,assumption,(incident(b2, b1c1)), introduced(assumption)).
% 1.65/1.32 tff(661,plain,
% 1.65/1.32 ((~line_equal(b1c1, b2c2)) <=> (~line_equal(b1c1, b2c2))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(662,plain,
% 1.65/1.32 (($false | (~line_equal(b1c1, b2c2))) <=> (~line_equal(b1c1, b2c2))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(663,plain,
% 1.65/1.32 ((goal | (~line_equal(b1c1, b2c2))) <=> ($false | (~line_equal(b1c1, b2c2)))),
% 1.65/1.32 inference(monotonicity,[status(thm)],[44])).
% 1.65/1.32 tff(664,plain,
% 1.65/1.32 ((goal | (~line_equal(b1c1, b2c2))) <=> (~line_equal(b1c1, b2c2))),
% 1.65/1.32 inference(transitivity,[status(thm)],[663, 662])).
% 1.65/1.32 tff(665,plain,
% 1.65/1.32 ((line_equal(b1c1, b2c2) => goal) <=> (goal | (~line_equal(b1c1, b2c2)))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(666,axiom,(line_equal(b1c1, b2c2) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notbc')).
% 1.65/1.32 tff(667,plain,
% 1.65/1.32 (goal | (~line_equal(b1c1, b2c2))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[666, 665])).
% 1.65/1.32 tff(668,plain,
% 1.65/1.32 (~line_equal(b1c1, b2c2)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[667, 664])).
% 1.65/1.32 tff(669,plain,
% 1.65/1.32 (~line_equal(b1c1, b2c2)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[668, 661])).
% 1.65/1.32 tff(670,plain,
% 1.65/1.32 (incident(bc, b1c1) <=> incident(bc, b1c1)),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(671,axiom,(incident(bc, b1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ibc1')).
% 1.65/1.32 tff(672,plain,
% 1.65/1.32 (incident(bc, b1c1)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[671, 670])).
% 1.65/1.32 tff(673,plain,
% 1.65/1.32 (((~![A: $i, B: $i, 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))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(674,plain,
% 1.65/1.32 ((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))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(675,plain,
% 1.65/1.32 (((~![A: $i, B: $i, 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)))),
% 1.65/1.32 inference(monotonicity,[status(thm)],[674])).
% 1.65/1.32 tff(676,plain,
% 1.65/1.32 (((~![A: $i, B: $i, 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))),
% 1.65/1.32 inference(transitivity,[status(thm)],[675, 673])).
% 1.65/1.32 tff(677,plain,
% 1.65/1.32 ((~![A: $i, B: $i, 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)))),
% 1.65/1.32 inference(quant_inst,[status(thm)],[])).
% 1.65/1.32 tff(678,plain,
% 1.65/1.32 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(b1c1, b2c2) | (~incident(b2, b1c1)) | (~incident(b2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, b2)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[677, 676])).
% 1.65/1.32 tff(679,plain,
% 1.65/1.32 ($false),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[678, 18, 672, 105, 669, 40, 660, 659])).
% 1.65/1.32 tff(680,plain,(point_equal(bc, b2) | (~incident(b2, b1c1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.32 tff(681,plain,
% 1.65/1.32 (~incident(b2, b1c1)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[680, 658])).
% 1.65/1.32 tff(682,assumption,(point_equal(b2, c1)), introduced(assumption)).
% 1.65/1.32 tff(683,assumption,(~incident(b2, b1c1)), introduced(assumption)).
% 1.65/1.32 tff(684,plain,
% 1.65/1.32 (incident(c1, b1c1) <=> incident(c1, b1c1)),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(685,axiom,(incident(c1, b1c1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ic1b1')).
% 1.65/1.32 tff(686,plain,
% 1.65/1.32 (incident(c1, b1c1)),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[685, 684])).
% 1.65/1.32 tff(687,plain,
% 1.65/1.32 (((~![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)))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(688,plain,
% 1.65/1.32 ((~![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)))),
% 1.65/1.32 inference(quant_inst,[status(thm)],[])).
% 1.65/1.32 tff(689,plain,
% 1.65/1.32 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(b2, b1c1) | (~incident(c1, b1c1)) | (~point_equal(b2, c1))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[688, 687])).
% 1.65/1.32 tff(690,plain,
% 1.65/1.32 ($false),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[689, 686, 171, 683, 682])).
% 1.65/1.32 tff(691,plain,(incident(b2, b1c1) | (~point_equal(b2, c1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.32 tff(692,plain,
% 1.65/1.32 (~point_equal(b2, c1)),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[691, 681])).
% 1.65/1.32 tff(693,plain,
% 1.65/1.32 (((~![A: $i, B: $i, 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, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, oc)) | (~incident(b2, oc)) | point_equal(b2, c1) | line_equal(a1c1, 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(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, oc)) | (~incident(b2, oc)) | point_equal(b2, c1) | line_equal(a1c1, oc))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(694,plain,
% 1.65/1.32 ((line_equal(a1c1, oc) | point_equal(b2, c1) | (~incident(c1, a1c1)) | (~incident(b2, a1c1)) | (~incident(b2, oc)) | (~incident(c1, oc))) <=> ((~incident(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, oc)) | (~incident(b2, oc)) | point_equal(b2, c1) | line_equal(a1c1, oc))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(695,plain,
% 1.65/1.32 (((~![A: $i, B: $i, 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, oc) | point_equal(b2, c1) | (~incident(c1, a1c1)) | (~incident(b2, a1c1)) | (~incident(b2, 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(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, oc)) | (~incident(b2, oc)) | point_equal(b2, c1) | line_equal(a1c1, oc)))),
% 1.65/1.32 inference(monotonicity,[status(thm)],[694])).
% 1.65/1.32 tff(696,plain,
% 1.65/1.32 (((~![A: $i, B: $i, 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, oc) | point_equal(b2, c1) | (~incident(c1, a1c1)) | (~incident(b2, a1c1)) | (~incident(b2, 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(b2, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, oc)) | (~incident(b2, oc)) | point_equal(b2, c1) | line_equal(a1c1, oc))),
% 1.65/1.33 inference(transitivity,[status(thm)],[695, 693])).
% 1.65/1.33 tff(697,plain,
% 1.65/1.33 ((~![A: $i, B: $i, 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, oc) | point_equal(b2, c1) | (~incident(c1, a1c1)) | (~incident(b2, a1c1)) | (~incident(b2, oc)) | (~incident(c1, oc)))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(698,plain,
% 1.65/1.33 ((~![A: $i, B: $i, 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, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, oc)) | (~incident(b2, oc)) | point_equal(b2, c1) | line_equal(a1c1, oc)),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[697, 696])).
% 1.65/1.33 tff(699,plain,
% 1.65/1.33 (~incident(b2, oc)),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[698, 595, 386, 306, 40, 692, 526])).
% 1.65/1.33 tff(700,plain,
% 1.65/1.33 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, oc)) | incident(b2, oc) | (~point_equal(b2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oc)) | incident(b2, oc) | (~point_equal(b2, o)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(701,plain,
% 1.65/1.33 ((incident(b2, oc) | (~incident(o, oc)) | (~point_equal(b2, o))) <=> ((~incident(o, oc)) | incident(b2, oc) | (~point_equal(b2, o)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(702,plain,
% 1.65/1.33 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, oc) | (~incident(o, oc)) | (~point_equal(b2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, oc)) | incident(b2, oc) | (~point_equal(b2, o))))),
% 1.65/1.33 inference(monotonicity,[status(thm)],[701])).
% 1.65/1.33 tff(703,plain,
% 1.65/1.33 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, oc) | (~incident(o, oc)) | (~point_equal(b2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oc)) | incident(b2, oc) | (~point_equal(b2, o)))),
% 1.65/1.33 inference(transitivity,[status(thm)],[702, 700])).
% 1.65/1.33 tff(704,plain,
% 1.65/1.33 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(b2, oc) | (~incident(o, oc)) | (~point_equal(b2, o)))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(705,plain,
% 1.65/1.33 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oc)) | incident(b2, oc) | (~point_equal(b2, o))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[704, 703])).
% 1.65/1.33 tff(706,plain,
% 1.65/1.33 (~point_equal(b2, o)),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[705, 320, 171, 699])).
% 1.65/1.33 tff(707,assumption,(~incident(a1, a2b2)), introduced(assumption)).
% 1.65/1.33 tff(708,plain,
% 1.65/1.33 (((~![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)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(709,plain,
% 1.65/1.33 ((incident(a1, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(a1, a1c1))) <=> ((~incident(a1, a1c1)) | incident(a1, a2b2) | (~line_equal(a1c1, a2b2)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(710,plain,
% 1.65/1.33 (((~![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))))),
% 1.65/1.33 inference(monotonicity,[status(thm)],[709])).
% 1.65/1.33 tff(711,plain,
% 1.65/1.33 (((~![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)))),
% 1.65/1.33 inference(transitivity,[status(thm)],[710, 708])).
% 1.65/1.33 tff(712,plain,
% 1.65/1.33 ((~![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)))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(713,plain,
% 1.65/1.33 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a1, a1c1)) | incident(a1, a2b2) | (~line_equal(a1c1, a2b2))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[712, 711])).
% 1.65/1.33 tff(714,plain,
% 1.65/1.33 ($false),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[713, 197, 15, 707, 629])).
% 1.65/1.33 tff(715,plain,(incident(a1, a2b2) | (~line_equal(a1c1, a2b2))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.33 tff(716,plain,
% 1.65/1.33 (incident(a1, a2b2)),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[715, 628])).
% 1.65/1.33 tff(717,plain,
% 1.65/1.33 (((~![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)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(718,plain,
% 1.65/1.33 ((incident(b1, a1c1) | (~incident(a1, a1c1)) | (~point_equal(b1, a1))) <=> ((~incident(a1, a1c1)) | incident(b1, a1c1) | (~point_equal(b1, a1)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(719,plain,
% 1.65/1.33 (((~![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))))),
% 1.65/1.33 inference(monotonicity,[status(thm)],[718])).
% 1.65/1.33 tff(720,plain,
% 1.65/1.33 (((~![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)))),
% 1.65/1.33 inference(transitivity,[status(thm)],[719, 717])).
% 1.65/1.33 tff(721,plain,
% 1.65/1.33 ((~![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)))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(722,plain,
% 1.65/1.33 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, a1c1)) | incident(b1, a1c1) | (~point_equal(b1, a1))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[721, 720])).
% 1.65/1.33 tff(723,plain,
% 1.65/1.33 (~point_equal(b1, a1)),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[722, 197, 171, 502])).
% 1.65/1.33 tff(724,plain,
% 1.65/1.33 ((~line_equal(a1b1, a2b2)) <=> (~line_equal(a1b1, a2b2))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(725,plain,
% 1.65/1.33 (($false | (~line_equal(a1b1, a2b2))) <=> (~line_equal(a1b1, a2b2))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(726,plain,
% 1.65/1.33 ((goal | (~line_equal(a1b1, a2b2))) <=> ($false | (~line_equal(a1b1, a2b2)))),
% 1.65/1.33 inference(monotonicity,[status(thm)],[44])).
% 1.65/1.33 tff(727,plain,
% 1.65/1.33 ((goal | (~line_equal(a1b1, a2b2))) <=> (~line_equal(a1b1, a2b2))),
% 1.65/1.33 inference(transitivity,[status(thm)],[726, 725])).
% 1.65/1.33 tff(728,plain,
% 1.65/1.33 ((line_equal(a1b1, a2b2) => goal) <=> (goal | (~line_equal(a1b1, a2b2)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(729,axiom,(line_equal(a1b1, a2b2) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notab')).
% 1.65/1.33 tff(730,plain,
% 1.65/1.33 (goal | (~line_equal(a1b1, a2b2))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[729, 728])).
% 1.65/1.33 tff(731,plain,
% 1.65/1.33 (~line_equal(a1b1, a2b2)),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[730, 727])).
% 1.65/1.33 tff(732,plain,
% 1.65/1.33 (~line_equal(a1b1, a2b2)),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[731, 724])).
% 1.65/1.33 tff(733,plain,
% 1.65/1.33 (((~![A: $i, B: $i, 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))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(734,plain,
% 1.65/1.33 ((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))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(735,plain,
% 1.65/1.33 (((~![A: $i, B: $i, 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)))),
% 1.65/1.33 inference(monotonicity,[status(thm)],[734])).
% 1.65/1.33 tff(736,plain,
% 1.65/1.33 (((~![A: $i, B: $i, 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))),
% 1.65/1.33 inference(transitivity,[status(thm)],[735, 733])).
% 1.65/1.33 tff(737,plain,
% 1.65/1.33 ((~![A: $i, B: $i, 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)))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(738,plain,
% 1.65/1.33 ((~![A: $i, B: $i, 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)),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[737, 736])).
% 1.65/1.33 tff(739,plain,
% 1.65/1.33 ((~incident(a1, a2b2)) | (~incident(b1, a2b2))),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[738, 127, 60, 732, 40, 723])).
% 1.65/1.33 tff(740,plain,
% 1.65/1.33 (~incident(b1, a2b2)),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[739, 716])).
% 1.65/1.33 tff(741,plain,
% 1.65/1.33 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, a2b2) | (~incident(b1, ob)) | (~line_equal(ob, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b1, a2b2) | (~incident(b1, ob)) | (~line_equal(ob, a2b2)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(742,plain,
% 1.65/1.33 ((incident(b1, a2b2) | (~line_equal(ob, a2b2)) | (~incident(b1, ob))) <=> (incident(b1, a2b2) | (~incident(b1, ob)) | (~line_equal(ob, a2b2)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(743,plain,
% 1.65/1.33 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, a2b2) | (~line_equal(ob, a2b2)) | (~incident(b1, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, a2b2) | (~incident(b1, ob)) | (~line_equal(ob, a2b2))))),
% 1.65/1.33 inference(monotonicity,[status(thm)],[742])).
% 1.65/1.33 tff(744,plain,
% 1.65/1.33 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, a2b2) | (~line_equal(ob, a2b2)) | (~incident(b1, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b1, a2b2) | (~incident(b1, ob)) | (~line_equal(ob, a2b2)))),
% 1.65/1.33 inference(transitivity,[status(thm)],[743, 741])).
% 1.65/1.33 tff(745,plain,
% 1.65/1.33 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(b1, a2b2) | (~line_equal(ob, a2b2)) | (~incident(b1, ob)))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(746,plain,
% 1.65/1.33 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(b1, a2b2) | (~incident(b1, ob)) | (~line_equal(ob, a2b2))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[745, 744])).
% 1.65/1.33 tff(747,plain,
% 1.65/1.33 (incident(b1, a2b2) | (~line_equal(ob, a2b2))),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[746, 57, 15])).
% 1.65/1.33 tff(748,plain,
% 1.65/1.33 (~line_equal(ob, a2b2)),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[747, 740])).
% 1.65/1.33 tff(749,plain,
% 1.65/1.33 (((~![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))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(750,plain,
% 1.65/1.33 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a2b2, ob)) | line_equal(ob, a2b2))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(751,plain,
% 1.65/1.33 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a2b2, ob)) | line_equal(ob, a2b2)),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[750, 749])).
% 1.65/1.33 tff(752,plain,
% 1.65/1.33 (~line_equal(a2b2, ob)),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[751, 97, 748])).
% 1.65/1.33 tff(753,plain,
% 1.65/1.33 (((~![A: $i, B: $i, 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(o, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob) | (~incident(o, a2b2)) | point_equal(b2, 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(b2, a2b2)) | (~incident(o, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob) | (~incident(o, a2b2)) | point_equal(b2, o))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(754,plain,
% 1.65/1.33 ((line_equal(a2b2, ob) | point_equal(b2, o) | (~incident(o, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(o, ob))) <=> ((~incident(b2, a2b2)) | (~incident(o, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob) | (~incident(o, a2b2)) | point_equal(b2, o))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(755,plain,
% 1.65/1.33 (((~![A: $i, B: $i, 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, o) | (~incident(o, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(o, 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(b2, a2b2)) | (~incident(o, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob) | (~incident(o, a2b2)) | point_equal(b2, o)))),
% 1.65/1.33 inference(monotonicity,[status(thm)],[754])).
% 1.65/1.33 tff(756,plain,
% 1.65/1.33 (((~![A: $i, B: $i, 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, o) | (~incident(o, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(o, 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(b2, a2b2)) | (~incident(o, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob) | (~incident(o, a2b2)) | point_equal(b2, o))),
% 1.65/1.33 inference(transitivity,[status(thm)],[755, 753])).
% 1.65/1.33 tff(757,plain,
% 1.65/1.33 ((~![A: $i, B: $i, 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, o) | (~incident(o, a2b2)) | (~incident(b2, a2b2)) | (~incident(b2, ob)) | (~incident(o, ob)))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(758,plain,
% 1.65/1.33 ((~![A: $i, B: $i, 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(o, ob)) | (~incident(b2, ob)) | line_equal(a2b2, ob) | (~incident(o, a2b2)) | point_equal(b2, o)),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[757, 756])).
% 1.65/1.33 tff(759,plain,
% 1.65/1.33 (~incident(o, a2b2)),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[758, 234, 333, 54, 40, 752, 706])).
% 1.65/1.33 tff(760,plain,
% 1.65/1.33 (((~![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))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(761,plain,
% 1.65/1.33 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a1c1, a2b2)) | line_equal(a2b2, a1c1))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(762,plain,
% 1.65/1.33 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a1c1, a2b2)) | line_equal(a2b2, a1c1)),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[761, 760])).
% 1.65/1.33 tff(763,plain,
% 1.65/1.33 (line_equal(a2b2, a1c1)),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[762, 97, 628])).
% 1.65/1.33 tff(764,assumption,(line_equal(a2b2, a1c1)), introduced(assumption)).
% 1.65/1.33 tff(765,assumption,(~incident(a2, a1c1)), introduced(assumption)).
% 1.65/1.33 tff(766,plain,
% 1.65/1.33 (((~![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)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(767,plain,
% 1.65/1.33 ((incident(a2, a1c1) | (~line_equal(a2b2, a1c1)) | (~incident(a2, a2b2))) <=> (incident(a2, a1c1) | (~incident(a2, a2b2)) | (~line_equal(a2b2, a1c1)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(768,plain,
% 1.65/1.33 (((~![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))))),
% 1.65/1.33 inference(monotonicity,[status(thm)],[767])).
% 1.65/1.33 tff(769,plain,
% 1.65/1.33 (((~![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)))),
% 1.65/1.33 inference(transitivity,[status(thm)],[768, 766])).
% 1.65/1.33 tff(770,plain,
% 1.65/1.33 ((~![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)))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(771,plain,
% 1.65/1.33 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(a2, a1c1) | (~incident(a2, a2b2)) | (~line_equal(a2b2, a1c1))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[770, 769])).
% 1.65/1.33 tff(772,plain,
% 1.65/1.33 ($false),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[771, 237, 15, 765, 764])).
% 1.65/1.33 tff(773,plain,(incident(a2, a1c1) | (~line_equal(a2b2, a1c1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.33 tff(774,plain,
% 1.65/1.33 (incident(a2, a1c1)),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[773, 763])).
% 1.65/1.33 tff(775,assumption,(~point_equal(ac, a2)), introduced(assumption)).
% 1.65/1.33 tff(776,assumption,(incident(a2, a1c1)), introduced(assumption)).
% 1.65/1.33 tff(777,plain,
% 1.65/1.33 (((~![A: $i, B: $i, 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(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, 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(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, a2))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(778,plain,
% 1.65/1.33 ((line_equal(a1c1, a2c2) | point_equal(ac, a2) | (~incident(a2, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | (~incident(a2, a2c2))) <=> (line_equal(a1c1, a2c2) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, a2))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(779,plain,
% 1.65/1.33 (((~![A: $i, B: $i, 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, a2) | (~incident(a2, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, 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(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, a2)))),
% 1.65/1.33 inference(monotonicity,[status(thm)],[778])).
% 1.65/1.33 tff(780,plain,
% 1.65/1.33 (((~![A: $i, B: $i, 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, a2) | (~incident(a2, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, 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(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, a2))),
% 1.65/1.33 inference(transitivity,[status(thm)],[779, 777])).
% 1.65/1.33 tff(781,plain,
% 1.65/1.33 ((~![A: $i, B: $i, 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, a2) | (~incident(a2, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | (~incident(a2, a2c2)))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(782,plain,
% 1.65/1.33 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1c1, a2c2) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(ac, a1c1)) | (~incident(ac, a2c2)) | point_equal(ac, a2)),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.65/1.33 tff(783,plain,
% 1.65/1.33 ($false),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[782, 257, 194, 191, 188, 40, 776, 775])).
% 1.65/1.33 tff(784,plain,(point_equal(ac, a2) | (~incident(a2, a1c1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.33 tff(785,plain,
% 1.65/1.33 (point_equal(ac, a2)),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[784, 774])).
% 1.65/1.33 tff(786,assumption,(point_equal(ac, a2)), introduced(assumption)).
% 1.65/1.33 tff(787,assumption,(~incident(ac, oa)), introduced(assumption)).
% 1.65/1.33 tff(788,plain,
% 1.65/1.33 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, oa)) | incident(ac, oa) | (~point_equal(ac, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, oa)) | incident(ac, oa) | (~point_equal(ac, a2)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(789,plain,
% 1.65/1.34 ((incident(ac, oa) | (~incident(a2, oa)) | (~point_equal(ac, a2))) <=> ((~incident(a2, oa)) | incident(ac, oa) | (~point_equal(ac, a2)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(790,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, oa) | (~incident(a2, oa)) | (~point_equal(ac, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, oa)) | incident(ac, oa) | (~point_equal(ac, a2))))),
% 1.65/1.34 inference(monotonicity,[status(thm)],[789])).
% 1.65/1.34 tff(791,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, oa) | (~incident(a2, oa)) | (~point_equal(ac, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, oa)) | incident(ac, oa) | (~point_equal(ac, a2)))),
% 1.65/1.34 inference(transitivity,[status(thm)],[790, 788])).
% 1.65/1.34 tff(792,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, oa) | (~incident(a2, oa)) | (~point_equal(ac, a2)))),
% 1.65/1.34 inference(quant_inst,[status(thm)],[])).
% 1.65/1.34 tff(793,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, oa)) | incident(ac, oa) | (~point_equal(ac, a2))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[792, 791])).
% 1.65/1.34 tff(794,plain,
% 1.65/1.34 ($false),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[793, 251, 171, 787, 786])).
% 1.65/1.34 tff(795,plain,(incident(ac, oa) | (~point_equal(ac, a2))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.34 tff(796,plain,
% 1.65/1.34 (incident(ac, oa)),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[795, 785])).
% 1.65/1.34 tff(797,assumption,(~point_equal(ab, a1)), introduced(assumption)).
% 1.65/1.34 tff(798,assumption,(incident(a1, a2b2)), introduced(assumption)).
% 1.65/1.34 tff(799,plain,
% 1.65/1.34 (((~![A: $i, B: $i, 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))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(800,plain,
% 1.65/1.34 ((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))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(801,plain,
% 1.65/1.34 (((~![A: $i, B: $i, 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)))),
% 1.65/1.34 inference(monotonicity,[status(thm)],[800])).
% 1.65/1.34 tff(802,plain,
% 1.65/1.34 (((~![A: $i, B: $i, 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))),
% 1.65/1.34 inference(transitivity,[status(thm)],[801, 799])).
% 1.65/1.34 tff(803,plain,
% 1.65/1.34 ((~![A: $i, B: $i, 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)))),
% 1.65/1.34 inference(quant_inst,[status(thm)],[])).
% 1.65/1.34 tff(804,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, a1)),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[803, 802])).
% 1.65/1.34 tff(805,plain,
% 1.65/1.34 ($false),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[804, 127, 134, 646, 732, 40, 798, 797])).
% 1.65/1.34 tff(806,plain,(point_equal(ab, a1) | (~incident(a1, a2b2))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.34 tff(807,plain,
% 1.65/1.34 (point_equal(ab, a1)),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[806, 716])).
% 1.65/1.34 tff(808,assumption,(point_equal(ab, a1)), introduced(assumption)).
% 1.65/1.34 tff(809,assumption,(~incident(ab, oa)), introduced(assumption)).
% 1.65/1.34 tff(810,plain,
% 1.65/1.34 (((~![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)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(811,plain,
% 1.65/1.34 ((incident(ab, oa) | (~incident(a1, oa)) | (~point_equal(ab, a1))) <=> ((~incident(a1, oa)) | incident(ab, oa) | (~point_equal(ab, a1)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(812,plain,
% 1.65/1.34 (((~![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))))),
% 1.65/1.34 inference(monotonicity,[status(thm)],[811])).
% 1.65/1.34 tff(813,plain,
% 1.65/1.34 (((~![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)))),
% 1.65/1.34 inference(transitivity,[status(thm)],[812, 810])).
% 1.65/1.34 tff(814,plain,
% 1.65/1.34 ((~![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)))),
% 1.65/1.34 inference(quant_inst,[status(thm)],[])).
% 1.65/1.34 tff(815,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a1, oa)) | incident(ab, oa) | (~point_equal(ab, a1))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[814, 813])).
% 1.65/1.34 tff(816,plain,
% 1.65/1.34 ($false),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[815, 207, 171, 809, 808])).
% 1.65/1.34 tff(817,plain,(incident(ab, oa) | (~point_equal(ab, a1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.34 tff(818,plain,
% 1.65/1.34 (incident(ab, oa)),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[817, 807])).
% 1.65/1.34 tff(819,assumption,(~incident(ab, a1c1)), introduced(assumption)).
% 1.65/1.34 tff(820,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, a1c1) | (~incident(ab, a2b2)) | (~line_equal(a2b2, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ab, a1c1) | (~incident(ab, a2b2)) | (~line_equal(a2b2, a1c1)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(821,plain,
% 1.65/1.34 ((incident(ab, a1c1) | (~line_equal(a2b2, a1c1)) | (~incident(ab, a2b2))) <=> (incident(ab, a1c1) | (~incident(ab, a2b2)) | (~line_equal(a2b2, a1c1)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(822,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, a1c1) | (~line_equal(a2b2, a1c1)) | (~incident(ab, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, a1c1) | (~incident(ab, a2b2)) | (~line_equal(a2b2, a1c1))))),
% 1.65/1.34 inference(monotonicity,[status(thm)],[821])).
% 1.65/1.34 tff(823,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, a1c1) | (~line_equal(a2b2, a1c1)) | (~incident(ab, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ab, a1c1) | (~incident(ab, a2b2)) | (~line_equal(a2b2, a1c1)))),
% 1.65/1.34 inference(transitivity,[status(thm)],[822, 820])).
% 1.65/1.34 tff(824,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, a1c1) | (~line_equal(a2b2, a1c1)) | (~incident(ab, a2b2)))),
% 1.65/1.34 inference(quant_inst,[status(thm)],[])).
% 1.65/1.34 tff(825,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ab, a1c1) | (~incident(ab, a2b2)) | (~line_equal(a2b2, a1c1))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[824, 823])).
% 1.65/1.34 tff(826,plain,
% 1.65/1.34 ($false),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[825, 646, 15, 819, 764])).
% 1.65/1.34 tff(827,plain,(incident(ab, a1c1) | (~line_equal(a2b2, a1c1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.34 tff(828,plain,
% 1.65/1.34 (incident(ab, a1c1)),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[827, 763])).
% 1.65/1.34 tff(829,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, a1b1) | (~incident(ab, a1b1)) | (~point_equal(a2, ab)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a2, a1b1) | (~incident(ab, a1b1)) | (~point_equal(a2, ab)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(830,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, a1b1) | (~incident(ab, a1b1)) | (~point_equal(a2, ab)))),
% 1.65/1.34 inference(quant_inst,[status(thm)],[])).
% 1.65/1.34 tff(831,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a2, a1b1) | (~incident(ab, a1b1)) | (~point_equal(a2, ab))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[830, 829])).
% 1.65/1.34 tff(832,plain,
% 1.65/1.34 (~point_equal(a2, ab)),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[831, 134, 171, 527])).
% 1.65/1.34 tff(833,plain,
% 1.65/1.34 (((~![A: $i, B: $i, 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(ab, a1c1)) | (~incident(ab, a2c2)) | point_equal(a2, 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)))) | line_equal(a1c1, a2c2) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(ab, a1c1)) | (~incident(ab, a2c2)) | point_equal(a2, ab))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(834,plain,
% 1.65/1.34 ((line_equal(a1c1, a2c2) | point_equal(a2, ab) | (~incident(ab, a1c1)) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(ab, a2c2))) <=> (line_equal(a1c1, a2c2) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(ab, a1c1)) | (~incident(ab, a2c2)) | point_equal(a2, ab))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(835,plain,
% 1.65/1.34 (((~![A: $i, B: $i, 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(a2, ab) | (~incident(ab, a1c1)) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(ab, 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(ab, a1c1)) | (~incident(ab, a2c2)) | point_equal(a2, ab)))),
% 1.65/1.34 inference(monotonicity,[status(thm)],[834])).
% 1.65/1.34 tff(836,plain,
% 1.65/1.34 (((~![A: $i, B: $i, 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(a2, ab) | (~incident(ab, a1c1)) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(ab, 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(ab, a1c1)) | (~incident(ab, a2c2)) | point_equal(a2, ab))),
% 1.65/1.34 inference(transitivity,[status(thm)],[835, 833])).
% 1.65/1.34 tff(837,plain,
% 1.65/1.34 ((~![A: $i, B: $i, 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(a2, ab) | (~incident(ab, a1c1)) | (~incident(a2, a1c1)) | (~incident(a2, a2c2)) | (~incident(ab, a2c2)))),
% 1.65/1.34 inference(quant_inst,[status(thm)],[])).
% 1.65/1.34 tff(838,plain,
% 1.65/1.34 ((~![A: $i, B: $i, 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(ab, a1c1)) | (~incident(ab, a2c2)) | point_equal(a2, ab)),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[837, 836])).
% 1.65/1.34 tff(839,plain,
% 1.65/1.34 ((~incident(a2, a1c1)) | (~incident(ab, a1c1)) | (~incident(ab, a2c2))),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[838, 257, 188, 40, 832])).
% 1.65/1.34 tff(840,plain,
% 1.65/1.34 (~incident(ab, a2c2)),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[839, 828, 774])).
% 1.65/1.34 tff(841,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(ac, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, ac)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(ac, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, ac)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(842,plain,
% 1.65/1.34 ((incident(ab, a2c2) | (~incident(ac, a2c2)) | (~point_equal(ab, ac))) <=> ((~incident(ac, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, ac)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(843,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, a2c2) | (~incident(ac, a2c2)) | (~point_equal(ab, ac)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(ac, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, ac))))),
% 1.65/1.34 inference(monotonicity,[status(thm)],[842])).
% 1.65/1.34 tff(844,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, a2c2) | (~incident(ac, a2c2)) | (~point_equal(ab, ac)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(ac, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, ac)))),
% 1.65/1.34 inference(transitivity,[status(thm)],[843, 841])).
% 1.65/1.34 tff(845,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ab, a2c2) | (~incident(ac, a2c2)) | (~point_equal(ab, ac)))),
% 1.65/1.34 inference(quant_inst,[status(thm)],[])).
% 1.65/1.34 tff(846,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(ac, a2c2)) | incident(ab, a2c2) | (~point_equal(ab, ac))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[845, 844])).
% 1.65/1.34 tff(847,plain,
% 1.65/1.34 (~point_equal(ab, ac)),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[846, 191, 171, 840])).
% 1.65/1.34 tff(848,plain,
% 1.65/1.34 (((~![A: $i, B: $i, 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(ac, a2b2)) | (~incident(ab, a2b2)) | (~incident(ac, oa)) | (~incident(ab, oa)) | line_equal(oa, a2b2) | point_equal(ab, ac))) <=> ((~![A: $i, B: $i, 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(ac, a2b2)) | (~incident(ab, a2b2)) | (~incident(ac, oa)) | (~incident(ab, oa)) | line_equal(oa, a2b2) | point_equal(ab, ac))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(849,plain,
% 1.65/1.34 ((line_equal(oa, a2b2) | point_equal(ab, ac) | (~incident(ac, oa)) | (~incident(ab, oa)) | (~incident(ab, a2b2)) | (~incident(ac, a2b2))) <=> ((~incident(ac, a2b2)) | (~incident(ab, a2b2)) | (~incident(ac, oa)) | (~incident(ab, oa)) | line_equal(oa, a2b2) | point_equal(ab, ac))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(850,plain,
% 1.65/1.34 (((~![A: $i, B: $i, 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(ab, ac) | (~incident(ac, oa)) | (~incident(ab, oa)) | (~incident(ab, a2b2)) | (~incident(ac, 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(ac, a2b2)) | (~incident(ab, a2b2)) | (~incident(ac, oa)) | (~incident(ab, oa)) | line_equal(oa, a2b2) | point_equal(ab, ac)))),
% 1.65/1.34 inference(monotonicity,[status(thm)],[849])).
% 1.65/1.34 tff(851,plain,
% 1.65/1.34 (((~![A: $i, B: $i, 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(ab, ac) | (~incident(ac, oa)) | (~incident(ab, oa)) | (~incident(ab, a2b2)) | (~incident(ac, 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(ac, a2b2)) | (~incident(ab, a2b2)) | (~incident(ac, oa)) | (~incident(ab, oa)) | line_equal(oa, a2b2) | point_equal(ab, ac))),
% 1.65/1.34 inference(transitivity,[status(thm)],[850, 848])).
% 1.65/1.34 tff(852,plain,
% 1.65/1.34 ((~![A: $i, B: $i, 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(ab, ac) | (~incident(ac, oa)) | (~incident(ab, oa)) | (~incident(ab, a2b2)) | (~incident(ac, a2b2)))),
% 1.65/1.34 inference(quant_inst,[status(thm)],[])).
% 1.65/1.34 tff(853,plain,
% 1.65/1.34 ((~![A: $i, B: $i, 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(ac, a2b2)) | (~incident(ab, a2b2)) | (~incident(ac, oa)) | (~incident(ab, oa)) | line_equal(oa, a2b2) | point_equal(ab, ac)),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[852, 851])).
% 1.65/1.34 tff(854,plain,
% 1.65/1.34 ((~incident(ac, a2b2)) | (~incident(ac, oa)) | (~incident(ab, oa)) | line_equal(oa, a2b2) | point_equal(ab, ac)),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[853, 646, 40])).
% 1.65/1.34 tff(855,plain,
% 1.65/1.34 (line_equal(oa, a2b2)),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[854, 847, 639, 818, 796])).
% 1.65/1.34 tff(856,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oa)) | incident(o, a2b2) | (~line_equal(oa, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a2b2) | (~line_equal(oa, a2b2)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(857,plain,
% 1.65/1.34 ((incident(o, a2b2) | (~line_equal(oa, a2b2)) | (~incident(o, oa))) <=> ((~incident(o, oa)) | incident(o, a2b2) | (~line_equal(oa, a2b2)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(858,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2b2) | (~line_equal(oa, a2b2)) | (~incident(o, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oa)) | incident(o, a2b2) | (~line_equal(oa, a2b2))))),
% 1.65/1.34 inference(monotonicity,[status(thm)],[857])).
% 1.65/1.34 tff(859,plain,
% 1.65/1.34 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2b2) | (~line_equal(oa, a2b2)) | (~incident(o, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a2b2) | (~line_equal(oa, a2b2)))),
% 1.65/1.34 inference(transitivity,[status(thm)],[858, 856])).
% 1.65/1.34 tff(860,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2b2) | (~line_equal(oa, a2b2)) | (~incident(o, oa)))),
% 1.65/1.34 inference(quant_inst,[status(thm)],[])).
% 1.65/1.34 tff(861,plain,
% 1.65/1.34 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a2b2) | (~line_equal(oa, a2b2))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[860, 859])).
% 1.65/1.34 tff(862,plain,
% 1.65/1.34 ($false),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[861, 268, 15, 855, 759])).
% 1.65/1.34 tff(863,plain,(incident(a2, a1b1) | line_equal(a1c1, oc) | line_equal(a2c2, b1c1) | point_equal(c1, b2) | line_equal(b2c2, a1b1) | point_equal(c2, a1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.34 tff(864,plain,
% 1.65/1.34 (incident(a2, a1b1)),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[863, 525, 343, 526, 342, 524])).
% 1.65/1.34 tff(865,plain,
% 1.65/1.34 ((~point_equal(a2, a1)) <=> (~point_equal(a2, a1))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(866,plain,
% 1.65/1.34 (($false | (~point_equal(a2, a1))) <=> (~point_equal(a2, a1))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(867,plain,
% 1.65/1.34 ((goal | (~point_equal(a2, a1))) <=> ($false | (~point_equal(a2, a1)))),
% 1.65/1.34 inference(monotonicity,[status(thm)],[44])).
% 1.65/1.34 tff(868,plain,
% 1.65/1.34 ((goal | (~point_equal(a2, a1))) <=> (~point_equal(a2, a1))),
% 1.65/1.34 inference(transitivity,[status(thm)],[867, 866])).
% 1.65/1.34 tff(869,plain,
% 1.65/1.34 ((point_equal(a2, a1) => goal) <=> (goal | (~point_equal(a2, a1)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(870,axiom,(point_equal(a2, a1) => goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','notaa')).
% 1.65/1.34 tff(871,plain,
% 1.65/1.34 (goal | (~point_equal(a2, a1))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[870, 869])).
% 1.65/1.34 tff(872,plain,
% 1.65/1.34 (~point_equal(a2, a1)),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[871, 868])).
% 1.65/1.34 tff(873,plain,
% 1.65/1.34 (~point_equal(a2, a1)),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[872, 865])).
% 1.65/1.34 tff(874,plain,
% 1.65/1.34 (((~![A: $i, B: $i, 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) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, 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)))) | point_equal(a2, a1) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(a1, a2b2)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(875,plain,
% 1.65/1.34 ((line_equal(a1b1, a2b2) | point_equal(a2, a1) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(a1, a2b2))) <=> (point_equal(a2, a1) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(a1, a2b2)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(876,plain,
% 1.65/1.34 (((~![A: $i, B: $i, 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(a2, a1) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, 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)))) | (point_equal(a2, a1) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(a1, a2b2))))),
% 1.65/1.35 inference(monotonicity,[status(thm)],[875])).
% 1.65/1.35 tff(877,plain,
% 1.65/1.35 (((~![A: $i, B: $i, 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(a2, a1) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, 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)))) | point_equal(a2, a1) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(a1, a2b2)))),
% 1.65/1.35 inference(transitivity,[status(thm)],[876, 874])).
% 1.65/1.35 tff(878,plain,
% 1.65/1.35 ((~![A: $i, B: $i, 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(a2, a1) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(a1, a2b2)))),
% 1.65/1.35 inference(quant_inst,[status(thm)],[])).
% 1.65/1.35 tff(879,plain,
% 1.65/1.35 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | point_equal(a2, a1) | line_equal(a1b1, a2b2) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(a1, a2b2))),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[878, 877])).
% 1.65/1.35 tff(880,plain,
% 1.65/1.35 ((~incident(a2, a1b1)) | (~incident(a1, a2b2))),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[879, 127, 237, 873, 732, 40])).
% 1.65/1.35 tff(881,plain,
% 1.65/1.35 (~incident(a1, a2b2)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[880, 864])).
% 1.65/1.35 tff(882,plain,
% 1.65/1.35 (~line_equal(a1c1, a2b2)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[715, 881])).
% 1.65/1.35 tff(883,plain,
% 1.65/1.35 (~incident(a1, b2c2)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[590, 523, 343, 342, 524])).
% 1.65/1.35 tff(884,plain,
% 1.65/1.35 (~incident(b2, a1c1)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[627, 523, 343, 597, 525])).
% 1.65/1.35 tff(885,plain,
% 1.65/1.35 ($false),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[594, 884, 883])).
% 1.65/1.35 tff(886,plain,(point_equal(a2, b1) | line_equal(a2c2, b1c1) | line_equal(a1c1, a2b2) | point_equal(c1, b2) | line_equal(b2c2, a1b1) | point_equal(c2, a1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.35 tff(887,plain,
% 1.65/1.35 (point_equal(a2, b1)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[886, 882, 343, 525, 342, 524])).
% 1.65/1.35 tff(888,plain,
% 1.65/1.35 (^[A: $i, B: $i] : refl(((~point_equal(A, B)) | point_equal(B, A)) <=> ((~point_equal(A, B)) | point_equal(B, A)))),
% 1.65/1.35 inference(bind,[status(th)],[])).
% 1.65/1.35 tff(889,plain,
% 1.65/1.35 (![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A)) <=> ![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.65/1.35 inference(quant_intro,[status(thm)],[888])).
% 1.65/1.35 tff(890,plain,
% 1.65/1.35 (![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A)) <=> ![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(891,plain,
% 1.65/1.35 (^[A: $i, B: $i] : rewrite((point_equal(A, B) => point_equal(B, A)) <=> ((~point_equal(A, B)) | point_equal(B, A)))),
% 1.65/1.35 inference(bind,[status(th)],[])).
% 1.65/1.35 tff(892,plain,
% 1.65/1.35 (![A: $i, B: $i] : (point_equal(A, B) => point_equal(B, A)) <=> ![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.65/1.35 inference(quant_intro,[status(thm)],[891])).
% 1.65/1.35 tff(893,axiom,(![A: $i, B: $i] : (point_equal(A, B) => point_equal(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_of_point_equal')).
% 1.65/1.35 tff(894,plain,
% 1.65/1.35 (![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[893, 892])).
% 1.65/1.35 tff(895,plain,
% 1.65/1.35 (![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[894, 890])).
% 1.65/1.35 tff(896,plain,(
% 1.65/1.35 ![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.65/1.35 inference(skolemize,[status(sab)],[895])).
% 1.65/1.35 tff(897,plain,
% 1.65/1.35 (![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[896, 889])).
% 1.65/1.35 tff(898,plain,
% 1.65/1.35 (((~![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))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(899,plain,
% 1.65/1.35 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(a2, b1)) | point_equal(b1, a2))),
% 1.65/1.35 inference(quant_inst,[status(thm)],[])).
% 1.65/1.35 tff(900,plain,
% 1.65/1.35 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(a2, b1)) | point_equal(b1, a2)),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[899, 898])).
% 1.65/1.35 tff(901,plain,
% 1.65/1.35 (point_equal(b1, a2)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[900, 897, 887])).
% 1.65/1.35 tff(902,assumption,(point_equal(b1, a2)), introduced(assumption)).
% 1.65/1.35 tff(903,assumption,(~incident(b1, a2b2)), introduced(assumption)).
% 1.65/1.35 tff(904,plain,
% 1.65/1.35 (((~![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)))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(905,plain,
% 1.65/1.35 ((incident(b1, a2b2) | (~incident(a2, a2b2)) | (~point_equal(b1, a2))) <=> ((~incident(a2, a2b2)) | incident(b1, a2b2) | (~point_equal(b1, a2)))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(906,plain,
% 1.65/1.35 (((~![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))))),
% 1.65/1.35 inference(monotonicity,[status(thm)],[905])).
% 1.65/1.35 tff(907,plain,
% 1.65/1.35 (((~![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)))),
% 1.65/1.35 inference(transitivity,[status(thm)],[906, 904])).
% 1.65/1.35 tff(908,plain,
% 1.65/1.35 ((~![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)))),
% 1.65/1.35 inference(quant_inst,[status(thm)],[])).
% 1.65/1.35 tff(909,plain,
% 1.65/1.35 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2b2)) | incident(b1, a2b2) | (~point_equal(b1, a2))),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[908, 907])).
% 1.65/1.35 tff(910,plain,
% 1.65/1.35 ($false),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[909, 237, 171, 903, 902])).
% 1.65/1.35 tff(911,plain,(incident(b1, a2b2) | (~point_equal(b1, a2))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.35 tff(912,plain,
% 1.65/1.35 (incident(b1, a2b2)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[911, 901])).
% 1.65/1.35 tff(913,plain,
% 1.65/1.35 (((~![A: $i, B: $i, 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(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)))) | point_equal(b2, b1) | (~incident(b2, a2b2)) | (~incident(b1, a2b2)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(ob, a2b2))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(914,plain,
% 1.65/1.35 ((line_equal(ob, a2b2) | point_equal(b2, b1) | (~incident(b1, ob)) | (~incident(b2, ob)) | (~incident(b2, a2b2)) | (~incident(b1, a2b2))) <=> (point_equal(b2, b1) | (~incident(b2, a2b2)) | (~incident(b1, a2b2)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(ob, a2b2))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(915,plain,
% 1.65/1.35 (((~![A: $i, B: $i, 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, b1) | (~incident(b1, ob)) | (~incident(b2, ob)) | (~incident(b2, a2b2)) | (~incident(b1, 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)))) | (point_equal(b2, b1) | (~incident(b2, a2b2)) | (~incident(b1, a2b2)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(ob, a2b2)))),
% 1.65/1.35 inference(monotonicity,[status(thm)],[914])).
% 1.65/1.35 tff(916,plain,
% 1.65/1.35 (((~![A: $i, B: $i, 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, b1) | (~incident(b1, ob)) | (~incident(b2, ob)) | (~incident(b2, a2b2)) | (~incident(b1, 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)))) | point_equal(b2, b1) | (~incident(b2, a2b2)) | (~incident(b1, a2b2)) | (~incident(b1, ob)) | (~incident(b2, ob)) | line_equal(ob, a2b2))),
% 1.65/1.35 inference(transitivity,[status(thm)],[915, 913])).
% 1.65/1.35 tff(917,plain,
% 1.65/1.35 ((~![A: $i, B: $i, 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, b1) | (~incident(b1, ob)) | (~incident(b2, ob)) | (~incident(b2, a2b2)) | (~incident(b1, a2b2)))),
% 1.65/1.35 inference(quant_inst,[status(thm)],[])).
% 1.65/1.35 tff(918,plain,
% 1.65/1.35 ((~![A: $i, B: $i, 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(ob, a2b2)),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[917, 916])).
% 1.65/1.35 tff(919,plain,
% 1.65/1.35 ((~incident(b1, a2b2)) | line_equal(ob, a2b2)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[918, 234, 57, 54, 51, 40])).
% 1.65/1.35 tff(920,plain,
% 1.65/1.35 (line_equal(ob, a2b2)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[919, 912])).
% 1.65/1.35 tff(921,assumption,(~incident(o, a2b2)), introduced(assumption)).
% 1.65/1.35 tff(922,assumption,(line_equal(ob, a2b2)), introduced(assumption)).
% 1.65/1.35 tff(923,plain,
% 1.65/1.35 (((~![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)))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(924,plain,
% 1.65/1.35 ((incident(o, a2b2) | (~line_equal(ob, a2b2)) | (~incident(o, ob))) <=> ((~incident(o, ob)) | incident(o, a2b2) | (~line_equal(ob, a2b2)))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(925,plain,
% 1.65/1.35 (((~![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))))),
% 1.65/1.35 inference(monotonicity,[status(thm)],[924])).
% 1.65/1.35 tff(926,plain,
% 1.65/1.35 (((~![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)))),
% 1.65/1.35 inference(transitivity,[status(thm)],[925, 923])).
% 1.65/1.35 tff(927,plain,
% 1.65/1.35 ((~![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)))),
% 1.65/1.35 inference(quant_inst,[status(thm)],[])).
% 1.65/1.35 tff(928,plain,
% 1.65/1.35 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, ob)) | incident(o, a2b2) | (~line_equal(ob, a2b2))),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[927, 926])).
% 1.65/1.35 tff(929,plain,
% 1.65/1.35 ($false),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[928, 333, 15, 922, 921])).
% 1.65/1.35 tff(930,plain,(incident(o, a2b2) | (~line_equal(ob, a2b2))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.35 tff(931,plain,
% 1.65/1.35 (incident(o, a2b2)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[930, 920])).
% 1.65/1.35 tff(932,assumption,(~point_equal(a2, o)), introduced(assumption)).
% 1.65/1.35 tff(933,assumption,(incident(o, a2b2)), introduced(assumption)).
% 1.65/1.35 tff(934,assumption,(incident(a2, a1b1)), introduced(assumption)).
% 1.65/1.35 tff(935,plain,
% 1.65/1.35 (((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(a1, a2)) | point_equal(a2, a1))) <=> ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(a1, a2)) | point_equal(a2, a1))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(936,plain,
% 1.65/1.35 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(a1, a2)) | point_equal(a2, a1))),
% 1.65/1.35 inference(quant_inst,[status(thm)],[])).
% 1.65/1.35 tff(937,plain,
% 1.65/1.35 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(a1, a2)) | point_equal(a2, a1)),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[936, 935])).
% 1.65/1.35 tff(938,plain,
% 1.65/1.35 (~point_equal(a1, a2)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[937, 873, 897])).
% 1.65/1.35 tff(939,plain,
% 1.65/1.35 (((~![A: $i, B: $i, 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(a2, a1b1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | point_equal(a1, a2) | line_equal(a1b1, 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)))) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | point_equal(a1, a2) | line_equal(a1b1, oa))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(940,plain,
% 1.65/1.35 ((line_equal(a1b1, oa) | point_equal(a1, a2) | (~incident(a2, a1b1)) | (~incident(a1, a1b1)) | (~incident(a1, oa)) | (~incident(a2, oa))) <=> ((~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | point_equal(a1, a2) | line_equal(a1b1, oa))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(941,plain,
% 1.65/1.35 (((~![A: $i, B: $i, 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, oa) | point_equal(a1, a2) | (~incident(a2, a1b1)) | (~incident(a1, a1b1)) | (~incident(a1, oa)) | (~incident(a2, 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)))) | ((~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | point_equal(a1, a2) | line_equal(a1b1, oa)))),
% 1.65/1.35 inference(monotonicity,[status(thm)],[940])).
% 1.65/1.35 tff(942,plain,
% 1.65/1.35 (((~![A: $i, B: $i, 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, oa) | point_equal(a1, a2) | (~incident(a2, a1b1)) | (~incident(a1, a1b1)) | (~incident(a1, oa)) | (~incident(a2, 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)))) | (~incident(a1, a1b1)) | (~incident(a2, a1b1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | point_equal(a1, a2) | line_equal(a1b1, oa))),
% 1.65/1.35 inference(transitivity,[status(thm)],[941, 939])).
% 1.65/1.35 tff(943,plain,
% 1.65/1.35 ((~![A: $i, B: $i, 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, oa) | point_equal(a1, a2) | (~incident(a2, a1b1)) | (~incident(a1, a1b1)) | (~incident(a1, oa)) | (~incident(a2, oa)))),
% 1.65/1.35 inference(quant_inst,[status(thm)],[])).
% 1.65/1.35 tff(944,plain,
% 1.65/1.35 ((~![A: $i, B: $i, 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(a2, a1b1)) | (~incident(a1, oa)) | (~incident(a2, oa)) | point_equal(a1, a2) | line_equal(a1b1, oa)),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[943, 942])).
% 1.65/1.35 tff(945,plain,
% 1.65/1.35 ((~incident(a2, a1b1)) | line_equal(a1b1, oa)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[944, 127, 207, 251, 40, 938])).
% 1.65/1.35 tff(946,plain,
% 1.65/1.35 (line_equal(a1b1, oa)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[945, 934])).
% 1.65/1.35 tff(947,plain,
% 1.65/1.35 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a1b1, oa)) | line_equal(oa, a1b1))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a1b1, oa)) | line_equal(oa, a1b1))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(948,plain,
% 1.65/1.35 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a1b1, oa)) | line_equal(oa, a1b1))),
% 1.65/1.35 inference(quant_inst,[status(thm)],[])).
% 1.65/1.35 tff(949,plain,
% 1.65/1.35 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a1b1, oa)) | line_equal(oa, a1b1)),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[948, 947])).
% 1.65/1.35 tff(950,plain,
% 1.65/1.35 (line_equal(oa, a1b1)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[949, 97, 946])).
% 1.65/1.35 tff(951,assumption,(line_equal(oa, a1b1)), introduced(assumption)).
% 1.65/1.35 tff(952,assumption,(~incident(o, a1b1)), introduced(assumption)).
% 1.65/1.35 tff(953,plain,
% 1.65/1.35 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oa)) | incident(o, a1b1) | (~line_equal(oa, a1b1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a1b1) | (~line_equal(oa, a1b1)))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(954,plain,
% 1.65/1.35 ((incident(o, a1b1) | (~line_equal(oa, a1b1)) | (~incident(o, oa))) <=> ((~incident(o, oa)) | incident(o, a1b1) | (~line_equal(oa, a1b1)))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(955,plain,
% 1.65/1.35 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1b1) | (~line_equal(oa, a1b1)) | (~incident(o, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oa)) | incident(o, a1b1) | (~line_equal(oa, a1b1))))),
% 1.65/1.35 inference(monotonicity,[status(thm)],[954])).
% 1.65/1.35 tff(956,plain,
% 1.65/1.35 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1b1) | (~line_equal(oa, a1b1)) | (~incident(o, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a1b1) | (~line_equal(oa, a1b1)))),
% 1.65/1.35 inference(transitivity,[status(thm)],[955, 953])).
% 1.65/1.35 tff(957,plain,
% 1.65/1.35 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a1b1) | (~line_equal(oa, a1b1)) | (~incident(o, oa)))),
% 1.65/1.35 inference(quant_inst,[status(thm)],[])).
% 1.65/1.35 tff(958,plain,
% 1.65/1.35 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oa)) | incident(o, a1b1) | (~line_equal(oa, a1b1))),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.65/1.35 tff(959,plain,
% 1.65/1.35 ($false),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[958, 268, 15, 952, 951])).
% 1.65/1.35 tff(960,plain,(incident(o, a1b1) | (~line_equal(oa, a1b1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.35 tff(961,plain,
% 1.65/1.35 (incident(o, a1b1)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[960, 950])).
% 1.65/1.35 tff(962,plain,
% 1.65/1.35 (((~![A: $i, B: $i, 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(o, a1b1)) | (~incident(o, a2b2)) | 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)))) | line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(o, a1b1)) | (~incident(o, a2b2)) | point_equal(a2, o))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(963,plain,
% 1.65/1.35 ((line_equal(a1b1, a2b2) | point_equal(a2, o) | (~incident(o, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(o, a2b2))) <=> (line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(o, a1b1)) | (~incident(o, a2b2)) | point_equal(a2, o))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(964,plain,
% 1.65/1.35 (((~![A: $i, B: $i, 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(a2, o) | (~incident(o, a1b1)) | (~incident(a2, a1b1)) | (~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)))) | (line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(o, a1b1)) | (~incident(o, a2b2)) | point_equal(a2, o)))),
% 1.65/1.35 inference(monotonicity,[status(thm)],[963])).
% 1.65/1.35 tff(965,plain,
% 1.65/1.35 (((~![A: $i, B: $i, 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(a2, o) | (~incident(o, a1b1)) | (~incident(a2, a1b1)) | (~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)))) | line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(o, a1b1)) | (~incident(o, a2b2)) | point_equal(a2, o))),
% 1.65/1.35 inference(transitivity,[status(thm)],[964, 962])).
% 1.65/1.35 tff(966,plain,
% 1.65/1.35 ((~![A: $i, B: $i, 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(a2, o) | (~incident(o, a1b1)) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(o, a2b2)))),
% 1.65/1.35 inference(quant_inst,[status(thm)],[])).
% 1.65/1.35 tff(967,plain,
% 1.65/1.35 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(a2, a1b1)) | (~incident(a2, a2b2)) | (~incident(o, a1b1)) | (~incident(o, a2b2)) | point_equal(a2, o)),
% 1.65/1.35 inference(modus_ponens,[status(thm)],[966, 965])).
% 1.65/1.35 tff(968,plain,
% 1.65/1.35 ($false),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[967, 237, 732, 40, 934, 961, 933, 932])).
% 1.65/1.35 tff(969,plain,(point_equal(a2, o) | (~incident(a2, a1b1)) | (~incident(o, a2b2))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.35 tff(970,plain,
% 1.65/1.35 (point_equal(a2, o)),
% 1.65/1.35 inference(unit_resolution,[status(thm)],[969, 931, 864])).
% 1.65/1.35 tff(971,assumption,(point_equal(a2, o)), introduced(assumption)).
% 1.65/1.35 tff(972,assumption,(~incident(a2, oc)), introduced(assumption)).
% 1.65/1.35 tff(973,plain,
% 1.65/1.35 (((~![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)))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(974,plain,
% 1.65/1.35 ((incident(a2, oc) | (~incident(o, oc)) | (~point_equal(a2, o))) <=> ((~incident(o, oc)) | incident(a2, oc) | (~point_equal(a2, o)))),
% 1.65/1.35 inference(rewrite,[status(thm)],[])).
% 1.65/1.35 tff(975,plain,
% 1.65/1.35 (((~![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))))),
% 1.65/1.36 inference(monotonicity,[status(thm)],[974])).
% 1.65/1.36 tff(976,plain,
% 1.65/1.36 (((~![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)))),
% 1.65/1.36 inference(transitivity,[status(thm)],[975, 973])).
% 1.65/1.36 tff(977,plain,
% 1.65/1.36 ((~![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)))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(978,plain,
% 1.65/1.36 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, oc)) | incident(a2, oc) | (~point_equal(a2, o))),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[977, 976])).
% 1.65/1.36 tff(979,plain,
% 1.65/1.36 ($false),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[978, 320, 171, 972, 971])).
% 1.65/1.36 tff(980,plain,(incident(a2, oc) | (~point_equal(a2, o))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.36 tff(981,plain,
% 1.65/1.36 (incident(a2, oc)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[980, 970])).
% 1.65/1.36 tff(982,plain,
% 1.65/1.36 (((~![A: $i, B: $i, 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))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(983,plain,
% 1.65/1.36 ((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))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(984,plain,
% 1.65/1.36 (((~![A: $i, B: $i, 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)))),
% 1.65/1.36 inference(monotonicity,[status(thm)],[983])).
% 1.65/1.36 tff(985,plain,
% 1.65/1.36 (((~![A: $i, B: $i, 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))),
% 1.65/1.36 inference(transitivity,[status(thm)],[984, 982])).
% 1.65/1.36 tff(986,plain,
% 1.65/1.36 ((~![A: $i, B: $i, 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)))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(987,plain,
% 1.65/1.36 ((~![A: $i, B: $i, 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)),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[986, 985])).
% 1.65/1.36 tff(988,plain,
% 1.65/1.36 ((~incident(a2, oc)) | line_equal(a2c2, oc)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[987, 257, 254, 317, 40, 248])).
% 1.65/1.36 tff(989,plain,
% 1.65/1.36 (line_equal(a2c2, oc)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[988, 981])).
% 1.65/1.36 tff(990,assumption,(~point_equal(ab, b1)), introduced(assumption)).
% 1.65/1.36 tff(991,assumption,(incident(b1, a2b2)), introduced(assumption)).
% 1.65/1.36 tff(992,plain,
% 1.65/1.36 (((~![A: $i, B: $i, 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(b1, a1b1)) | (~incident(b1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | 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)))) | line_equal(a1b1, a2b2) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, b1))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(993,plain,
% 1.65/1.36 ((line_equal(a1b1, a2b2) | point_equal(ab, b1) | (~incident(b1, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(b1, a2b2))) <=> (line_equal(a1b1, a2b2) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, b1))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(994,plain,
% 1.65/1.36 (((~![A: $i, B: $i, 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, b1) | (~incident(b1, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(b1, 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(b1, a1b1)) | (~incident(b1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, b1)))),
% 1.65/1.36 inference(monotonicity,[status(thm)],[993])).
% 1.65/1.36 tff(995,plain,
% 1.65/1.36 (((~![A: $i, B: $i, 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, b1) | (~incident(b1, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(b1, 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(b1, a1b1)) | (~incident(b1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, b1))),
% 1.65/1.36 inference(transitivity,[status(thm)],[994, 992])).
% 1.65/1.36 tff(996,plain,
% 1.65/1.36 ((~![A: $i, B: $i, 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, b1) | (~incident(b1, a1b1)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | (~incident(b1, a2b2)))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(997,plain,
% 1.65/1.36 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(a1b1, a2b2) | (~incident(b1, a1b1)) | (~incident(b1, a2b2)) | (~incident(ab, a1b1)) | (~incident(ab, a2b2)) | point_equal(ab, b1)),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[996, 995])).
% 1.65/1.36 tff(998,plain,
% 1.65/1.36 ($false),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[997, 60, 134, 646, 732, 40, 991, 990])).
% 1.65/1.36 tff(999,plain,(point_equal(ab, b1) | (~incident(b1, a2b2))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.36 tff(1000,plain,
% 1.65/1.36 (point_equal(ab, b1)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[999, 912])).
% 1.65/1.36 tff(1001,assumption,(point_equal(ab, b1)), introduced(assumption)).
% 1.65/1.36 tff(1002,assumption,(~incident(ab, b1c1)), introduced(assumption)).
% 1.65/1.36 tff(1003,plain,
% 1.65/1.36 (((~![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)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1004,plain,
% 1.65/1.36 ((incident(ab, b1c1) | (~incident(b1, b1c1)) | (~point_equal(ab, b1))) <=> ((~incident(b1, b1c1)) | incident(ab, b1c1) | (~point_equal(ab, b1)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1005,plain,
% 1.65/1.36 (((~![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))))),
% 1.65/1.36 inference(monotonicity,[status(thm)],[1004])).
% 1.65/1.36 tff(1006,plain,
% 1.65/1.36 (((~![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)))),
% 1.65/1.36 inference(transitivity,[status(thm)],[1005, 1003])).
% 1.65/1.36 tff(1007,plain,
% 1.65/1.36 ((~![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)))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(1008,plain,
% 1.65/1.36 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b1, b1c1)) | incident(ab, b1c1) | (~point_equal(ab, b1))),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 1.65/1.36 tff(1009,plain,
% 1.65/1.36 ($false),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1008, 568, 171, 1002, 1001])).
% 1.65/1.36 tff(1010,plain,(incident(ab, b1c1) | (~point_equal(ab, b1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.36 tff(1011,plain,
% 1.65/1.36 (incident(ab, b1c1)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1010, 1000])).
% 1.65/1.36 tff(1012,plain,
% 1.65/1.36 (((~![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))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1013,plain,
% 1.65/1.36 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(c1, b1c1)) | line_equal(b1c1, b1c1))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(1014,plain,
% 1.65/1.36 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(c1, b1c1)) | line_equal(b1c1, b1c1)),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 1.65/1.36 tff(1015,plain,
% 1.65/1.36 (line_equal(b1c1, b1c1)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1014, 686, 124])).
% 1.65/1.36 tff(1016,plain,
% 1.65/1.36 (((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ac, b1c1)) | (~incident(ab, b1c1)))) <=> ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ac, b1c1)) | (~incident(ab, b1c1)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1017,plain,
% 1.65/1.36 (((~line_equal(b1c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(ac, b1c1)) | (~incident(ab, b1c1))) <=> ((~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ac, b1c1)) | (~incident(ab, b1c1)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1018,plain,
% 1.65/1.36 (((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(b1c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(ac, b1c1)) | (~incident(ab, b1c1)))) <=> ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ac, b1c1)) | (~incident(ab, b1c1))))),
% 1.65/1.36 inference(monotonicity,[status(thm)],[1017])).
% 1.65/1.36 tff(1019,plain,
% 1.65/1.36 (((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(b1c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(ac, b1c1)) | (~incident(ab, b1c1)))) <=> ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ac, b1c1)) | (~incident(ab, b1c1)))),
% 1.65/1.36 inference(transitivity,[status(thm)],[1018, 1016])).
% 1.65/1.36 tff(1020,plain,
% 1.65/1.36 ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(b1c1, b1c1)) | (~incident(bc, b1c1)) | (~incident(ac, b1c1)) | (~incident(ab, b1c1)))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(1021,plain,
% 1.65/1.36 ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~incident(bc, b1c1)) | (~line_equal(b1c1, b1c1)) | (~incident(ac, b1c1)) | (~incident(ab, b1c1))),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 1.65/1.36 tff(1022,plain,
% 1.65/1.36 ((~incident(ac, b1c1)) | (~incident(ab, b1c1))),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1021, 150, 672, 1015])).
% 1.65/1.36 tff(1023,plain,
% 1.65/1.36 (~incident(ac, b1c1)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1022, 1011])).
% 1.65/1.36 tff(1024,plain,
% 1.65/1.36 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c1, b1c1)) | incident(ac, b1c1) | (~point_equal(ac, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, b1c1)) | incident(ac, b1c1) | (~point_equal(ac, c1)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1025,plain,
% 1.65/1.36 ((incident(ac, b1c1) | (~incident(c1, b1c1)) | (~point_equal(ac, c1))) <=> ((~incident(c1, b1c1)) | incident(ac, b1c1) | (~point_equal(ac, c1)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1026,plain,
% 1.65/1.36 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, b1c1) | (~incident(c1, b1c1)) | (~point_equal(ac, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c1, b1c1)) | incident(ac, b1c1) | (~point_equal(ac, c1))))),
% 1.65/1.36 inference(monotonicity,[status(thm)],[1025])).
% 1.65/1.36 tff(1027,plain,
% 1.65/1.36 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, b1c1) | (~incident(c1, b1c1)) | (~point_equal(ac, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, b1c1)) | incident(ac, b1c1) | (~point_equal(ac, c1)))),
% 1.65/1.36 inference(transitivity,[status(thm)],[1026, 1024])).
% 1.65/1.36 tff(1028,plain,
% 1.65/1.36 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(ac, b1c1) | (~incident(c1, b1c1)) | (~point_equal(ac, c1)))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(1029,plain,
% 1.65/1.36 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, b1c1)) | incident(ac, b1c1) | (~point_equal(ac, c1))),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 1.65/1.36 tff(1030,plain,
% 1.65/1.36 (~point_equal(ac, c1)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1029, 686, 171, 1023])).
% 1.65/1.36 tff(1031,plain,
% 1.65/1.36 (((~![A: $i, B: $i, 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(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | line_equal(a1c1, oc) | point_equal(ac, 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, a1c1)) | (~incident(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | line_equal(a1c1, oc) | point_equal(ac, c1))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1032,plain,
% 1.65/1.36 ((line_equal(a1c1, oc) | point_equal(ac, c1) | (~incident(c1, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | (~incident(c1, oc))) <=> ((~incident(c1, a1c1)) | (~incident(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | line_equal(a1c1, oc) | point_equal(ac, c1))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1033,plain,
% 1.65/1.36 (((~![A: $i, B: $i, 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, oc) | point_equal(ac, c1) | (~incident(c1, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, 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(c1, a1c1)) | (~incident(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | line_equal(a1c1, oc) | point_equal(ac, c1)))),
% 1.65/1.36 inference(monotonicity,[status(thm)],[1032])).
% 1.65/1.36 tff(1034,plain,
% 1.65/1.36 (((~![A: $i, B: $i, 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, oc) | point_equal(ac, c1) | (~incident(c1, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, 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(c1, a1c1)) | (~incident(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | line_equal(a1c1, oc) | point_equal(ac, c1))),
% 1.65/1.36 inference(transitivity,[status(thm)],[1033, 1031])).
% 1.65/1.36 tff(1035,plain,
% 1.65/1.36 ((~![A: $i, B: $i, 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, oc) | point_equal(ac, c1) | (~incident(c1, a1c1)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | (~incident(c1, oc)))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(1036,plain,
% 1.65/1.36 ((~![A: $i, B: $i, 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(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | line_equal(a1c1, oc) | point_equal(ac, c1)),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 1.65/1.36 tff(1037,plain,
% 1.65/1.36 ((~incident(ac, oc)) | line_equal(a1c1, oc) | point_equal(ac, c1)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1036, 386, 306, 194, 40])).
% 1.65/1.36 tff(1038,plain,
% 1.65/1.36 (~incident(ac, oc)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1037, 1030, 526])).
% 1.65/1.36 tff(1039,plain,
% 1.65/1.36 (((~![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)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1040,plain,
% 1.65/1.36 ((incident(ac, oc) | (~line_equal(a2c2, oc)) | (~incident(ac, a2c2))) <=> ((~incident(ac, a2c2)) | incident(ac, oc) | (~line_equal(a2c2, oc)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1041,plain,
% 1.65/1.36 (((~![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))))),
% 1.65/1.36 inference(monotonicity,[status(thm)],[1040])).
% 1.65/1.36 tff(1042,plain,
% 1.65/1.36 (((~![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)))),
% 1.65/1.36 inference(transitivity,[status(thm)],[1041, 1039])).
% 1.65/1.36 tff(1043,plain,
% 1.65/1.36 ((~![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)))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(1044,plain,
% 1.65/1.36 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ac, a2c2)) | incident(ac, oc) | (~line_equal(a2c2, oc))),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 1.65/1.36 tff(1045,plain,
% 1.65/1.36 ($false),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1044, 191, 15, 1038, 989])).
% 1.65/1.36 tff(1046,plain,(point_equal(c1, b2) | line_equal(a1c1, oc) | line_equal(a2c2, b1c1) | line_equal(b2c2, a1b1) | point_equal(c2, a1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.36 tff(1047,plain,
% 1.65/1.36 (line_equal(a1c1, oc)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1046, 525, 343, 342, 524])).
% 1.65/1.36 tff(1048,plain,
% 1.65/1.36 (line_equal(oc, a1c1)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[397, 97, 1047])).
% 1.65/1.36 tff(1049,plain,
% 1.65/1.36 (line_equal(a1c1, a2b2)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[886, 525, 343, 523, 342, 524])).
% 1.65/1.36 tff(1050,plain,
% 1.65/1.36 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(c2, a1c1)) | incident(c2, a2b2) | (~line_equal(a1c1, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c2, a1c1)) | incident(c2, a2b2) | (~line_equal(a1c1, a2b2)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1051,plain,
% 1.65/1.36 ((incident(c2, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(c2, a1c1))) <=> ((~incident(c2, a1c1)) | incident(c2, a2b2) | (~line_equal(a1c1, a2b2)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1052,plain,
% 1.65/1.36 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(c2, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(c2, a1c1)) | incident(c2, a2b2) | (~line_equal(a1c1, a2b2))))),
% 1.65/1.36 inference(monotonicity,[status(thm)],[1051])).
% 1.65/1.36 tff(1053,plain,
% 1.65/1.36 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(c2, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c2, a1c1)) | incident(c2, a2b2) | (~line_equal(a1c1, a2b2)))),
% 1.65/1.36 inference(transitivity,[status(thm)],[1052, 1050])).
% 1.65/1.36 tff(1054,plain,
% 1.65/1.36 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, a2b2) | (~line_equal(a1c1, a2b2)) | (~incident(c2, a1c1)))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(1055,plain,
% 1.65/1.36 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c2, a1c1)) | incident(c2, a2b2) | (~line_equal(a1c1, a2b2))),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 1.65/1.36 tff(1056,plain,
% 1.65/1.36 (~incident(c2, a1c1)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1055, 15, 241, 1049])).
% 1.65/1.36 tff(1057,plain,
% 1.65/1.36 (((~![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)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1058,plain,
% 1.65/1.36 ((incident(c2, a1c1) | (~line_equal(oc, a1c1)) | (~incident(c2, oc))) <=> (incident(c2, a1c1) | (~incident(c2, oc)) | (~line_equal(oc, a1c1)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1059,plain,
% 1.65/1.36 (((~![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))))),
% 1.65/1.36 inference(monotonicity,[status(thm)],[1058])).
% 1.65/1.36 tff(1060,plain,
% 1.65/1.36 (((~![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)))),
% 1.65/1.36 inference(transitivity,[status(thm)],[1059, 1057])).
% 1.65/1.36 tff(1061,plain,
% 1.65/1.36 ((~![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)))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(1062,plain,
% 1.65/1.36 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, a1c1) | (~incident(c2, oc)) | (~line_equal(oc, a1c1))),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 1.65/1.36 tff(1063,plain,
% 1.65/1.36 (incident(c2, a1c1) | (~line_equal(oc, a1c1))),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1062, 317, 15])).
% 1.65/1.36 tff(1064,plain,
% 1.65/1.36 ($false),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1063, 1056, 1048])).
% 1.65/1.36 tff(1065,plain,(point_equal(c1, b2) | line_equal(a2c2, b1c1) | point_equal(a2, b1) | line_equal(b2c2, a1b1) | point_equal(c2, a1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.36 tff(1066,plain,
% 1.65/1.36 (point_equal(c1, b2)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1065, 524, 523, 342, 343])).
% 1.65/1.36 tff(1067,assumption,(point_equal(c1, b2)), introduced(assumption)).
% 1.65/1.36 tff(1068,assumption,(~incident(c1, b2c2)), introduced(assumption)).
% 1.65/1.36 tff(1069,plain,
% 1.65/1.36 (((~![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)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1070,plain,
% 1.65/1.36 ((incident(c1, b2c2) | (~incident(b2, b2c2)) | (~point_equal(c1, b2))) <=> ((~incident(b2, b2c2)) | incident(c1, b2c2) | (~point_equal(c1, b2)))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1071,plain,
% 1.65/1.36 (((~![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))))),
% 1.65/1.36 inference(monotonicity,[status(thm)],[1070])).
% 1.65/1.36 tff(1072,plain,
% 1.65/1.36 (((~![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)))),
% 1.65/1.36 inference(transitivity,[status(thm)],[1071, 1069])).
% 1.65/1.36 tff(1073,plain,
% 1.65/1.36 ((~![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)))),
% 1.65/1.36 inference(quant_inst,[status(thm)],[])).
% 1.65/1.36 tff(1074,plain,
% 1.65/1.36 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, b2c2)) | incident(c1, b2c2) | (~point_equal(c1, b2))),
% 1.65/1.36 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 1.65/1.36 tff(1075,plain,
% 1.65/1.36 ($false),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1074, 18, 171, 1068, 1067])).
% 1.65/1.36 tff(1076,plain,(incident(c1, b2c2) | (~point_equal(c1, b2))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.36 tff(1077,plain,
% 1.65/1.36 (incident(c1, b2c2)),
% 1.65/1.36 inference(unit_resolution,[status(thm)],[1076, 1066])).
% 1.65/1.36 tff(1078,plain,
% 1.65/1.36 (((~![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))),
% 1.65/1.36 inference(rewrite,[status(thm)],[])).
% 1.65/1.36 tff(1079,plain,
% 1.65/1.36 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(c1, c2)) | point_equal(c2, c1))),
% 1.65/1.37 inference(quant_inst,[status(thm)],[])).
% 1.65/1.37 tff(1080,plain,
% 1.65/1.37 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(c1, c2)) | point_equal(c2, c1)),
% 1.65/1.37 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 1.65/1.37 tff(1081,plain,
% 1.65/1.37 (~point_equal(c1, c2)),
% 1.65/1.37 inference(unit_resolution,[status(thm)],[1080, 383, 897])).
% 1.65/1.37 tff(1082,plain,
% 1.65/1.37 (((~![A: $i, B: $i, 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, b2c2)) | (~incident(c1, b2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | 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(c2, b2c2)) | (~incident(c1, b2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | line_equal(oc, b2c2))),
% 1.65/1.37 inference(rewrite,[status(thm)],[])).
% 1.65/1.37 tff(1083,plain,
% 1.65/1.37 ((line_equal(oc, b2c2) | point_equal(c1, c2) | (~incident(c2, oc)) | (~incident(c1, oc)) | (~incident(c1, b2c2)) | (~incident(c2, b2c2))) <=> ((~incident(c2, b2c2)) | (~incident(c1, b2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | line_equal(oc, b2c2))),
% 1.65/1.37 inference(rewrite,[status(thm)],[])).
% 1.65/1.37 tff(1084,plain,
% 1.65/1.37 (((~![A: $i, B: $i, 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(c1, c2) | (~incident(c2, oc)) | (~incident(c1, oc)) | (~incident(c1, b2c2)) | (~incident(c2, 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(c2, b2c2)) | (~incident(c1, b2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | line_equal(oc, b2c2)))),
% 1.65/1.37 inference(monotonicity,[status(thm)],[1083])).
% 1.65/1.37 tff(1085,plain,
% 1.65/1.37 (((~![A: $i, B: $i, 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(c1, c2) | (~incident(c2, oc)) | (~incident(c1, oc)) | (~incident(c1, b2c2)) | (~incident(c2, 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(c2, b2c2)) | (~incident(c1, b2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | line_equal(oc, b2c2))),
% 1.65/1.37 inference(transitivity,[status(thm)],[1084, 1082])).
% 1.65/1.37 tff(1086,plain,
% 1.65/1.37 ((~![A: $i, B: $i, 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(c1, c2) | (~incident(c2, oc)) | (~incident(c1, oc)) | (~incident(c1, b2c2)) | (~incident(c2, b2c2)))),
% 1.65/1.37 inference(quant_inst,[status(thm)],[])).
% 1.65/1.37 tff(1087,plain,
% 1.65/1.37 ((~![A: $i, B: $i, 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, b2c2)) | (~incident(c1, b2c2)) | (~incident(c1, oc)) | (~incident(c2, oc)) | point_equal(c1, c2) | line_equal(oc, b2c2)),
% 1.65/1.37 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 1.65/1.37 tff(1088,plain,
% 1.65/1.37 ((~incident(c1, b2c2)) | line_equal(oc, b2c2)),
% 1.65/1.37 inference(unit_resolution,[status(thm)],[1087, 323, 306, 317, 40, 1081])).
% 1.65/1.37 tff(1089,plain,
% 1.65/1.37 (line_equal(oc, b2c2)),
% 1.65/1.37 inference(unit_resolution,[status(thm)],[1088, 1077])).
% 1.65/1.37 tff(1090,plain,
% 1.65/1.37 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oc)) | incident(o, b2c2) | (~line_equal(oc, b2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oc)) | incident(o, b2c2) | (~line_equal(oc, b2c2)))),
% 1.65/1.37 inference(rewrite,[status(thm)],[])).
% 1.65/1.37 tff(1091,plain,
% 1.65/1.37 ((incident(o, b2c2) | (~line_equal(oc, b2c2)) | (~incident(o, oc))) <=> ((~incident(o, oc)) | incident(o, b2c2) | (~line_equal(oc, b2c2)))),
% 1.65/1.37 inference(rewrite,[status(thm)],[])).
% 1.65/1.37 tff(1092,plain,
% 1.65/1.37 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, b2c2) | (~line_equal(oc, b2c2)) | (~incident(o, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oc)) | incident(o, b2c2) | (~line_equal(oc, b2c2))))),
% 1.65/1.37 inference(monotonicity,[status(thm)],[1091])).
% 1.65/1.37 tff(1093,plain,
% 1.65/1.37 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, b2c2) | (~line_equal(oc, b2c2)) | (~incident(o, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oc)) | incident(o, b2c2) | (~line_equal(oc, b2c2)))),
% 1.65/1.37 inference(transitivity,[status(thm)],[1092, 1090])).
% 1.65/1.37 tff(1094,plain,
% 1.65/1.37 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, b2c2) | (~line_equal(oc, b2c2)) | (~incident(o, oc)))),
% 1.65/1.37 inference(quant_inst,[status(thm)],[])).
% 1.65/1.37 tff(1095,plain,
% 1.65/1.37 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oc)) | incident(o, b2c2) | (~line_equal(oc, b2c2))),
% 1.65/1.37 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.65/1.37 tff(1096,plain,
% 1.65/1.37 (incident(o, b2c2) | (~line_equal(oc, b2c2))),
% 1.65/1.37 inference(unit_resolution,[status(thm)],[1095, 320, 15])).
% 1.65/1.37 tff(1097,plain,
% 1.65/1.37 (incident(o, b2c2)),
% 1.65/1.37 inference(unit_resolution,[status(thm)],[1096, 1089])).
% 1.65/1.37 tff(1098,plain,
% 1.65/1.37 (((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | ((~incident(a2, b2c2)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)))) <=> ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (~incident(a2, b2c2)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)))),
% 1.65/1.37 inference(rewrite,[status(thm)],[])).
% 1.65/1.37 tff(1099,plain,
% 1.65/1.37 ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | ((~incident(a2, b2c2)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2)))),
% 1.65/1.37 inference(quant_inst,[status(thm)],[])).
% 1.65/1.37 tff(1100,plain,
% 1.65/1.37 ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (~incident(a2, b2c2)) | (~incident(b2, b2c2)) | (~incident(c2, b2c2))),
% 1.65/1.37 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 1.65/1.37 tff(1101,plain,
% 1.65/1.37 (~incident(a2, b2c2)),
% 1.65/1.37 inference(unit_resolution,[status(thm)],[1100, 323, 18, 231])).
% 1.65/1.37 tff(1102,plain,
% 1.65/1.37 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, b2c2) | (~incident(o, b2c2)) | (~point_equal(a2, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a2, b2c2) | (~incident(o, b2c2)) | (~point_equal(a2, o)))),
% 1.65/1.37 inference(rewrite,[status(thm)],[])).
% 1.65/1.37 tff(1103,plain,
% 1.65/1.37 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a2, b2c2) | (~incident(o, b2c2)) | (~point_equal(a2, o)))),
% 1.65/1.37 inference(quant_inst,[status(thm)],[])).
% 1.65/1.37 tff(1104,plain,
% 1.65/1.37 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(a2, b2c2) | (~incident(o, b2c2)) | (~point_equal(a2, o))),
% 1.65/1.37 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 1.65/1.37 tff(1105,plain,
% 1.65/1.37 (~point_equal(a2, o)),
% 1.65/1.37 inference(unit_resolution,[status(thm)],[1104, 171, 1101, 1097])).
% 1.65/1.37 tff(1106,assumption,(~incident(c1, ob)), introduced(assumption)).
% 1.65/1.37 tff(1107,plain,
% 1.65/1.37 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, ob) | (~incident(b2, ob)) | (~point_equal(c1, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(c1, ob) | (~incident(b2, ob)) | (~point_equal(c1, b2)))),
% 1.65/1.37 inference(rewrite,[status(thm)],[])).
% 1.65/1.37 tff(1108,plain,
% 1.65/1.37 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, ob) | (~incident(b2, ob)) | (~point_equal(c1, b2)))),
% 1.72/1.37 inference(quant_inst,[status(thm)],[])).
% 1.72/1.37 tff(1109,plain,
% 1.72/1.37 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(c1, ob) | (~incident(b2, ob)) | (~point_equal(c1, b2))),
% 1.72/1.37 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.72/1.37 tff(1110,plain,
% 1.72/1.37 ($false),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1109, 54, 171, 1106, 1067])).
% 1.72/1.37 tff(1111,plain,(incident(c1, ob) | (~point_equal(c1, b2))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.37 tff(1112,plain,
% 1.72/1.37 (incident(c1, ob)),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1111, 1066])).
% 1.72/1.37 tff(1113,plain,
% 1.72/1.37 (((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(c1, b2)) | point_equal(b2, c1))) <=> ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(c1, b2)) | point_equal(b2, c1))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1114,plain,
% 1.72/1.37 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(c1, b2)) | point_equal(b2, c1))),
% 1.72/1.37 inference(quant_inst,[status(thm)],[])).
% 1.72/1.37 tff(1115,plain,
% 1.72/1.37 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(c1, b2)) | point_equal(b2, c1)),
% 1.72/1.37 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 1.72/1.37 tff(1116,plain,
% 1.72/1.37 (point_equal(b2, c1)),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1115, 897, 1066])).
% 1.72/1.37 tff(1117,plain,
% 1.72/1.37 (incident(b2, b1c1)),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[691, 1116])).
% 1.72/1.37 tff(1118,plain,
% 1.72/1.37 (((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(b1, b2)) | point_equal(b2, b1))) <=> ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(b1, b2)) | point_equal(b2, b1))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1119,plain,
% 1.72/1.37 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(b1, b2)) | point_equal(b2, b1))),
% 1.72/1.37 inference(quant_inst,[status(thm)],[])).
% 1.72/1.37 tff(1120,plain,
% 1.72/1.37 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(b1, b2)) | point_equal(b2, b1)),
% 1.72/1.37 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 1.72/1.37 tff(1121,plain,
% 1.72/1.37 (~point_equal(b1, b2)),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1120, 51, 897])).
% 1.72/1.37 tff(1122,plain,
% 1.72/1.37 (((~![A: $i, B: $i, 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(b2, b1c1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | point_equal(b1, b2) | 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(b2, b1c1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | point_equal(b1, b2) | line_equal(b1c1, ob))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1123,plain,
% 1.72/1.37 ((line_equal(b1c1, ob) | point_equal(b1, b2) | (~incident(b2, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(b2, ob))) <=> ((~incident(b1, b1c1)) | (~incident(b2, b1c1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | point_equal(b1, b2) | line_equal(b1c1, ob))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1124,plain,
% 1.72/1.37 (((~![A: $i, B: $i, 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, b2) | (~incident(b2, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(b2, 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(b2, b1c1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | point_equal(b1, b2) | line_equal(b1c1, ob)))),
% 1.72/1.37 inference(monotonicity,[status(thm)],[1123])).
% 1.72/1.37 tff(1125,plain,
% 1.72/1.37 (((~![A: $i, B: $i, 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, b2) | (~incident(b2, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(b2, 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(b2, b1c1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | point_equal(b1, b2) | line_equal(b1c1, ob))),
% 1.72/1.37 inference(transitivity,[status(thm)],[1124, 1122])).
% 1.72/1.37 tff(1126,plain,
% 1.72/1.37 ((~![A: $i, B: $i, 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, b2) | (~incident(b2, b1c1)) | (~incident(b1, b1c1)) | (~incident(b1, ob)) | (~incident(b2, ob)))),
% 1.72/1.37 inference(quant_inst,[status(thm)],[])).
% 1.72/1.37 tff(1127,plain,
% 1.72/1.37 ((~![A: $i, B: $i, 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(b2, b1c1)) | (~incident(b1, ob)) | (~incident(b2, ob)) | point_equal(b1, b2) | line_equal(b1c1, ob)),
% 1.72/1.37 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 1.72/1.37 tff(1128,plain,
% 1.72/1.37 ((~incident(b2, b1c1)) | line_equal(b1c1, ob)),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1127, 568, 57, 54, 40, 1121])).
% 1.72/1.37 tff(1129,plain,
% 1.72/1.37 (line_equal(b1c1, ob)),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1128, 1117])).
% 1.72/1.37 tff(1130,plain,
% 1.72/1.37 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(b1c1, ob)) | line_equal(ob, b1c1))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(b1c1, ob)) | line_equal(ob, b1c1))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1131,plain,
% 1.72/1.37 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(b1c1, ob)) | line_equal(ob, b1c1))),
% 1.72/1.37 inference(quant_inst,[status(thm)],[])).
% 1.72/1.37 tff(1132,plain,
% 1.72/1.37 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(b1c1, ob)) | line_equal(ob, b1c1)),
% 1.72/1.37 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 1.72/1.37 tff(1133,plain,
% 1.72/1.37 (line_equal(ob, b1c1)),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1132, 97, 1129])).
% 1.72/1.37 tff(1134,plain,
% 1.72/1.37 (((~![A: $i, B: $i, 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) | line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, 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)))) | point_equal(c2, c1) | line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(c1, b2c2)))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1135,plain,
% 1.72/1.37 ((line_equal(b1c1, b2c2) | point_equal(c2, c1) | (~incident(c1, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(c1, b2c2))) <=> (point_equal(c2, c1) | line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(c1, b2c2)))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1136,plain,
% 1.72/1.37 (((~![A: $i, B: $i, 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, c1) | (~incident(c1, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, 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)))) | (point_equal(c2, c1) | line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(c1, b2c2))))),
% 1.72/1.37 inference(monotonicity,[status(thm)],[1135])).
% 1.72/1.37 tff(1137,plain,
% 1.72/1.37 (((~![A: $i, B: $i, 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, c1) | (~incident(c1, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, 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)))) | point_equal(c2, c1) | line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(c1, b2c2)))),
% 1.72/1.37 inference(transitivity,[status(thm)],[1136, 1134])).
% 1.72/1.37 tff(1138,plain,
% 1.72/1.37 ((~![A: $i, B: $i, 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, c1) | (~incident(c1, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(c1, b2c2)))),
% 1.72/1.37 inference(quant_inst,[status(thm)],[])).
% 1.72/1.37 tff(1139,plain,
% 1.72/1.37 ((~![A: $i, B: $i, 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) | line_equal(b1c1, b2c2) | (~incident(c1, b1c1)) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(c1, b2c2))),
% 1.72/1.37 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 1.72/1.37 tff(1140,plain,
% 1.72/1.37 ((~incident(c2, b1c1)) | (~incident(c1, b2c2))),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1139, 686, 323, 383, 669, 40])).
% 1.72/1.37 tff(1141,plain,
% 1.72/1.37 (~incident(c2, b1c1)),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1140, 1077])).
% 1.72/1.37 tff(1142,plain,
% 1.72/1.37 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, b1c1) | (~incident(c2, ob)) | (~line_equal(ob, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, b1c1) | (~incident(c2, ob)) | (~line_equal(ob, b1c1)))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1143,plain,
% 1.72/1.37 ((incident(c2, b1c1) | (~line_equal(ob, b1c1)) | (~incident(c2, ob))) <=> (incident(c2, b1c1) | (~incident(c2, ob)) | (~line_equal(ob, b1c1)))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1144,plain,
% 1.72/1.37 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, b1c1) | (~line_equal(ob, b1c1)) | (~incident(c2, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, b1c1) | (~incident(c2, ob)) | (~line_equal(ob, b1c1))))),
% 1.72/1.37 inference(monotonicity,[status(thm)],[1143])).
% 1.72/1.37 tff(1145,plain,
% 1.72/1.37 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, b1c1) | (~line_equal(ob, b1c1)) | (~incident(c2, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, b1c1) | (~incident(c2, ob)) | (~line_equal(ob, b1c1)))),
% 1.72/1.37 inference(transitivity,[status(thm)],[1144, 1142])).
% 1.72/1.37 tff(1146,plain,
% 1.72/1.37 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, b1c1) | (~line_equal(ob, b1c1)) | (~incident(c2, ob)))),
% 1.72/1.37 inference(quant_inst,[status(thm)],[])).
% 1.72/1.37 tff(1147,plain,
% 1.72/1.37 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, b1c1) | (~incident(c2, ob)) | (~line_equal(ob, b1c1))),
% 1.72/1.37 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 1.72/1.37 tff(1148,plain,
% 1.72/1.37 (~incident(c2, ob)),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1147, 15, 1141, 1133])).
% 1.72/1.37 tff(1149,assumption,(line_equal(oc, ob)), introduced(assumption)).
% 1.72/1.37 tff(1150,assumption,(~incident(c2, ob)), introduced(assumption)).
% 1.72/1.37 tff(1151,plain,
% 1.72/1.37 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, ob) | (~incident(c2, oc)) | (~line_equal(oc, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, ob) | (~incident(c2, oc)) | (~line_equal(oc, ob)))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1152,plain,
% 1.72/1.37 ((incident(c2, ob) | (~line_equal(oc, ob)) | (~incident(c2, oc))) <=> (incident(c2, ob) | (~incident(c2, oc)) | (~line_equal(oc, ob)))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1153,plain,
% 1.72/1.37 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, ob) | (~line_equal(oc, ob)) | (~incident(c2, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, ob) | (~incident(c2, oc)) | (~line_equal(oc, ob))))),
% 1.72/1.37 inference(monotonicity,[status(thm)],[1152])).
% 1.72/1.37 tff(1154,plain,
% 1.72/1.37 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, ob) | (~line_equal(oc, ob)) | (~incident(c2, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, ob) | (~incident(c2, oc)) | (~line_equal(oc, ob)))),
% 1.72/1.37 inference(transitivity,[status(thm)],[1153, 1151])).
% 1.72/1.37 tff(1155,plain,
% 1.72/1.37 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(c2, ob) | (~line_equal(oc, ob)) | (~incident(c2, oc)))),
% 1.72/1.37 inference(quant_inst,[status(thm)],[])).
% 1.72/1.37 tff(1156,plain,
% 1.72/1.37 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, ob) | (~incident(c2, oc)) | (~line_equal(oc, ob))),
% 1.72/1.37 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 1.72/1.37 tff(1157,plain,
% 1.72/1.37 ($false),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1156, 317, 15, 1150, 1149])).
% 1.72/1.37 tff(1158,plain,((~line_equal(oc, ob)) | incident(c2, ob)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.37 tff(1159,plain,
% 1.72/1.37 (~line_equal(oc, ob)),
% 1.72/1.37 inference(unit_resolution,[status(thm)],[1158, 1148])).
% 1.72/1.37 tff(1160,plain,
% 1.72/1.37 (((~![A: $i, B: $i, 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, ob)) | (~incident(o, oc)) | (~incident(c1, ob)) | (~incident(c1, oc)) | line_equal(oc, ob) | point_equal(o, 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(o, ob)) | (~incident(o, oc)) | (~incident(c1, ob)) | (~incident(c1, oc)) | line_equal(oc, ob) | point_equal(o, c1))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1161,plain,
% 1.72/1.37 ((line_equal(oc, ob) | point_equal(o, c1) | (~incident(c1, oc)) | (~incident(o, oc)) | (~incident(o, ob)) | (~incident(c1, ob))) <=> ((~incident(o, ob)) | (~incident(o, oc)) | (~incident(c1, ob)) | (~incident(c1, oc)) | line_equal(oc, ob) | point_equal(o, c1))),
% 1.72/1.37 inference(rewrite,[status(thm)],[])).
% 1.72/1.37 tff(1162,plain,
% 1.72/1.37 (((~![A: $i, B: $i, 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, ob) | point_equal(o, c1) | (~incident(c1, oc)) | (~incident(o, oc)) | (~incident(o, ob)) | (~incident(c1, 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(o, ob)) | (~incident(o, oc)) | (~incident(c1, ob)) | (~incident(c1, oc)) | line_equal(oc, ob) | point_equal(o, c1)))),
% 1.72/1.37 inference(monotonicity,[status(thm)],[1161])).
% 1.72/1.37 tff(1163,plain,
% 1.72/1.37 (((~![A: $i, B: $i, 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, ob) | point_equal(o, c1) | (~incident(c1, oc)) | (~incident(o, oc)) | (~incident(o, ob)) | (~incident(c1, 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(o, ob)) | (~incident(o, oc)) | (~incident(c1, ob)) | (~incident(c1, oc)) | line_equal(oc, ob) | point_equal(o, c1))),
% 1.72/1.37 inference(transitivity,[status(thm)],[1162, 1160])).
% 1.72/1.37 tff(1164,plain,
% 1.72/1.37 ((~![A: $i, B: $i, 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, ob) | point_equal(o, c1) | (~incident(c1, oc)) | (~incident(o, oc)) | (~incident(o, ob)) | (~incident(c1, ob)))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1165,plain,
% 1.72/1.38 ((~![A: $i, B: $i, 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, ob)) | (~incident(o, oc)) | (~incident(c1, ob)) | (~incident(c1, oc)) | line_equal(oc, ob) | point_equal(o, c1)),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 1.72/1.38 tff(1166,plain,
% 1.72/1.38 ((~incident(c1, ob)) | line_equal(oc, ob) | point_equal(o, c1)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1165, 333, 320, 306, 40])).
% 1.72/1.38 tff(1167,plain,
% 1.72/1.38 (point_equal(o, c1)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1166, 1159, 1112])).
% 1.72/1.38 tff(1168,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | ((~point_equal(c1, b2)) | (~point_equal(o, c1)) | point_equal(o, b2))) <=> ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (~point_equal(c1, b2)) | (~point_equal(o, c1)) | point_equal(o, b2))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1169,plain,
% 1.72/1.38 ((point_equal(o, b2) | (~point_equal(c1, b2)) | (~point_equal(o, c1))) <=> ((~point_equal(c1, b2)) | (~point_equal(o, c1)) | point_equal(o, b2))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1170,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (point_equal(o, b2) | (~point_equal(c1, b2)) | (~point_equal(o, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | ((~point_equal(c1, b2)) | (~point_equal(o, c1)) | point_equal(o, b2)))),
% 1.72/1.38 inference(monotonicity,[status(thm)],[1169])).
% 1.72/1.38 tff(1171,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (point_equal(o, b2) | (~point_equal(c1, b2)) | (~point_equal(o, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (~point_equal(c1, b2)) | (~point_equal(o, c1)) | point_equal(o, b2))),
% 1.72/1.38 inference(transitivity,[status(thm)],[1170, 1168])).
% 1.72/1.38 tff(1172,plain,
% 1.72/1.38 ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (point_equal(o, b2) | (~point_equal(c1, b2)) | (~point_equal(o, c1)))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1173,plain,
% 1.72/1.38 ((~![A: $i, B: $i, C: $i] : (point_equal(A, C) | (~point_equal(B, C)) | (~point_equal(A, B)))) | (~point_equal(c1, b2)) | (~point_equal(o, c1)) | point_equal(o, b2)),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 1.72/1.38 tff(1174,plain,
% 1.72/1.38 (point_equal(o, b2)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1173, 462, 1066, 1167])).
% 1.72/1.38 tff(1175,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, a2b2)) | incident(o, a2b2) | (~point_equal(o, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a2b2)) | incident(o, a2b2) | (~point_equal(o, b2)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1176,plain,
% 1.72/1.38 ((incident(o, a2b2) | (~incident(b2, a2b2)) | (~point_equal(o, b2))) <=> ((~incident(b2, a2b2)) | incident(o, a2b2) | (~point_equal(o, b2)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1177,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a2b2) | (~incident(b2, a2b2)) | (~point_equal(o, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(b2, a2b2)) | incident(o, a2b2) | (~point_equal(o, b2))))),
% 1.72/1.38 inference(monotonicity,[status(thm)],[1176])).
% 1.72/1.38 tff(1178,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a2b2) | (~incident(b2, a2b2)) | (~point_equal(o, b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a2b2)) | incident(o, a2b2) | (~point_equal(o, b2)))),
% 1.72/1.38 inference(transitivity,[status(thm)],[1177, 1175])).
% 1.72/1.38 tff(1179,plain,
% 1.72/1.38 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a2b2) | (~incident(b2, a2b2)) | (~point_equal(o, b2)))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1180,plain,
% 1.72/1.38 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(b2, a2b2)) | incident(o, a2b2) | (~point_equal(o, b2))),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 1.72/1.38 tff(1181,plain,
% 1.72/1.38 (incident(o, a2b2) | (~point_equal(o, b2))),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1180, 234, 171])).
% 1.72/1.38 tff(1182,plain,
% 1.72/1.38 (incident(o, a2b2)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1181, 1174])).
% 1.72/1.38 tff(1183,plain,
% 1.72/1.38 (((~![A: $i, B: $i, 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)) | line_equal(a2b2, oa) | (~incident(o, a2b2)) | 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(a2, a2b2)) | (~incident(o, oa)) | (~incident(a2, oa)) | line_equal(a2b2, oa) | (~incident(o, a2b2)) | point_equal(a2, o))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1184,plain,
% 1.72/1.38 ((line_equal(a2b2, oa) | point_equal(a2, o) | (~incident(o, a2b2)) | (~incident(a2, a2b2)) | (~incident(a2, oa)) | (~incident(o, oa))) <=> ((~incident(a2, a2b2)) | (~incident(o, oa)) | (~incident(a2, oa)) | line_equal(a2b2, oa) | (~incident(o, a2b2)) | point_equal(a2, o))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1185,plain,
% 1.72/1.38 (((~![A: $i, B: $i, 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, oa) | point_equal(a2, o) | (~incident(o, a2b2)) | (~incident(a2, a2b2)) | (~incident(a2, oa)) | (~incident(o, 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)))) | ((~incident(a2, a2b2)) | (~incident(o, oa)) | (~incident(a2, oa)) | line_equal(a2b2, oa) | (~incident(o, a2b2)) | point_equal(a2, o)))),
% 1.72/1.38 inference(monotonicity,[status(thm)],[1184])).
% 1.72/1.38 tff(1186,plain,
% 1.72/1.38 (((~![A: $i, B: $i, 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, oa) | point_equal(a2, o) | (~incident(o, a2b2)) | (~incident(a2, a2b2)) | (~incident(a2, oa)) | (~incident(o, 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)))) | (~incident(a2, a2b2)) | (~incident(o, oa)) | (~incident(a2, oa)) | line_equal(a2b2, oa) | (~incident(o, a2b2)) | point_equal(a2, o))),
% 1.72/1.38 inference(transitivity,[status(thm)],[1185, 1183])).
% 1.72/1.38 tff(1187,plain,
% 1.72/1.38 ((~![A: $i, B: $i, 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, oa) | point_equal(a2, o) | (~incident(o, a2b2)) | (~incident(a2, a2b2)) | (~incident(a2, oa)) | (~incident(o, oa)))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1188,plain,
% 1.72/1.38 ((~![A: $i, B: $i, 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)) | line_equal(a2b2, oa) | (~incident(o, a2b2)) | point_equal(a2, o)),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 1.72/1.38 tff(1189,plain,
% 1.72/1.38 (line_equal(a2b2, oa) | (~incident(o, a2b2)) | point_equal(a2, o)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1188, 237, 268, 251, 40])).
% 1.72/1.38 tff(1190,plain,
% 1.72/1.38 (line_equal(a2b2, oa)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1189, 1182, 1105])).
% 1.72/1.38 tff(1191,plain,
% 1.72/1.38 (((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | ((~incident(a1, ob)) | (~incident(b1, ob)) | (~incident(c1, ob)))) <=> ((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (~incident(a1, ob)) | (~incident(b1, ob)) | (~incident(c1, ob)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1192,plain,
% 1.72/1.38 ((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | ((~incident(a1, ob)) | (~incident(b1, ob)) | (~incident(c1, ob)))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1193,plain,
% 1.72/1.38 ((~![A: $i] : ((~incident(a1, A)) | (~incident(b1, A)) | (~incident(c1, A)))) | (~incident(a1, ob)) | (~incident(b1, ob)) | (~incident(c1, ob))),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 1.72/1.38 tff(1194,plain,
% 1.72/1.38 ((~incident(a1, ob)) | (~incident(c1, ob))),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1193, 57, 292])).
% 1.72/1.38 tff(1195,plain,
% 1.72/1.38 (~incident(a1, ob)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1194, 1112])).
% 1.72/1.38 tff(1196,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, ob)) | incident(a1, ob) | (~point_equal(a1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(a1, ob) | (~point_equal(a1, o)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1197,plain,
% 1.72/1.38 ((incident(a1, ob) | (~incident(o, ob)) | (~point_equal(a1, o))) <=> ((~incident(o, ob)) | incident(a1, ob) | (~point_equal(a1, o)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1198,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a1, ob) | (~incident(o, ob)) | (~point_equal(a1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(o, ob)) | incident(a1, ob) | (~point_equal(a1, o))))),
% 1.72/1.38 inference(monotonicity,[status(thm)],[1197])).
% 1.72/1.38 tff(1199,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a1, ob) | (~incident(o, ob)) | (~point_equal(a1, o)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(a1, ob) | (~point_equal(a1, o)))),
% 1.72/1.38 inference(transitivity,[status(thm)],[1198, 1196])).
% 1.72/1.38 tff(1200,plain,
% 1.72/1.38 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(a1, ob) | (~incident(o, ob)) | (~point_equal(a1, o)))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1201,plain,
% 1.72/1.38 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(o, ob)) | incident(a1, ob) | (~point_equal(a1, o))),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 1.72/1.38 tff(1202,plain,
% 1.72/1.38 (incident(a1, ob) | (~point_equal(a1, o))),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1201, 333, 171])).
% 1.72/1.38 tff(1203,plain,
% 1.72/1.38 (~point_equal(a1, o)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1202, 1195])).
% 1.72/1.38 tff(1204,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c1, a1c1)) | incident(o, a1c1) | (~point_equal(o, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, a1c1)) | incident(o, a1c1) | (~point_equal(o, c1)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1205,plain,
% 1.72/1.38 ((incident(o, a1c1) | (~incident(c1, a1c1)) | (~point_equal(o, c1))) <=> ((~incident(c1, a1c1)) | incident(o, a1c1) | (~point_equal(o, c1)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1206,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a1c1) | (~incident(c1, a1c1)) | (~point_equal(o, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c1, a1c1)) | incident(o, a1c1) | (~point_equal(o, c1))))),
% 1.72/1.38 inference(monotonicity,[status(thm)],[1205])).
% 1.72/1.38 tff(1207,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a1c1) | (~incident(c1, a1c1)) | (~point_equal(o, c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, a1c1)) | incident(o, a1c1) | (~point_equal(o, c1)))),
% 1.72/1.38 inference(transitivity,[status(thm)],[1206, 1204])).
% 1.72/1.38 tff(1208,plain,
% 1.72/1.38 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a1c1) | (~incident(c1, a1c1)) | (~point_equal(o, c1)))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1209,plain,
% 1.72/1.38 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c1, a1c1)) | incident(o, a1c1) | (~point_equal(o, c1))),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 1.72/1.38 tff(1210,plain,
% 1.72/1.38 (incident(o, a1c1) | (~point_equal(o, c1))),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1209, 386, 171])).
% 1.72/1.38 tff(1211,plain,
% 1.72/1.38 (incident(o, a1c1)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1210, 1167])).
% 1.72/1.38 tff(1212,plain,
% 1.72/1.38 (((~![A: $i, B: $i, 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(o, oa)) | (~incident(a1, oa)) | line_equal(oa, a1c1) | (~incident(o, a1c1)) | 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, a1c1)) | (~incident(o, oa)) | (~incident(a1, oa)) | line_equal(oa, a1c1) | (~incident(o, a1c1)) | point_equal(a1, o))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1213,plain,
% 1.72/1.38 ((line_equal(oa, a1c1) | point_equal(a1, o) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(a1, a1c1)) | (~incident(o, a1c1))) <=> ((~incident(a1, a1c1)) | (~incident(o, oa)) | (~incident(a1, oa)) | line_equal(oa, a1c1) | (~incident(o, a1c1)) | point_equal(a1, o))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1214,plain,
% 1.72/1.38 (((~![A: $i, B: $i, 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, a1c1) | point_equal(a1, o) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(a1, 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(a1, a1c1)) | (~incident(o, oa)) | (~incident(a1, oa)) | line_equal(oa, a1c1) | (~incident(o, a1c1)) | point_equal(a1, o)))),
% 1.72/1.38 inference(monotonicity,[status(thm)],[1213])).
% 1.72/1.38 tff(1215,plain,
% 1.72/1.38 (((~![A: $i, B: $i, 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, a1c1) | point_equal(a1, o) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(a1, 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(a1, a1c1)) | (~incident(o, oa)) | (~incident(a1, oa)) | line_equal(oa, a1c1) | (~incident(o, a1c1)) | point_equal(a1, o))),
% 1.72/1.38 inference(transitivity,[status(thm)],[1214, 1212])).
% 1.72/1.38 tff(1216,plain,
% 1.72/1.38 ((~![A: $i, B: $i, 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, a1c1) | point_equal(a1, o) | (~incident(o, oa)) | (~incident(a1, oa)) | (~incident(a1, a1c1)) | (~incident(o, a1c1)))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1217,plain,
% 1.72/1.38 ((~![A: $i, B: $i, 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(o, oa)) | (~incident(a1, oa)) | line_equal(oa, a1c1) | (~incident(o, a1c1)) | point_equal(a1, o)),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 1.72/1.38 tff(1218,plain,
% 1.72/1.38 (line_equal(oa, a1c1) | (~incident(o, a1c1)) | point_equal(a1, o)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1217, 197, 268, 207, 40])).
% 1.72/1.38 tff(1219,plain,
% 1.72/1.38 (line_equal(oa, a1c1)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1218, 1211, 1203])).
% 1.72/1.38 tff(1220,plain,
% 1.72/1.38 (~incident(a1, b2c2)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[590, 524, 343, 342, 523])).
% 1.72/1.38 tff(1221,plain,
% 1.72/1.38 (incident(b2, a1c1)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[594, 1220])).
% 1.72/1.38 tff(1222,plain,
% 1.72/1.38 (point_equal(bc, b2)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[680, 1117])).
% 1.72/1.38 tff(1223,plain,
% 1.72/1.38 (((~![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)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1224,plain,
% 1.72/1.38 ((incident(bc, a1c1) | (~incident(b2, a1c1)) | (~point_equal(bc, b2))) <=> ((~incident(b2, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, b2)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1225,plain,
% 1.72/1.38 (((~![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))))),
% 1.72/1.38 inference(monotonicity,[status(thm)],[1224])).
% 1.72/1.38 tff(1226,plain,
% 1.72/1.38 (((~![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)))),
% 1.72/1.38 inference(transitivity,[status(thm)],[1225, 1223])).
% 1.72/1.38 tff(1227,plain,
% 1.72/1.38 ((~![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)))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1228,plain,
% 1.72/1.38 ((~![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))),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 1.72/1.38 tff(1229,plain,
% 1.72/1.38 ((~incident(b2, a1c1)) | incident(bc, a1c1) | (~point_equal(bc, b2))),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1228, 171])).
% 1.72/1.38 tff(1230,plain,
% 1.72/1.38 (incident(bc, a1c1)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1229, 1222, 1221])).
% 1.72/1.38 tff(1231,plain,
% 1.72/1.38 (((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(a1, a1c1)) | line_equal(a1c1, a1c1))) <=> ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(a1, a1c1)) | line_equal(a1c1, a1c1))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1232,plain,
% 1.72/1.38 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | ((~incident(a1, a1c1)) | line_equal(a1c1, a1c1))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1233,plain,
% 1.72/1.38 ((~![A: $i, B: $i] : ((~incident(A, B)) | line_equal(B, B))) | (~incident(a1, a1c1)) | line_equal(a1c1, a1c1)),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 1.72/1.38 tff(1234,plain,
% 1.72/1.38 (line_equal(a1c1, a1c1)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1233, 197, 124])).
% 1.72/1.38 tff(1235,plain,
% 1.72/1.38 (((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~incident(ac, a1c1)) | (~line_equal(a1c1, a1c1)) | (~incident(bc, a1c1)) | (~incident(ab, a1c1)))) <=> ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~incident(ac, a1c1)) | (~line_equal(a1c1, a1c1)) | (~incident(bc, a1c1)) | (~incident(ab, a1c1)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1236,plain,
% 1.72/1.38 (((~line_equal(a1c1, a1c1)) | (~incident(bc, a1c1)) | (~incident(ac, a1c1)) | (~incident(ab, a1c1))) <=> ((~incident(ac, a1c1)) | (~line_equal(a1c1, a1c1)) | (~incident(bc, a1c1)) | (~incident(ab, a1c1)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1237,plain,
% 1.72/1.38 (((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(a1c1, a1c1)) | (~incident(bc, a1c1)) | (~incident(ac, a1c1)) | (~incident(ab, a1c1)))) <=> ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~incident(ac, a1c1)) | (~line_equal(a1c1, a1c1)) | (~incident(bc, a1c1)) | (~incident(ab, a1c1))))),
% 1.72/1.38 inference(monotonicity,[status(thm)],[1236])).
% 1.72/1.38 tff(1238,plain,
% 1.72/1.38 (((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(a1c1, a1c1)) | (~incident(bc, a1c1)) | (~incident(ac, a1c1)) | (~incident(ab, a1c1)))) <=> ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~incident(ac, a1c1)) | (~line_equal(a1c1, a1c1)) | (~incident(bc, a1c1)) | (~incident(ab, a1c1)))),
% 1.72/1.38 inference(transitivity,[status(thm)],[1237, 1235])).
% 1.72/1.38 tff(1239,plain,
% 1.72/1.38 ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | ((~line_equal(a1c1, a1c1)) | (~incident(bc, a1c1)) | (~incident(ac, a1c1)) | (~incident(ab, a1c1)))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1240,plain,
% 1.72/1.38 ((~![A: $i] : ((~line_equal(A, A)) | (~incident(bc, A)) | (~incident(ac, A)) | (~incident(ab, A)))) | (~incident(ac, a1c1)) | (~line_equal(a1c1, a1c1)) | (~incident(bc, a1c1)) | (~incident(ab, a1c1))),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 1.72/1.38 tff(1241,plain,
% 1.72/1.38 ((~incident(bc, a1c1)) | (~incident(ab, a1c1))),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1240, 150, 194, 1234])).
% 1.72/1.38 tff(1242,plain,
% 1.72/1.38 (~incident(ab, a1c1)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1241, 1230])).
% 1.72/1.38 tff(1243,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, a1c1) | (~incident(ab, oa)) | (~line_equal(oa, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ab, a1c1) | (~incident(ab, oa)) | (~line_equal(oa, a1c1)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1244,plain,
% 1.72/1.38 ((incident(ab, a1c1) | (~line_equal(oa, a1c1)) | (~incident(ab, oa))) <=> (incident(ab, a1c1) | (~incident(ab, oa)) | (~line_equal(oa, a1c1)))),
% 1.72/1.38 inference(rewrite,[status(thm)],[])).
% 1.72/1.38 tff(1245,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, a1c1) | (~line_equal(oa, a1c1)) | (~incident(ab, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, a1c1) | (~incident(ab, oa)) | (~line_equal(oa, a1c1))))),
% 1.72/1.38 inference(monotonicity,[status(thm)],[1244])).
% 1.72/1.38 tff(1246,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, a1c1) | (~line_equal(oa, a1c1)) | (~incident(ab, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ab, a1c1) | (~incident(ab, oa)) | (~line_equal(oa, a1c1)))),
% 1.72/1.38 inference(transitivity,[status(thm)],[1245, 1243])).
% 1.72/1.38 tff(1247,plain,
% 1.72/1.38 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, a1c1) | (~line_equal(oa, a1c1)) | (~incident(ab, oa)))),
% 1.72/1.38 inference(quant_inst,[status(thm)],[])).
% 1.72/1.38 tff(1248,plain,
% 1.72/1.38 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ab, a1c1) | (~incident(ab, oa)) | (~line_equal(oa, a1c1))),
% 1.72/1.38 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 1.72/1.38 tff(1249,plain,
% 1.72/1.38 (~incident(ab, oa)),
% 1.72/1.38 inference(unit_resolution,[status(thm)],[1248, 15, 1242, 1219])).
% 1.72/1.38 tff(1250,plain,
% 1.72/1.38 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ab, a2b2)) | incident(ab, oa) | (~line_equal(a2b2, oa)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ab, a2b2)) | incident(ab, oa) | (~line_equal(a2b2, oa)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1251,plain,
% 1.72/1.39 ((incident(ab, oa) | (~line_equal(a2b2, oa)) | (~incident(ab, a2b2))) <=> ((~incident(ab, a2b2)) | incident(ab, oa) | (~line_equal(a2b2, oa)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1252,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, oa) | (~line_equal(a2b2, oa)) | (~incident(ab, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ab, a2b2)) | incident(ab, oa) | (~line_equal(a2b2, oa))))),
% 1.72/1.39 inference(monotonicity,[status(thm)],[1251])).
% 1.72/1.39 tff(1253,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, oa) | (~line_equal(a2b2, oa)) | (~incident(ab, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ab, a2b2)) | incident(ab, oa) | (~line_equal(a2b2, oa)))),
% 1.72/1.39 inference(transitivity,[status(thm)],[1252, 1250])).
% 1.72/1.39 tff(1254,plain,
% 1.72/1.39 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ab, oa) | (~line_equal(a2b2, oa)) | (~incident(ab, a2b2)))),
% 1.72/1.39 inference(quant_inst,[status(thm)],[])).
% 1.72/1.39 tff(1255,plain,
% 1.72/1.39 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ab, a2b2)) | incident(ab, oa) | (~line_equal(a2b2, oa))),
% 1.72/1.39 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 1.72/1.39 tff(1256,plain,
% 1.72/1.39 ($false),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1255, 646, 15, 1249, 1190])).
% 1.72/1.39 tff(1257,plain,(point_equal(c2, a1) | point_equal(a2, b1) | line_equal(b2c2, a1b1) | line_equal(a2c2, b1c1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.39 tff(1258,plain,
% 1.72/1.39 (point_equal(a2, b1) | line_equal(b2c2, a1b1) | line_equal(a2c2, b1c1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1257, 522])).
% 1.72/1.39 tff(1259,plain,
% 1.72/1.39 (point_equal(a2, b1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1258, 343, 342])).
% 1.72/1.39 tff(1260,plain,
% 1.72/1.39 (point_equal(b1, a2)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[900, 897, 1259])).
% 1.72/1.39 tff(1261,plain,
% 1.72/1.39 (incident(b1, a2b2)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[911, 1260])).
% 1.72/1.39 tff(1262,plain,
% 1.72/1.39 (((~![A: $i, B: $i, 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))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1263,plain,
% 1.72/1.39 ((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))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1264,plain,
% 1.72/1.39 (((~![A: $i, B: $i, 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)))),
% 1.72/1.39 inference(monotonicity,[status(thm)],[1263])).
% 1.72/1.39 tff(1265,plain,
% 1.72/1.39 (((~![A: $i, B: $i, 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))),
% 1.72/1.39 inference(transitivity,[status(thm)],[1264, 1262])).
% 1.72/1.39 tff(1266,plain,
% 1.72/1.39 ((~![A: $i, B: $i, 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)))),
% 1.72/1.39 inference(quant_inst,[status(thm)],[])).
% 1.72/1.39 tff(1267,plain,
% 1.72/1.39 ((~![A: $i, B: $i, 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)),
% 1.72/1.39 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 1.72/1.39 tff(1268,plain,
% 1.72/1.39 ((~incident(b1, a2b2)) | line_equal(a2b2, ob)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1267, 234, 57, 54, 51, 40])).
% 1.72/1.39 tff(1269,plain,
% 1.72/1.39 (line_equal(a2b2, ob)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1268, 1261])).
% 1.72/1.39 tff(1270,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a2, a2b2)) | incident(a2, ob) | (~line_equal(a2b2, ob)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a2, a2b2)) | incident(a2, ob) | (~line_equal(a2b2, ob)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1271,plain,
% 1.72/1.39 ((incident(a2, ob) | (~line_equal(a2b2, ob)) | (~incident(a2, a2b2))) <=> ((~incident(a2, a2b2)) | incident(a2, ob) | (~line_equal(a2b2, ob)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1272,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, ob) | (~line_equal(a2b2, ob)) | (~incident(a2, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(a2, a2b2)) | incident(a2, ob) | (~line_equal(a2b2, ob))))),
% 1.72/1.39 inference(monotonicity,[status(thm)],[1271])).
% 1.72/1.39 tff(1273,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, ob) | (~line_equal(a2b2, ob)) | (~incident(a2, a2b2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a2, a2b2)) | incident(a2, ob) | (~line_equal(a2b2, ob)))),
% 1.72/1.39 inference(transitivity,[status(thm)],[1272, 1270])).
% 1.72/1.39 tff(1274,plain,
% 1.72/1.39 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(a2, ob) | (~line_equal(a2b2, ob)) | (~incident(a2, a2b2)))),
% 1.72/1.39 inference(quant_inst,[status(thm)],[])).
% 1.72/1.39 tff(1275,plain,
% 1.72/1.39 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(a2, a2b2)) | incident(a2, ob) | (~line_equal(a2b2, ob))),
% 1.72/1.39 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 1.72/1.39 tff(1276,plain,
% 1.72/1.39 (incident(a2, ob) | (~line_equal(a2b2, ob))),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1275, 237, 15])).
% 1.72/1.39 tff(1277,plain,
% 1.72/1.39 (incident(a2, ob)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1276, 1269])).
% 1.72/1.39 tff(1278,plain,
% 1.72/1.39 (((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | ((~incident(a2, ob)) | (~incident(b2, ob)) | (~incident(c2, ob)))) <=> ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (~incident(a2, ob)) | (~incident(b2, ob)) | (~incident(c2, ob)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1279,plain,
% 1.72/1.39 ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | ((~incident(a2, ob)) | (~incident(b2, ob)) | (~incident(c2, ob)))),
% 1.72/1.39 inference(quant_inst,[status(thm)],[])).
% 1.72/1.39 tff(1280,plain,
% 1.72/1.39 ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (~incident(a2, ob)) | (~incident(b2, ob)) | (~incident(c2, ob))),
% 1.72/1.39 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 1.72/1.39 tff(1281,plain,
% 1.72/1.39 ((~incident(a2, ob)) | (~incident(c2, ob))),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1280, 54, 231])).
% 1.72/1.39 tff(1282,plain,
% 1.72/1.39 (~incident(c2, ob)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1281, 1277])).
% 1.72/1.39 tff(1283,plain,
% 1.72/1.39 (~point_equal(c2, o)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[424, 1282])).
% 1.72/1.39 tff(1284,plain,
% 1.72/1.39 (incident(a2, a1b1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[533, 1259])).
% 1.72/1.39 tff(1285,plain,
% 1.72/1.39 (line_equal(ob, a2b2)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[919, 1261])).
% 1.72/1.39 tff(1286,plain,
% 1.72/1.39 (incident(o, a2b2)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[930, 1285])).
% 1.72/1.39 tff(1287,plain,
% 1.72/1.39 (point_equal(a2, o)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[969, 1286, 1284])).
% 1.72/1.39 tff(1288,plain,
% 1.72/1.39 (((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(a2, o)) | point_equal(o, a2))) <=> ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(a2, o)) | point_equal(o, a2))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1289,plain,
% 1.72/1.39 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | ((~point_equal(a2, o)) | point_equal(o, a2))),
% 1.72/1.39 inference(quant_inst,[status(thm)],[])).
% 1.72/1.39 tff(1290,plain,
% 1.72/1.39 ((~![A: $i, B: $i] : ((~point_equal(A, B)) | point_equal(B, A))) | (~point_equal(a2, o)) | point_equal(o, a2)),
% 1.72/1.39 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 1.72/1.39 tff(1291,plain,
% 1.72/1.39 (point_equal(o, a2)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1290, 897, 1287])).
% 1.72/1.39 tff(1292,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, a2c2)) | incident(o, a2c2) | (~point_equal(o, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2c2)) | incident(o, a2c2) | (~point_equal(o, a2)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1293,plain,
% 1.72/1.39 ((incident(o, a2c2) | (~incident(a2, a2c2)) | (~point_equal(o, a2))) <=> ((~incident(a2, a2c2)) | incident(o, a2c2) | (~point_equal(o, a2)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1294,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a2c2) | (~incident(a2, a2c2)) | (~point_equal(o, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(a2, a2c2)) | incident(o, a2c2) | (~point_equal(o, a2))))),
% 1.72/1.39 inference(monotonicity,[status(thm)],[1293])).
% 1.72/1.39 tff(1295,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a2c2) | (~incident(a2, a2c2)) | (~point_equal(o, a2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2c2)) | incident(o, a2c2) | (~point_equal(o, a2)))),
% 1.72/1.39 inference(transitivity,[status(thm)],[1294, 1292])).
% 1.72/1.39 tff(1296,plain,
% 1.72/1.39 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(o, a2c2) | (~incident(a2, a2c2)) | (~point_equal(o, a2)))),
% 1.72/1.39 inference(quant_inst,[status(thm)],[])).
% 1.72/1.39 tff(1297,plain,
% 1.72/1.39 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(a2, a2c2)) | incident(o, a2c2) | (~point_equal(o, a2))),
% 1.72/1.39 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 1.72/1.39 tff(1298,plain,
% 1.72/1.39 (incident(o, a2c2) | (~point_equal(o, a2))),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1297, 257, 171])).
% 1.72/1.39 tff(1299,plain,
% 1.72/1.39 (incident(o, a2c2)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1298, 1291])).
% 1.72/1.39 tff(1300,plain,
% 1.72/1.39 (~incident(c2, a1c1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[416, 1299, 1283])).
% 1.72/1.39 tff(1301,plain,
% 1.72/1.39 (~line_equal(oc, a1c1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1063, 1300])).
% 1.72/1.39 tff(1302,plain,
% 1.72/1.39 (point_equal(ab, b1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[999, 1261])).
% 1.72/1.39 tff(1303,plain,
% 1.72/1.39 (incident(ab, b1c1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1010, 1302])).
% 1.72/1.39 tff(1304,plain,
% 1.72/1.39 (~incident(ac, b1c1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1022, 1303])).
% 1.72/1.39 tff(1305,plain,
% 1.72/1.39 (~point_equal(ac, c1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1029, 686, 171, 1304])).
% 1.72/1.39 tff(1306,plain,
% 1.72/1.39 (incident(a2, oc)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[980, 1287])).
% 1.72/1.39 tff(1307,plain,
% 1.72/1.39 (((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | ((~incident(a2, oc)) | (~incident(b2, oc)) | (~incident(c2, oc)))) <=> ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (~incident(a2, oc)) | (~incident(b2, oc)) | (~incident(c2, oc)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1308,plain,
% 1.72/1.39 ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | ((~incident(a2, oc)) | (~incident(b2, oc)) | (~incident(c2, oc)))),
% 1.72/1.39 inference(quant_inst,[status(thm)],[])).
% 1.72/1.39 tff(1309,plain,
% 1.72/1.39 ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (~incident(a2, oc)) | (~incident(b2, oc)) | (~incident(c2, oc))),
% 1.72/1.39 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 1.72/1.39 tff(1310,plain,
% 1.72/1.39 ((~incident(a2, oc)) | (~incident(b2, oc))),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1309, 317, 231])).
% 1.72/1.39 tff(1311,plain,
% 1.72/1.39 (~incident(b2, oc)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1310, 1306])).
% 1.72/1.39 tff(1312,plain,
% 1.72/1.39 (((~![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)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1313,plain,
% 1.72/1.39 ((incident(b2, oc) | (~incident(c1, oc)) | (~point_equal(b2, c1))) <=> ((~incident(c1, oc)) | incident(b2, oc) | (~point_equal(b2, c1)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1314,plain,
% 1.72/1.39 (((~![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))))),
% 1.72/1.39 inference(monotonicity,[status(thm)],[1313])).
% 1.72/1.39 tff(1315,plain,
% 1.72/1.39 (((~![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)))),
% 1.72/1.39 inference(transitivity,[status(thm)],[1314, 1312])).
% 1.72/1.39 tff(1316,plain,
% 1.72/1.39 ((~![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)))),
% 1.72/1.39 inference(quant_inst,[status(thm)],[])).
% 1.72/1.39 tff(1317,plain,
% 1.72/1.39 ((~![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))),
% 1.72/1.39 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 1.72/1.39 tff(1318,plain,
% 1.72/1.39 (incident(b2, oc) | (~point_equal(b2, c1))),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1317, 306, 171])).
% 1.72/1.39 tff(1319,plain,
% 1.72/1.39 (~point_equal(b2, c1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1318, 1311])).
% 1.72/1.39 tff(1320,plain,
% 1.72/1.39 (~point_equal(c1, b2)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1115, 897, 1319])).
% 1.72/1.39 tff(1321,plain,
% 1.72/1.39 (point_equal(c1, b2) | line_equal(a1c1, oc) | line_equal(a2c2, b1c1) | line_equal(b2c2, a1b1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1046, 522])).
% 1.72/1.39 tff(1322,plain,
% 1.72/1.39 (line_equal(a1c1, oc)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1321, 1320, 343, 342])).
% 1.72/1.39 tff(1323,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ac, a1c1)) | incident(ac, oc) | (~line_equal(a1c1, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ac, a1c1)) | incident(ac, oc) | (~line_equal(a1c1, oc)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1324,plain,
% 1.72/1.39 ((incident(ac, oc) | (~line_equal(a1c1, oc)) | (~incident(ac, a1c1))) <=> ((~incident(ac, a1c1)) | incident(ac, oc) | (~line_equal(a1c1, oc)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1325,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, oc) | (~line_equal(a1c1, oc)) | (~incident(ac, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(ac, a1c1)) | incident(ac, oc) | (~line_equal(a1c1, oc))))),
% 1.72/1.39 inference(monotonicity,[status(thm)],[1324])).
% 1.72/1.39 tff(1326,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, oc) | (~line_equal(a1c1, oc)) | (~incident(ac, a1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ac, a1c1)) | incident(ac, oc) | (~line_equal(a1c1, oc)))),
% 1.72/1.39 inference(transitivity,[status(thm)],[1325, 1323])).
% 1.72/1.39 tff(1327,plain,
% 1.72/1.39 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(ac, oc) | (~line_equal(a1c1, oc)) | (~incident(ac, a1c1)))),
% 1.72/1.39 inference(quant_inst,[status(thm)],[])).
% 1.72/1.39 tff(1328,plain,
% 1.72/1.39 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(ac, a1c1)) | incident(ac, oc) | (~line_equal(a1c1, oc))),
% 1.72/1.39 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 1.72/1.39 tff(1329,plain,
% 1.72/1.39 (incident(ac, oc) | (~line_equal(a1c1, oc))),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1328, 194, 15])).
% 1.72/1.39 tff(1330,plain,
% 1.72/1.39 (incident(ac, oc)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1329, 1322])).
% 1.72/1.39 tff(1331,plain,
% 1.72/1.39 (((~![A: $i, B: $i, 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(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | point_equal(ac, c1) | 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(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | point_equal(ac, c1) | line_equal(oc, a1c1))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1332,plain,
% 1.72/1.39 ((line_equal(oc, a1c1) | point_equal(ac, c1) | (~incident(c1, oc)) | (~incident(ac, oc)) | (~incident(ac, a1c1)) | (~incident(c1, a1c1))) <=> ((~incident(c1, a1c1)) | (~incident(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | point_equal(ac, c1) | line_equal(oc, a1c1))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1333,plain,
% 1.72/1.39 (((~![A: $i, B: $i, 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(ac, c1) | (~incident(c1, oc)) | (~incident(ac, oc)) | (~incident(ac, 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, a1c1)) | (~incident(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | point_equal(ac, c1) | line_equal(oc, a1c1)))),
% 1.72/1.39 inference(monotonicity,[status(thm)],[1332])).
% 1.72/1.39 tff(1334,plain,
% 1.72/1.39 (((~![A: $i, B: $i, 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(ac, c1) | (~incident(c1, oc)) | (~incident(ac, oc)) | (~incident(ac, 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, a1c1)) | (~incident(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | point_equal(ac, c1) | line_equal(oc, a1c1))),
% 1.72/1.39 inference(transitivity,[status(thm)],[1333, 1331])).
% 1.72/1.39 tff(1335,plain,
% 1.72/1.39 ((~![A: $i, B: $i, 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(ac, c1) | (~incident(c1, oc)) | (~incident(ac, oc)) | (~incident(ac, a1c1)) | (~incident(c1, a1c1)))),
% 1.72/1.39 inference(quant_inst,[status(thm)],[])).
% 1.72/1.39 tff(1336,plain,
% 1.72/1.39 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | (~incident(c1, a1c1)) | (~incident(c1, oc)) | (~incident(ac, a1c1)) | (~incident(ac, oc)) | point_equal(ac, c1) | line_equal(oc, a1c1)),
% 1.72/1.39 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 1.72/1.39 tff(1337,plain,
% 1.72/1.39 ($false),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1336, 386, 306, 194, 40, 1330, 1305, 1301])).
% 1.72/1.39 tff(1338,plain,(line_equal(a2c2, b1c1) | line_equal(b2c2, a1b1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.39 tff(1339,plain,
% 1.72/1.39 (line_equal(a2c2, b1c1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1338, 341])).
% 1.72/1.39 tff(1340,assumption,(line_equal(a2c2, b1c1)), introduced(assumption)).
% 1.72/1.39 tff(1341,assumption,(~incident(c2, b1c1)), introduced(assumption)).
% 1.72/1.39 tff(1342,plain,
% 1.72/1.39 (((~![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)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1343,plain,
% 1.72/1.39 ((incident(c2, b1c1) | (~line_equal(a2c2, b1c1)) | (~incident(c2, a2c2))) <=> (incident(c2, b1c1) | (~incident(c2, a2c2)) | (~line_equal(a2c2, b1c1)))),
% 1.72/1.39 inference(rewrite,[status(thm)],[])).
% 1.72/1.39 tff(1344,plain,
% 1.72/1.39 (((~![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))))),
% 1.72/1.39 inference(monotonicity,[status(thm)],[1343])).
% 1.72/1.39 tff(1345,plain,
% 1.72/1.39 (((~![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)))),
% 1.72/1.39 inference(transitivity,[status(thm)],[1344, 1342])).
% 1.72/1.39 tff(1346,plain,
% 1.72/1.39 ((~![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)))),
% 1.72/1.39 inference(quant_inst,[status(thm)],[])).
% 1.72/1.39 tff(1347,plain,
% 1.72/1.39 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(c2, b1c1) | (~incident(c2, a2c2)) | (~line_equal(a2c2, b1c1))),
% 1.72/1.39 inference(modus_ponens,[status(thm)],[1346, 1345])).
% 1.72/1.39 tff(1348,plain,
% 1.72/1.39 ($false),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1347, 254, 15, 1341, 1340])).
% 1.72/1.39 tff(1349,plain,((~line_equal(a2c2, b1c1)) | incident(c2, b1c1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.39 tff(1350,plain,
% 1.72/1.39 (incident(c2, b1c1)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1349, 1339])).
% 1.72/1.39 tff(1351,plain,
% 1.72/1.39 (~incident(c1, b2c2)),
% 1.72/1.39 inference(unit_resolution,[status(thm)],[1140, 1350])).
% 1.72/1.39 tff(1352,plain,
% 1.72/1.39 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, b2c2) | (~incident(bc, b2c2)) | (~point_equal(c1, bc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(c1, b2c2) | (~incident(bc, b2c2)) | (~point_equal(c1, bc)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1353,plain,
% 1.72/1.40 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(c1, b2c2) | (~incident(bc, b2c2)) | (~point_equal(c1, bc)))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1354,plain,
% 1.72/1.40 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | incident(c1, b2c2) | (~incident(bc, b2c2)) | (~point_equal(c1, bc))),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 1.72/1.40 tff(1355,plain,
% 1.72/1.40 (incident(c1, b2c2) | (~point_equal(c1, bc))),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1354, 105, 171])).
% 1.72/1.40 tff(1356,plain,
% 1.72/1.40 (~point_equal(c1, bc)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1355, 1351])).
% 1.72/1.40 tff(1357,assumption,(~point_equal(bc, c2)), introduced(assumption)).
% 1.72/1.40 tff(1358,assumption,(incident(c2, b1c1)), introduced(assumption)).
% 1.72/1.40 tff(1359,plain,
% 1.72/1.40 (((~![A: $i, B: $i, 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(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, 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(b1c1, b2c2) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, c2))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1360,plain,
% 1.72/1.40 ((line_equal(b1c1, b2c2) | point_equal(bc, c2) | (~incident(c2, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(c2, b2c2))) <=> (line_equal(b1c1, b2c2) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, c2))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1361,plain,
% 1.72/1.40 (((~![A: $i, B: $i, 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, c2) | (~incident(c2, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(c2, 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(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, c2)))),
% 1.72/1.40 inference(monotonicity,[status(thm)],[1360])).
% 1.72/1.40 tff(1362,plain,
% 1.72/1.40 (((~![A: $i, B: $i, 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, c2) | (~incident(c2, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(c2, 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(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, c2))),
% 1.72/1.40 inference(transitivity,[status(thm)],[1361, 1359])).
% 1.72/1.40 tff(1363,plain,
% 1.72/1.40 ((~![A: $i, B: $i, 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, c2) | (~incident(c2, b1c1)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | (~incident(c2, b2c2)))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1364,plain,
% 1.72/1.40 ((~![A: $i, B: $i, C: $i, D: $i] : (line_equal(C, D) | point_equal(A, B) | (~incident(B, C)) | (~incident(A, C)) | (~incident(A, D)) | (~incident(B, D)))) | line_equal(b1c1, b2c2) | (~incident(c2, b1c1)) | (~incident(c2, b2c2)) | (~incident(bc, b1c1)) | (~incident(bc, b2c2)) | point_equal(bc, c2)),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1363, 1362])).
% 1.72/1.40 tff(1365,plain,
% 1.72/1.40 ($false),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1364, 323, 672, 105, 669, 40, 1358, 1357])).
% 1.72/1.40 tff(1366,plain,(point_equal(bc, c2) | (~incident(c2, b1c1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.40 tff(1367,plain,
% 1.72/1.40 (point_equal(bc, c2)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1366, 1350])).
% 1.72/1.40 tff(1368,assumption,(point_equal(bc, c2)), introduced(assumption)).
% 1.72/1.40 tff(1369,assumption,(~incident(bc, oc)), introduced(assumption)).
% 1.72/1.40 tff(1370,plain,
% 1.72/1.40 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c2, oc)) | incident(bc, oc) | (~point_equal(bc, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c2, oc)) | incident(bc, oc) | (~point_equal(bc, c2)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1371,plain,
% 1.72/1.40 ((incident(bc, oc) | (~incident(c2, oc)) | (~point_equal(bc, c2))) <=> ((~incident(c2, oc)) | incident(bc, oc) | (~point_equal(bc, c2)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1372,plain,
% 1.72/1.40 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, oc) | (~incident(c2, oc)) | (~point_equal(bc, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | ((~incident(c2, oc)) | incident(bc, oc) | (~point_equal(bc, c2))))),
% 1.72/1.40 inference(monotonicity,[status(thm)],[1371])).
% 1.72/1.40 tff(1373,plain,
% 1.72/1.40 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, oc) | (~incident(c2, oc)) | (~point_equal(bc, c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c2, oc)) | incident(bc, oc) | (~point_equal(bc, c2)))),
% 1.72/1.40 inference(transitivity,[status(thm)],[1372, 1370])).
% 1.72/1.40 tff(1374,plain,
% 1.72/1.40 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (incident(bc, oc) | (~incident(c2, oc)) | (~point_equal(bc, c2)))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1375,plain,
% 1.72/1.40 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~incident(B, C)) | (~point_equal(A, B)))) | (~incident(c2, oc)) | incident(bc, oc) | (~point_equal(bc, c2))),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 1.72/1.40 tff(1376,plain,
% 1.72/1.40 ($false),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1375, 317, 171, 1369, 1368])).
% 1.72/1.40 tff(1377,plain,(incident(bc, oc) | (~point_equal(bc, c2))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.40 tff(1378,plain,
% 1.72/1.40 (incident(bc, oc)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1377, 1367])).
% 1.72/1.40 tff(1379,plain,
% 1.72/1.40 (((~![A: $i, B: $i, 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, b1c1)) | (~incident(c1, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | line_equal(b1c1, oc) | point_equal(c1, bc))) <=> ((~![A: $i, B: $i, 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, b1c1)) | (~incident(c1, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | line_equal(b1c1, oc) | point_equal(c1, bc))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1380,plain,
% 1.72/1.40 ((line_equal(b1c1, oc) | point_equal(c1, bc) | (~incident(bc, b1c1)) | (~incident(c1, b1c1)) | (~incident(c1, oc)) | (~incident(bc, oc))) <=> ((~incident(c1, b1c1)) | (~incident(c1, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | line_equal(b1c1, oc) | point_equal(c1, bc))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1381,plain,
% 1.72/1.40 (((~![A: $i, B: $i, 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(c1, bc) | (~incident(bc, b1c1)) | (~incident(c1, b1c1)) | (~incident(c1, 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(c1, b1c1)) | (~incident(c1, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | line_equal(b1c1, oc) | point_equal(c1, bc)))),
% 1.72/1.40 inference(monotonicity,[status(thm)],[1380])).
% 1.72/1.40 tff(1382,plain,
% 1.72/1.40 (((~![A: $i, B: $i, 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(c1, bc) | (~incident(bc, b1c1)) | (~incident(c1, b1c1)) | (~incident(c1, 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(c1, b1c1)) | (~incident(c1, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | line_equal(b1c1, oc) | point_equal(c1, bc))),
% 1.72/1.40 inference(transitivity,[status(thm)],[1381, 1379])).
% 1.72/1.40 tff(1383,plain,
% 1.72/1.40 ((~![A: $i, B: $i, 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(c1, bc) | (~incident(bc, b1c1)) | (~incident(c1, b1c1)) | (~incident(c1, oc)) | (~incident(bc, oc)))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1384,plain,
% 1.72/1.40 ((~![A: $i, B: $i, 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, b1c1)) | (~incident(c1, oc)) | (~incident(bc, b1c1)) | (~incident(bc, oc)) | line_equal(b1c1, oc) | point_equal(c1, bc)),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 1.72/1.40 tff(1385,plain,
% 1.72/1.40 ((~incident(bc, oc)) | line_equal(b1c1, oc) | point_equal(c1, bc)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1384, 686, 306, 672, 40])).
% 1.72/1.40 tff(1386,plain,
% 1.72/1.40 (line_equal(b1c1, oc)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1385, 1378, 1356])).
% 1.72/1.40 tff(1387,plain,
% 1.72/1.40 (((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(a2c2, oc) | (~line_equal(a2c2, b1c1)) | (~line_equal(b1c1, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | line_equal(a2c2, oc) | (~line_equal(a2c2, b1c1)) | (~line_equal(b1c1, oc)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1388,plain,
% 1.72/1.40 ((line_equal(a2c2, oc) | (~line_equal(b1c1, oc)) | (~line_equal(a2c2, b1c1))) <=> (line_equal(a2c2, oc) | (~line_equal(a2c2, b1c1)) | (~line_equal(b1c1, oc)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1389,plain,
% 1.72/1.40 (((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(a2c2, oc) | (~line_equal(b1c1, oc)) | (~line_equal(a2c2, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(a2c2, oc) | (~line_equal(a2c2, b1c1)) | (~line_equal(b1c1, oc))))),
% 1.72/1.40 inference(monotonicity,[status(thm)],[1388])).
% 1.72/1.40 tff(1390,plain,
% 1.72/1.40 (((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(a2c2, oc) | (~line_equal(b1c1, oc)) | (~line_equal(a2c2, b1c1)))) <=> ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | line_equal(a2c2, oc) | (~line_equal(a2c2, b1c1)) | (~line_equal(b1c1, oc)))),
% 1.72/1.40 inference(transitivity,[status(thm)],[1389, 1387])).
% 1.72/1.40 tff(1391,plain,
% 1.72/1.40 ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | (line_equal(a2c2, oc) | (~line_equal(b1c1, oc)) | (~line_equal(a2c2, b1c1)))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1392,plain,
% 1.72/1.40 ((~![A: $i, B: $i, C: $i] : (line_equal(A, C) | (~line_equal(B, C)) | (~line_equal(A, B)))) | line_equal(a2c2, oc) | (~line_equal(a2c2, b1c1)) | (~line_equal(b1c1, oc))),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 1.72/1.40 tff(1393,plain,
% 1.72/1.40 (line_equal(a2c2, oc)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1392, 80, 1339, 1386])).
% 1.72/1.40 tff(1394,plain,
% 1.72/1.40 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a2c2, oc)) | line_equal(oc, a2c2))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a2c2, oc)) | line_equal(oc, a2c2))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1395,plain,
% 1.72/1.40 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a2c2, oc)) | line_equal(oc, a2c2))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1396,plain,
% 1.72/1.40 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a2c2, oc)) | line_equal(oc, a2c2)),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.72/1.40 tff(1397,plain,
% 1.72/1.40 (line_equal(oc, a2c2)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1396, 97, 1393])).
% 1.72/1.40 tff(1398,assumption,(~incident(ac, b1c1)), introduced(assumption)).
% 1.72/1.40 tff(1399,plain,
% 1.72/1.40 (((~![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)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1400,plain,
% 1.72/1.40 ((incident(ac, b1c1) | (~line_equal(a2c2, b1c1)) | (~incident(ac, a2c2))) <=> (incident(ac, b1c1) | (~incident(ac, a2c2)) | (~line_equal(a2c2, b1c1)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1401,plain,
% 1.72/1.40 (((~![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))))),
% 1.72/1.40 inference(monotonicity,[status(thm)],[1400])).
% 1.72/1.40 tff(1402,plain,
% 1.72/1.40 (((~![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)))),
% 1.72/1.40 inference(transitivity,[status(thm)],[1401, 1399])).
% 1.72/1.40 tff(1403,plain,
% 1.72/1.40 ((~![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)))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1404,plain,
% 1.72/1.40 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | incident(ac, b1c1) | (~incident(ac, a2c2)) | (~line_equal(a2c2, b1c1))),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 1.72/1.40 tff(1405,plain,
% 1.72/1.40 ($false),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1404, 191, 15, 1398, 1340])).
% 1.72/1.40 tff(1406,plain,(incident(ac, b1c1) | (~line_equal(a2c2, b1c1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.40 tff(1407,plain,
% 1.72/1.40 (incident(ac, b1c1)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1406, 1339])).
% 1.72/1.40 tff(1408,plain,
% 1.72/1.40 (~incident(ab, b1c1)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1022, 1407])).
% 1.72/1.40 tff(1409,plain,
% 1.72/1.40 (~point_equal(ab, b1)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1010, 1408])).
% 1.72/1.40 tff(1410,plain,
% 1.72/1.40 (~incident(b1, a2b2)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[999, 1409])).
% 1.72/1.40 tff(1411,plain,
% 1.72/1.40 (~line_equal(ob, a2b2)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[747, 1410])).
% 1.72/1.40 tff(1412,plain,
% 1.72/1.40 (((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | ((~incident(a2, a2c2)) | (~incident(b2, a2c2)) | (~incident(c2, a2c2)))) <=> ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (~incident(a2, a2c2)) | (~incident(b2, a2c2)) | (~incident(c2, a2c2)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1413,plain,
% 1.72/1.40 ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | ((~incident(a2, a2c2)) | (~incident(b2, a2c2)) | (~incident(c2, a2c2)))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1414,plain,
% 1.72/1.40 ((~![A: $i] : ((~incident(a2, A)) | (~incident(b2, A)) | (~incident(c2, A)))) | (~incident(a2, a2c2)) | (~incident(b2, a2c2)) | (~incident(c2, a2c2))),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 1.72/1.40 tff(1415,plain,
% 1.72/1.40 (~incident(b2, a2c2)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1414, 257, 254, 231])).
% 1.72/1.40 tff(1416,plain,
% 1.72/1.40 (((~![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)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1417,plain,
% 1.72/1.40 ((incident(b2, a2c2) | (~incident(a2, a2c2)) | (~point_equal(b2, a2))) <=> ((~incident(a2, a2c2)) | incident(b2, a2c2) | (~point_equal(b2, a2)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1418,plain,
% 1.72/1.40 (((~![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))))),
% 1.72/1.40 inference(monotonicity,[status(thm)],[1417])).
% 1.72/1.40 tff(1419,plain,
% 1.72/1.40 (((~![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)))),
% 1.72/1.40 inference(transitivity,[status(thm)],[1418, 1416])).
% 1.72/1.40 tff(1420,plain,
% 1.72/1.40 ((~![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)))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1421,plain,
% 1.72/1.40 ((~![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))),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 1.72/1.40 tff(1422,plain,
% 1.72/1.40 (~point_equal(b2, a2)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1421, 257, 171, 1415])).
% 1.72/1.40 tff(1423,plain,
% 1.72/1.40 (((~![A: $i, B: $i, 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(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(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(a2, ob)) | (~incident(b2, ob)) | point_equal(b2, a2) | line_equal(ob, a2b2))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1424,plain,
% 1.72/1.40 ((line_equal(ob, a2b2) | point_equal(b2, a2) | (~incident(a2, ob)) | (~incident(b2, ob)) | (~incident(b2, a2b2)) | (~incident(a2, a2b2))) <=> ((~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(a2, ob)) | (~incident(b2, ob)) | point_equal(b2, a2) | line_equal(ob, a2b2))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1425,plain,
% 1.72/1.40 (((~![A: $i, B: $i, 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, a2) | (~incident(a2, ob)) | (~incident(b2, ob)) | (~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)))) | ((~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(a2, ob)) | (~incident(b2, ob)) | point_equal(b2, a2) | line_equal(ob, a2b2)))),
% 1.72/1.40 inference(monotonicity,[status(thm)],[1424])).
% 1.72/1.40 tff(1426,plain,
% 1.72/1.40 (((~![A: $i, B: $i, 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, a2) | (~incident(a2, ob)) | (~incident(b2, ob)) | (~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)))) | (~incident(a2, a2b2)) | (~incident(b2, a2b2)) | (~incident(a2, ob)) | (~incident(b2, ob)) | point_equal(b2, a2) | line_equal(ob, a2b2))),
% 1.72/1.40 inference(transitivity,[status(thm)],[1425, 1423])).
% 1.72/1.40 tff(1427,plain,
% 1.72/1.40 ((~![A: $i, B: $i, 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, a2) | (~incident(a2, ob)) | (~incident(b2, ob)) | (~incident(b2, a2b2)) | (~incident(a2, a2b2)))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1428,plain,
% 1.72/1.40 ((~![A: $i, B: $i, 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(ob, a2b2)),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 1.72/1.40 tff(1429,plain,
% 1.72/1.40 (~incident(a2, ob)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1428, 237, 234, 54, 40, 1422, 1411])).
% 1.72/1.40 tff(1430,plain,
% 1.72/1.40 (((~![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)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1431,plain,
% 1.72/1.40 ((incident(a2, ob) | (~incident(o, ob)) | (~point_equal(a2, o))) <=> ((~incident(o, ob)) | incident(a2, ob) | (~point_equal(a2, o)))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1432,plain,
% 1.72/1.40 (((~![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))))),
% 1.72/1.40 inference(monotonicity,[status(thm)],[1431])).
% 1.72/1.40 tff(1433,plain,
% 1.72/1.40 (((~![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)))),
% 1.72/1.40 inference(transitivity,[status(thm)],[1432, 1430])).
% 1.72/1.40 tff(1434,plain,
% 1.72/1.40 ((~![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)))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1435,plain,
% 1.72/1.40 ((~![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))),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 1.72/1.40 tff(1436,plain,
% 1.72/1.40 (~point_equal(a2, o)),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1435, 333, 171, 1429])).
% 1.72/1.40 tff(1437,assumption,(~line_equal(b1c1, a2c2)), introduced(assumption)).
% 1.72/1.40 tff(1438,plain,
% 1.72/1.40 (((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a2c2, b1c1)) | line_equal(b1c1, a2c2))) <=> ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a2c2, b1c1)) | line_equal(b1c1, a2c2))),
% 1.72/1.40 inference(rewrite,[status(thm)],[])).
% 1.72/1.40 tff(1439,plain,
% 1.72/1.40 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | ((~line_equal(a2c2, b1c1)) | line_equal(b1c1, a2c2))),
% 1.72/1.40 inference(quant_inst,[status(thm)],[])).
% 1.72/1.40 tff(1440,plain,
% 1.72/1.40 ((~![A: $i, B: $i] : ((~line_equal(A, B)) | line_equal(B, A))) | (~line_equal(a2c2, b1c1)) | line_equal(b1c1, a2c2)),
% 1.72/1.40 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 1.72/1.40 tff(1441,plain,
% 1.72/1.40 ($false),
% 1.72/1.40 inference(unit_resolution,[status(thm)],[1440, 97, 1340, 1437])).
% 1.72/1.41 tff(1442,plain,((~line_equal(a2c2, b1c1)) | line_equal(b1c1, a2c2)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.41 tff(1443,plain,
% 1.72/1.41 (line_equal(b1c1, a2c2)),
% 1.72/1.41 inference(unit_resolution,[status(thm)],[1442, 1339])).
% 1.72/1.41 tff(1444,assumption,(line_equal(b1c1, a2c2)), introduced(assumption)).
% 1.72/1.41 tff(1445,assumption,(~incident(c1, a2c2)), introduced(assumption)).
% 1.72/1.41 tff(1446,plain,
% 1.72/1.41 (((~![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)))),
% 1.72/1.41 inference(rewrite,[status(thm)],[])).
% 1.72/1.41 tff(1447,plain,
% 1.72/1.41 ((incident(c1, a2c2) | (~line_equal(b1c1, a2c2)) | (~incident(c1, b1c1))) <=> ((~incident(c1, b1c1)) | incident(c1, a2c2) | (~line_equal(b1c1, a2c2)))),
% 1.72/1.41 inference(rewrite,[status(thm)],[])).
% 1.72/1.41 tff(1448,plain,
% 1.72/1.41 (((~![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))))),
% 1.72/1.41 inference(monotonicity,[status(thm)],[1447])).
% 1.72/1.41 tff(1449,plain,
% 1.72/1.41 (((~![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)))),
% 1.72/1.41 inference(transitivity,[status(thm)],[1448, 1446])).
% 1.72/1.41 tff(1450,plain,
% 1.72/1.41 ((~![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)))),
% 1.72/1.41 inference(quant_inst,[status(thm)],[])).
% 1.72/1.41 tff(1451,plain,
% 1.72/1.41 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(c1, b1c1)) | incident(c1, a2c2) | (~line_equal(b1c1, a2c2))),
% 1.72/1.41 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 1.72/1.41 tff(1452,plain,
% 1.72/1.41 ($false),
% 1.72/1.41 inference(unit_resolution,[status(thm)],[1451, 686, 15, 1445, 1444])).
% 1.72/1.41 tff(1453,plain,((~line_equal(b1c1, a2c2)) | incident(c1, a2c2)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.41 tff(1454,plain,
% 1.72/1.41 (incident(c1, a2c2)),
% 1.72/1.41 inference(unit_resolution,[status(thm)],[1453, 1443])).
% 1.72/1.41 tff(1455,plain,
% 1.72/1.41 (((~![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)))),
% 1.72/1.41 inference(rewrite,[status(thm)],[])).
% 1.72/1.41 tff(1456,plain,
% 1.72/1.41 ((incident(c1, a1b1) | (~incident(a1, a1b1)) | (~point_equal(c1, a1))) <=> ((~incident(a1, a1b1)) | incident(c1, a1b1) | (~point_equal(c1, a1)))),
% 1.72/1.41 inference(rewrite,[status(thm)],[])).
% 1.72/1.41 tff(1457,plain,
% 1.72/1.41 (((~![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))))),
% 1.72/1.41 inference(monotonicity,[status(thm)],[1456])).
% 1.72/1.41 tff(1458,plain,
% 1.72/1.41 (((~![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)))),
% 1.72/1.41 inference(transitivity,[status(thm)],[1457, 1455])).
% 1.72/1.41 tff(1459,plain,
% 1.72/1.41 ((~![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)))),
% 1.72/1.41 inference(quant_inst,[status(thm)],[])).
% 1.72/1.41 tff(1460,plain,
% 1.72/1.41 ((~![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))),
% 1.72/1.41 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 1.72/1.41 tff(1461,plain,
% 1.72/1.41 (~point_equal(c1, a1)),
% 1.72/1.41 inference(unit_resolution,[status(thm)],[1460, 127, 171, 296])).
% 1.72/1.41 tff(1462,plain,
% 1.72/1.41 (((~![A: $i, B: $i, 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(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(c1, a1c1)) | (~incident(c1, a2c2)) | point_equal(c1, 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(a1c1, a2c2) | (~incident(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(c1, a1c1)) | (~incident(c1, a2c2)) | point_equal(c1, a1))),
% 1.72/1.41 inference(rewrite,[status(thm)],[])).
% 1.72/1.41 tff(1463,plain,
% 1.72/1.41 ((line_equal(a1c1, a2c2) | point_equal(c1, a1) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2c2)) | (~incident(a1, a2c2))) <=> (line_equal(a1c1, a2c2) | (~incident(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(c1, a1c1)) | (~incident(c1, a2c2)) | point_equal(c1, a1))),
% 1.72/1.41 inference(rewrite,[status(thm)],[])).
% 1.72/1.41 tff(1464,plain,
% 1.72/1.41 (((~![A: $i, B: $i, 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(c1, a1) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2c2)) | (~incident(a1, 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(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(c1, a1c1)) | (~incident(c1, a2c2)) | point_equal(c1, a1)))),
% 1.72/1.41 inference(monotonicity,[status(thm)],[1463])).
% 1.72/1.41 tff(1465,plain,
% 1.72/1.41 (((~![A: $i, B: $i, 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(c1, a1) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2c2)) | (~incident(a1, 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(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(c1, a1c1)) | (~incident(c1, a2c2)) | point_equal(c1, a1))),
% 1.72/1.41 inference(transitivity,[status(thm)],[1464, 1462])).
% 1.72/1.41 tff(1466,plain,
% 1.72/1.41 ((~![A: $i, B: $i, 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(c1, a1) | (~incident(a1, a1c1)) | (~incident(c1, a1c1)) | (~incident(c1, a2c2)) | (~incident(a1, a2c2)))),
% 1.72/1.41 inference(quant_inst,[status(thm)],[])).
% 1.72/1.41 tff(1467,plain,
% 1.72/1.41 ((~![A: $i, B: $i, 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(a1, a1c1)) | (~incident(a1, a2c2)) | (~incident(c1, a1c1)) | (~incident(c1, a2c2)) | point_equal(c1, a1)),
% 1.72/1.41 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 1.72/1.41 tff(1468,plain,
% 1.72/1.41 ((~incident(a1, a2c2)) | (~incident(c1, a2c2))),
% 1.72/1.41 inference(unit_resolution,[status(thm)],[1467, 197, 386, 188, 40, 1461])).
% 1.72/1.41 tff(1469,plain,
% 1.72/1.41 (~incident(a1, a2c2)),
% 1.72/1.41 inference(unit_resolution,[status(thm)],[1468, 1454])).
% 1.72/1.41 tff(1470,plain,
% 1.72/1.41 (~line_equal(oa, a2c2)),
% 1.72/1.41 inference(unit_resolution,[status(thm)],[214, 1469])).
% 1.72/1.41 tff(1471,plain,
% 1.72/1.41 (((~![A: $i, B: $i, 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(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2c2)) | line_equal(oa, a2c2) | 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(a2, a2c2)) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2c2)) | line_equal(oa, a2c2) | point_equal(a2, o))),
% 1.72/1.41 inference(rewrite,[status(thm)],[])).
% 1.72/1.41 tff(1472,plain,
% 1.72/1.41 ((line_equal(oa, a2c2) | point_equal(a2, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, a2c2)) | (~incident(o, a2c2))) <=> ((~incident(a2, a2c2)) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2c2)) | line_equal(oa, a2c2) | point_equal(a2, o))),
% 1.72/1.41 inference(rewrite,[status(thm)],[])).
% 1.72/1.41 tff(1473,plain,
% 1.72/1.41 (((~![A: $i, B: $i, 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, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, 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)))) | ((~incident(a2, a2c2)) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2c2)) | line_equal(oa, a2c2) | point_equal(a2, o)))),
% 1.72/1.41 inference(monotonicity,[status(thm)],[1472])).
% 1.72/1.41 tff(1474,plain,
% 1.72/1.41 (((~![A: $i, B: $i, 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, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, 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)))) | (~incident(a2, a2c2)) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2c2)) | line_equal(oa, a2c2) | point_equal(a2, o))),
% 1.72/1.41 inference(transitivity,[status(thm)],[1473, 1471])).
% 1.72/1.41 tff(1475,plain,
% 1.72/1.41 ((~![A: $i, B: $i, 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, o) | (~incident(o, oa)) | (~incident(a2, oa)) | (~incident(a2, a2c2)) | (~incident(o, a2c2)))),
% 1.72/1.41 inference(quant_inst,[status(thm)],[])).
% 1.72/1.41 tff(1476,plain,
% 1.72/1.41 ((~![A: $i, B: $i, 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(o, oa)) | (~incident(a2, oa)) | (~incident(o, a2c2)) | line_equal(oa, a2c2) | point_equal(a2, o)),
% 1.72/1.41 inference(modus_ponens,[status(thm)],[1475, 1474])).
% 1.72/1.41 tff(1477,plain,
% 1.72/1.41 (~incident(o, a2c2)),
% 1.72/1.41 inference(unit_resolution,[status(thm)],[1476, 257, 268, 251, 40, 1470, 1436])).
% 1.72/1.41 tff(1478,plain,
% 1.72/1.41 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oc)) | incident(o, a2c2) | (~line_equal(oc, a2c2)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oc)) | incident(o, a2c2) | (~line_equal(oc, a2c2)))),
% 1.72/1.41 inference(rewrite,[status(thm)],[])).
% 1.72/1.41 tff(1479,plain,
% 1.72/1.41 ((incident(o, a2c2) | (~line_equal(oc, a2c2)) | (~incident(o, oc))) <=> ((~incident(o, oc)) | incident(o, a2c2) | (~line_equal(oc, a2c2)))),
% 1.72/1.41 inference(rewrite,[status(thm)],[])).
% 1.72/1.41 tff(1480,plain,
% 1.72/1.41 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2c2) | (~line_equal(oc, a2c2)) | (~incident(o, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | ((~incident(o, oc)) | incident(o, a2c2) | (~line_equal(oc, a2c2))))),
% 1.72/1.41 inference(monotonicity,[status(thm)],[1479])).
% 1.72/1.41 tff(1481,plain,
% 1.72/1.41 (((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2c2) | (~line_equal(oc, a2c2)) | (~incident(o, oc)))) <=> ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oc)) | incident(o, a2c2) | (~line_equal(oc, a2c2)))),
% 1.72/1.41 inference(transitivity,[status(thm)],[1480, 1478])).
% 1.72/1.41 tff(1482,plain,
% 1.72/1.41 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (incident(o, a2c2) | (~line_equal(oc, a2c2)) | (~incident(o, oc)))),
% 1.72/1.41 inference(quant_inst,[status(thm)],[])).
% 1.72/1.41 tff(1483,plain,
% 1.72/1.41 ((~![A: $i, B: $i, C: $i] : (incident(A, C) | (~line_equal(B, C)) | (~incident(A, B)))) | (~incident(o, oc)) | incident(o, a2c2) | (~line_equal(oc, a2c2))),
% 1.72/1.41 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 1.72/1.41 tff(1484,plain,
% 1.72/1.41 ($false),
% 1.72/1.41 inference(unit_resolution,[status(thm)],[1483, 320, 15, 1477, 1397])).
% 1.72/1.41 % SZS output end Proof
%------------------------------------------------------------------------------