TSTP Solution File: GEO169+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO169+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.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 : Wed Aug 30 23:21:47 EDT 2023
% Result : Theorem 88.93s 12.87s
% Output : Proof 89.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO169+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 23:50:21 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.20/1.26 Prover 1: Preprocessing ...
% 3.20/1.26 Prover 4: Preprocessing ...
% 3.20/1.29 Prover 0: Preprocessing ...
% 3.20/1.29 Prover 6: Preprocessing ...
% 3.20/1.29 Prover 3: Preprocessing ...
% 3.20/1.29 Prover 5: Preprocessing ...
% 3.20/1.29 Prover 2: Preprocessing ...
% 5.92/1.78 Prover 2: Constructing countermodel ...
% 5.92/1.78 Prover 5: Constructing countermodel ...
% 6.46/1.83 Prover 3: Constructing countermodel ...
% 7.05/1.90 Prover 6: Constructing countermodel ...
% 7.99/2.06 Prover 1: Constructing countermodel ...
% 8.48/2.26 Prover 0: Proving ...
% 8.48/2.26 Prover 4: Constructing countermodel ...
% 13.58/2.81 Prover 3: gave up
% 13.58/2.82 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.58/2.94 Prover 7: Preprocessing ...
% 14.62/3.12 Prover 7: Constructing countermodel ...
% 18.25/3.48 Prover 1: gave up
% 18.45/3.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.89/3.58 Prover 8: Preprocessing ...
% 18.89/3.70 Prover 6: gave up
% 18.89/3.70 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 18.89/3.76 Prover 9: Preprocessing ...
% 18.89/3.81 Prover 8: Warning: ignoring some quantifiers
% 18.89/3.81 Prover 8: Constructing countermodel ...
% 22.53/4.04 Prover 9: Constructing countermodel ...
% 25.76/4.55 Prover 8: gave up
% 25.76/4.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.76/4.68 Prover 10: Preprocessing ...
% 28.24/4.80 Prover 10: Constructing countermodel ...
% 50.73/8.10 Prover 2: stopped
% 50.73/8.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 52.26/8.17 Prover 11: Preprocessing ...
% 56.46/8.51 Prover 11: Constructing countermodel ...
% 88.27/12.79 Prover 10: Found proof (size 775)
% 88.27/12.79 Prover 10: proved (8218ms)
% 88.27/12.79 Prover 9: stopped
% 88.27/12.79 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 88.27/12.79 Prover 0: stopped
% 88.27/12.80 Prover 5: stopped
% 88.27/12.80 Prover 7: stopped
% 88.27/12.80 Prover 11: stopped
% 88.73/12.81 Prover 4: stopped
% 88.73/12.83 Prover 12: Preprocessing ...
% 88.93/12.87 Prover 12: stopped
% 88.93/12.87
% 88.93/12.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 88.93/12.87
% 88.93/12.90 % SZS output start Proof for theBenchmark
% 88.93/12.91 Assumptions after simplification:
% 88.93/12.91 ---------------------------------
% 88.93/12.91
% 88.93/12.91 (gap_a)
% 88.93/12.92 $i(a1c1) & $i(b2) & $i(b2c2) & $i(a1) & (incident(b2, a1c1) | incident(a1,
% 88.93/12.92 b2c2))
% 88.93/12.92
% 88.93/12.92 (gap_b)
% 88.93/12.92 $i(a1b1) & $i(c2) & $i(a2c2) & $i(b1) & (incident(c2, a1b1) | incident(b1,
% 88.93/12.92 a2c2))
% 88.93/12.92
% 88.93/12.92 (gap_c)
% 88.93/12.92 $i(b1c1) & $i(a2) & $i(a2b2) & $i(c1) & (incident(a2, b1c1) | incident(c1,
% 88.93/12.92 a2b2))
% 88.93/12.92
% 88.93/12.92 (goal_normal)
% 88.93/12.92 $i(ab) & $i(ac) & $i(bc) & ! [v0: $i] : ( ~ $i(v0) | ~ incident(ab, v0) | ~
% 88.93/12.92 incident(ac, v0) | ~ incident(bc, v0) | ~ line_equal(v0, v0) | goal)
% 88.93/12.92
% 88.93/12.92 (goal_to_be_proved)
% 88.93/12.92 ~ goal
% 88.93/12.92
% 88.93/12.92 (ia1b1)
% 88.93/12.92 $i(a1b1) & $i(a1) & incident(a1, a1b1)
% 88.93/12.92
% 88.93/12.92 (ia1c1)
% 88.93/12.92 $i(a1c1) & $i(a1) & incident(a1, a1c1)
% 88.93/12.92
% 88.93/12.92 (ia1oa)
% 88.93/12.93 $i(oa) & $i(a1) & incident(a1, oa)
% 88.93/12.93
% 88.93/12.93 (ia2b2)
% 88.93/12.93 $i(a2) & $i(a2b2) & incident(a2, a2b2)
% 88.93/12.93
% 88.93/12.93 (ia2c2)
% 88.93/12.93 $i(a2) & $i(a2c2) & incident(a2, a2c2)
% 88.93/12.93
% 88.93/12.93 (ia2oa)
% 88.93/12.93 $i(oa) & $i(a2) & incident(a2, oa)
% 88.93/12.93
% 88.93/12.93 (iab1)
% 88.93/12.94 $i(a1b1) & $i(ab) & incident(ab, a1b1)
% 88.93/12.94
% 88.93/12.94 (iab2)
% 88.93/12.94 $i(a2b2) & $i(ab) & incident(ab, a2b2)
% 88.93/12.94
% 88.93/12.94 (iac1)
% 88.93/12.94 $i(a1c1) & $i(ac) & incident(ac, a1c1)
% 88.93/12.94
% 88.93/12.94 (iac2)
% 88.93/12.94 $i(a2c2) & $i(ac) & incident(ac, a2c2)
% 88.93/12.94
% 88.93/12.94 (ib1a1)
% 88.93/12.94 $i(a1b1) & $i(b1) & incident(b1, a1b1)
% 88.93/12.94
% 88.93/12.94 (ib1c1)
% 88.93/12.94 $i(b1c1) & $i(b1) & incident(b1, b1c1)
% 88.93/12.94
% 88.93/12.94 (ib1ob)
% 88.93/12.94 $i(ob) & $i(b1) & incident(b1, ob)
% 88.93/12.94
% 88.93/12.94 (ib2a2)
% 88.93/12.94 $i(b2) & $i(a2b2) & incident(b2, a2b2)
% 88.93/12.94
% 88.93/12.94 (ib2c2)
% 88.93/12.94 $i(b2) & $i(b2c2) & incident(b2, b2c2)
% 88.93/12.94
% 88.93/12.94 (ib2ob)
% 88.93/12.94 $i(ob) & $i(b2) & incident(b2, ob)
% 88.93/12.94
% 88.93/12.94 (ibc1)
% 88.93/12.94 $i(b1c1) & $i(bc) & incident(bc, b1c1)
% 88.93/12.94
% 88.93/12.94 (ibc2)
% 88.93/12.94 $i(b2c2) & $i(bc) & incident(bc, b2c2)
% 88.93/12.94
% 88.93/12.94 (ic1a1)
% 88.93/12.94 $i(a1c1) & $i(c1) & incident(c1, a1c1)
% 88.93/12.94
% 88.93/12.94 (ic1b1)
% 88.93/12.94 $i(b1c1) & $i(c1) & incident(c1, b1c1)
% 88.93/12.94
% 88.93/12.94 (ic1oc)
% 88.93/12.94 $i(oc) & $i(c1) & incident(c1, oc)
% 88.93/12.94
% 88.93/12.94 (ic2a2)
% 88.93/12.94 $i(c2) & $i(a2c2) & incident(c2, a2c2)
% 88.93/12.94
% 88.93/12.94 (ic2b2)
% 88.93/12.94 $i(c2) & $i(b2c2) & incident(c2, b2c2)
% 88.93/12.94
% 88.93/12.94 (ic2oc)
% 88.93/12.94 $i(oc) & $i(c2) & incident(c2, oc)
% 88.93/12.94
% 88.93/12.94 (iooa)
% 88.93/12.94 $i(oa) & $i(o) & incident(o, oa)
% 88.93/12.94
% 88.93/12.94 (ioob)
% 88.93/12.94 $i(ob) & $i(o) & incident(o, ob)
% 88.93/12.94
% 88.93/12.94 (iooc)
% 88.93/12.94 $i(oc) & $i(o) & incident(o, oc)
% 88.93/12.94
% 88.93/12.94 (lcon)
% 88.93/12.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 88.93/12.95 ~ incident(v0, v1) | ~ line_equal(v1, v2) | incident(v0, v2))
% 88.93/12.95
% 88.93/12.95 (notaa)
% 88.93/12.95 $i(a2) & $i(a1) & ( ~ point_equal(a2, a1) | goal)
% 88.93/12.95
% 88.93/12.95 (notab)
% 88.93/12.95 $i(a1b1) & $i(a2b2) & ( ~ line_equal(a1b1, a2b2) | goal)
% 88.93/12.95
% 88.93/12.95 (notac)
% 89.31/12.95 $i(a1c1) & $i(a2c2) & ( ~ line_equal(a1c1, a2c2) | goal)
% 89.31/12.95
% 89.31/12.95 (notbb)
% 89.31/12.95 $i(b2) & $i(b1) & ( ~ point_equal(b2, b1) | goal)
% 89.31/12.95
% 89.31/12.95 (notbc)
% 89.31/12.95 $i(b1c1) & $i(b2c2) & ( ~ line_equal(b1c1, b2c2) | goal)
% 89.31/12.95
% 89.31/12.95 (notcc)
% 89.31/12.95 $i(c2) & $i(c1) & ( ~ point_equal(c2, c1) | goal)
% 89.31/12.95
% 89.31/12.95 (pcon)
% 89.31/12.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 89.31/12.95 ~ point_equal(v0, v1) | ~ incident(v1, v2) | incident(v0, v2))
% 89.31/12.95
% 89.31/12.95 (reflexivity_of_line_equal)
% 89.31/12.95 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ incident(v0, v1) |
% 89.31/12.95 line_equal(v1, v1))
% 89.31/12.95
% 89.31/12.95 (symmetry_of_point_equal)
% 89.31/12.95 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ point_equal(v0, v1) |
% 89.31/12.95 point_equal(v1, v0))
% 89.31/12.95
% 89.31/12.95 (t1in2)
% 89.31/12.95 $i(a2b2) & $i(c1) & $i(a2c2) & $i(b1) & $i(b2c2) & $i(a1) & ( ~ incident(c1,
% 89.31/12.95 a2b2) | ~ incident(b1, a2c2) | ~ incident(a1, b2c2) | goal)
% 89.31/12.95
% 89.31/12.95 (t2in1)
% 89.31/12.95 $i(a1b1) & $i(c2) & $i(a1c1) & $i(b2) & $i(b1c1) & $i(a2) & ( ~ incident(c2,
% 89.31/12.95 a1b1) | ~ incident(b2, a1c1) | ~ incident(a2, b1c1) | goal)
% 89.31/12.95
% 89.31/12.95 (triangle1)
% 89.31/12.96 $i(c1) & $i(b1) & $i(a1) & ! [v0: $i] : ( ~ $i(v0) | ~ incident(c1, v0) | ~
% 89.31/12.96 incident(b1, v0) | ~ incident(a1, v0) | goal)
% 89.31/12.96
% 89.31/12.96 (triangle2)
% 89.31/12.96 $i(c2) & $i(b2) & $i(a2) & ! [v0: $i] : ( ~ $i(v0) | ~ incident(c2, v0) | ~
% 89.31/12.96 incident(b2, v0) | ~ incident(a2, v0) | goal)
% 89.31/12.96
% 89.31/12.96 (unique)
% 89.31/12.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 89.31/12.96 | ~ $i(v1) | ~ $i(v0) | ~ incident(v1, v3) | ~ incident(v1, v2) | ~
% 89.31/12.96 incident(v0, v3) | ~ incident(v0, v2) | point_equal(v0, v1) |
% 89.31/12.96 line_equal(v2, v3))
% 89.31/12.96
% 89.31/12.96 Further assumptions not needed in the proof:
% 89.31/12.96 --------------------------------------------
% 89.31/12.96 reflexivity_of_point_equal, symmetry_of_line_equal, transitivity_of_line_equal,
% 89.31/12.96 transitivity_of_point_equal
% 89.31/12.96
% 89.31/12.96 Those formulas are unsatisfiable:
% 89.31/12.96 ---------------------------------
% 89.31/12.96
% 89.31/12.96 Begin of proof
% 89.31/12.96 |
% 89.31/12.96 | ALPHA: (notab) implies:
% 89.31/12.96 | (1) ~ line_equal(a1b1, a2b2) | goal
% 89.31/12.96 |
% 89.31/12.96 | ALPHA: (notac) implies:
% 89.31/12.96 | (2) ~ line_equal(a1c1, a2c2) | goal
% 89.31/12.96 |
% 89.31/12.96 | ALPHA: (notbc) implies:
% 89.31/12.96 | (3) ~ line_equal(b1c1, b2c2) | goal
% 89.31/12.96 |
% 89.31/12.96 | ALPHA: (notcc) implies:
% 89.31/12.96 | (4) ~ point_equal(c2, c1) | goal
% 89.31/12.96 |
% 89.31/12.96 | ALPHA: (notbb) implies:
% 89.31/12.96 | (5) ~ point_equal(b2, b1) | goal
% 89.31/12.96 |
% 89.31/12.96 | ALPHA: (notaa) implies:
% 89.31/12.96 | (6) ~ point_equal(a2, a1) | goal
% 89.31/12.96 |
% 89.31/12.96 | ALPHA: (triangle2) implies:
% 89.31/12.96 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ incident(c2, v0) | ~ incident(b2, v0) |
% 89.31/12.96 | ~ incident(a2, v0) | goal)
% 89.31/12.96 |
% 89.31/12.96 | ALPHA: (triangle1) implies:
% 89.31/12.97 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ incident(c1, v0) | ~ incident(b1, v0) |
% 89.31/12.97 | ~ incident(a1, v0) | goal)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (iab2) implies:
% 89.31/12.97 | (9) incident(ab, a2b2)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (iab1) implies:
% 89.31/12.97 | (10) incident(ab, a1b1)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (iac2) implies:
% 89.31/12.97 | (11) incident(ac, a2c2)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (iac1) implies:
% 89.31/12.97 | (12) incident(ac, a1c1)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ibc2) implies:
% 89.31/12.97 | (13) incident(bc, b2c2)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ibc1) implies:
% 89.31/12.97 | (14) incident(bc, b1c1)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ic2oc) implies:
% 89.31/12.97 | (15) incident(c2, oc)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ic1oc) implies:
% 89.31/12.97 | (16) incident(c1, oc)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ib2ob) implies:
% 89.31/12.97 | (17) incident(b2, ob)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ib1ob) implies:
% 89.31/12.97 | (18) incident(b1, ob)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ia2oa) implies:
% 89.31/12.97 | (19) incident(a2, oa)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ia1oa) implies:
% 89.31/12.97 | (20) incident(a1, oa)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (iooc) implies:
% 89.31/12.97 | (21) incident(o, oc)
% 89.31/12.97 | (22) $i(oc)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ioob) implies:
% 89.31/12.97 | (23) incident(o, ob)
% 89.31/12.97 | (24) $i(ob)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (iooa) implies:
% 89.31/12.97 | (25) incident(o, oa)
% 89.31/12.97 | (26) $i(o)
% 89.31/12.97 | (27) $i(oa)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ib2c2) implies:
% 89.31/12.97 | (28) incident(b2, b2c2)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ic2b2) implies:
% 89.31/12.97 | (29) incident(c2, b2c2)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ib1c1) implies:
% 89.31/12.97 | (30) incident(b1, b1c1)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ic1b1) implies:
% 89.31/12.97 | (31) incident(c1, b1c1)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ic2a2) implies:
% 89.31/12.97 | (32) incident(c2, a2c2)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ia2c2) implies:
% 89.31/12.97 | (33) incident(a2, a2c2)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ic1a1) implies:
% 89.31/12.97 | (34) incident(c1, a1c1)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ia1c1) implies:
% 89.31/12.97 | (35) incident(a1, a1c1)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ib2a2) implies:
% 89.31/12.97 | (36) incident(b2, a2b2)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ia2b2) implies:
% 89.31/12.97 | (37) incident(a2, a2b2)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ib1a1) implies:
% 89.31/12.97 | (38) incident(b1, a1b1)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (ia1b1) implies:
% 89.31/12.97 | (39) incident(a1, a1b1)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (gap_c) implies:
% 89.31/12.97 | (40) incident(a2, b1c1) | incident(c1, a2b2)
% 89.31/12.97 |
% 89.31/12.97 | ALPHA: (gap_b) implies:
% 89.31/12.97 | (41) incident(c2, a1b1) | incident(b1, a2c2)
% 89.31/12.98 |
% 89.31/12.98 | ALPHA: (gap_a) implies:
% 89.31/12.98 | (42) incident(b2, a1c1) | incident(a1, b2c2)
% 89.31/12.98 |
% 89.31/12.98 | ALPHA: (t2in1) implies:
% 89.31/12.98 | (43) $i(a2)
% 89.31/12.98 | (44) $i(b1c1)
% 89.31/12.98 | (45) $i(b2)
% 89.31/12.98 | (46) $i(a1c1)
% 89.31/12.98 | (47) $i(c2)
% 89.31/12.98 | (48) $i(a1b1)
% 89.31/12.98 | (49) ~ incident(c2, a1b1) | ~ incident(b2, a1c1) | ~ incident(a2, b1c1)
% 89.31/12.98 | | goal
% 89.31/12.98 |
% 89.31/12.98 | ALPHA: (t1in2) implies:
% 89.31/12.98 | (50) $i(a1)
% 89.31/12.98 | (51) $i(b2c2)
% 89.31/12.98 | (52) $i(b1)
% 89.31/12.98 | (53) $i(a2c2)
% 89.31/12.98 | (54) $i(c1)
% 89.31/12.98 | (55) $i(a2b2)
% 89.31/12.98 | (56) ~ incident(c1, a2b2) | ~ incident(b1, a2c2) | ~ incident(a1, b2c2)
% 89.31/12.98 | | goal
% 89.31/12.98 |
% 89.31/12.98 | ALPHA: (goal_normal) implies:
% 89.31/12.98 | (57) $i(bc)
% 89.31/12.98 | (58) $i(ac)
% 89.31/12.98 | (59) $i(ab)
% 89.31/12.98 | (60) ! [v0: $i] : ( ~ $i(v0) | ~ incident(ab, v0) | ~ incident(ac, v0) |
% 89.31/12.98 | ~ incident(bc, v0) | ~ line_equal(v0, v0) | goal)
% 89.31/12.98 |
% 89.31/12.98 | BETA: splitting (6) gives:
% 89.31/12.98 |
% 89.31/12.98 | Case 1:
% 89.31/12.98 | |
% 89.31/12.98 | | (61) ~ point_equal(a2, a1)
% 89.31/12.98 | |
% 89.31/12.98 | | BETA: splitting (4) gives:
% 89.31/12.98 | |
% 89.31/12.98 | | Case 1:
% 89.31/12.98 | | |
% 89.31/12.98 | | | (62) ~ point_equal(c2, c1)
% 89.31/12.98 | | |
% 89.31/12.98 | | | BETA: splitting (1) gives:
% 89.31/12.98 | | |
% 89.31/12.98 | | | Case 1:
% 89.31/12.98 | | | |
% 89.31/12.98 | | | | (63) ~ line_equal(a1b1, a2b2)
% 89.31/12.98 | | | |
% 89.31/12.98 | | | | BETA: splitting (5) gives:
% 89.31/12.98 | | | |
% 89.31/12.98 | | | | Case 1:
% 89.31/12.98 | | | | |
% 89.31/12.98 | | | | | (64) ~ point_equal(b2, b1)
% 89.31/12.98 | | | | |
% 89.31/12.98 | | | | | BETA: splitting (2) gives:
% 89.31/12.98 | | | | |
% 89.31/12.98 | | | | | Case 1:
% 89.31/12.98 | | | | | |
% 89.31/12.98 | | | | | | (65) ~ line_equal(a1c1, a2c2)
% 89.31/12.98 | | | | | |
% 89.31/12.98 | | | | | | BETA: splitting (3) gives:
% 89.31/12.98 | | | | | |
% 89.31/12.98 | | | | | | Case 1:
% 89.31/12.98 | | | | | | |
% 89.31/12.98 | | | | | | | (66) ~ line_equal(b1c1, b2c2)
% 89.31/12.98 | | | | | | |
% 89.31/12.99 | | | | | | | GROUND_INST: instantiating (reflexivity_of_line_equal) with b2,
% 89.31/12.99 | | | | | | | a2b2, simplifying with (36), (45), (55) gives:
% 89.31/12.99 | | | | | | | (67) line_equal(a2b2, a2b2)
% 89.31/12.99 | | | | | | |
% 89.31/12.99 | | | | | | | GROUND_INST: instantiating (reflexivity_of_line_equal) with c2,
% 89.31/12.99 | | | | | | | b2c2, simplifying with (29), (47), (51) gives:
% 89.31/12.99 | | | | | | | (68) line_equal(b2c2, b2c2)
% 89.31/12.99 | | | | | | |
% 89.52/12.99 | | | | | | | GROUND_INST: instantiating (reflexivity_of_line_equal) with c2,
% 89.52/12.99 | | | | | | | a2c2, simplifying with (32), (47), (53) gives:
% 89.52/12.99 | | | | | | | (69) line_equal(a2c2, a2c2)
% 89.52/12.99 | | | | | | |
% 89.52/12.99 | | | | | | | BETA: splitting (42) gives:
% 89.52/12.99 | | | | | | |
% 89.52/12.99 | | | | | | | Case 1:
% 89.52/12.99 | | | | | | | |
% 89.52/12.99 | | | | | | | | (70) incident(b2, a1c1)
% 89.52/12.99 | | | | | | | |
% 89.52/12.99 | | | | | | | | BETA: splitting (41) gives:
% 89.52/12.99 | | | | | | | |
% 89.52/12.99 | | | | | | | | Case 1:
% 89.52/12.99 | | | | | | | | |
% 89.52/12.99 | | | | | | | | | (71) incident(c2, a1b1)
% 89.52/12.99 | | | | | | | | |
% 89.52/12.99 | | | | | | | | | BETA: splitting (49) gives:
% 89.52/12.99 | | | | | | | | |
% 89.52/12.99 | | | | | | | | | Case 1:
% 89.52/12.99 | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | (72) ~ incident(c2, a1b1)
% 89.52/12.99 | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | PRED_UNIFY: (71), (72) imply:
% 89.52/12.99 | | | | | | | | | | (73) $false
% 89.52/12.99 | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | CLOSE: (73) is inconsistent.
% 89.52/12.99 | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | Case 2:
% 89.52/12.99 | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | (74) ~ incident(b2, a1c1) | ~ incident(a2, b1c1) | goal
% 89.52/12.99 | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | BETA: splitting (74) gives:
% 89.52/12.99 | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | Case 1:
% 89.52/12.99 | | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | | (75) ~ incident(b2, a1c1)
% 89.52/12.99 | | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | | PRED_UNIFY: (70), (75) imply:
% 89.52/12.99 | | | | | | | | | | | (76) $false
% 89.52/12.99 | | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | | CLOSE: (76) is inconsistent.
% 89.52/12.99 | | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | Case 2:
% 89.52/12.99 | | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | | (77) ~ incident(a2, b1c1) | goal
% 89.52/12.99 | | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | | BETA: splitting (77) gives:
% 89.52/12.99 | | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | | Case 1:
% 89.52/12.99 | | | | | | | | | | | |
% 89.52/12.99 | | | | | | | | | | | | (78) ~ incident(a2, b1c1)
% 89.52/12.99 | | | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 89.52/13.00 | | | | | | | | | | | | (16), (17), (18), (19), (20), (21), (22), (23),
% 89.52/13.00 | | | | | | | | | | | | (24), (25), (26), (27), (28), (29), (30), (31),
% 89.52/13.00 | | | | | | | | | | | | (32), (33), (34), (35), (36), (37), (38), (39),
% 89.52/13.00 | | | | | | | | | | | | (40), (41), (43), (44), (45), (46), (47), (48),
% 89.52/13.00 | | | | | | | | | | | | (50), (51), (52), (53), (54), (55), (56), (57),
% 89.52/13.00 | | | | | | | | | | | | (58), (59), (60), (61), (62), (63), (64), (65),
% 89.52/13.00 | | | | | | | | | | | | (66), (67), (68), (69), (70), (78),
% 89.52/13.00 | | | | | | | | | | | | (goal_to_be_proved), (lcon), (pcon),
% 89.52/13.00 | | | | | | | | | | | | (symmetry_of_point_equal), (unique) are
% 89.52/13.00 | | | | | | | | | | | | inconsistent by sub-proof #1.
% 89.52/13.00 | | | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | | Case 2:
% 89.52/13.00 | | | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | | | (79) goal
% 89.52/13.00 | | | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | | | PRED_UNIFY: (79), (goal_to_be_proved) imply:
% 89.52/13.00 | | | | | | | | | | | | (80) $false
% 89.52/13.00 | | | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | | | CLOSE: (80) is inconsistent.
% 89.52/13.00 | | | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | | End of split
% 89.52/13.00 | | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | End of split
% 89.52/13.00 | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | End of split
% 89.52/13.00 | | | | | | | | |
% 89.52/13.00 | | | | | | | | Case 2:
% 89.52/13.00 | | | | | | | | |
% 89.52/13.00 | | | | | | | | | (81) incident(b1, a2c2)
% 89.52/13.00 | | | | | | | | |
% 89.52/13.00 | | | | | | | | | BETA: splitting (40) gives:
% 89.52/13.00 | | | | | | | | |
% 89.52/13.00 | | | | | | | | | Case 1:
% 89.52/13.00 | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | (82) incident(a2, b1c1)
% 89.52/13.00 | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | GROUND_INST: instantiating (unique) with a2, b1, a2c2, b1c1,
% 89.52/13.00 | | | | | | | | | | simplifying with (30), (33), (43), (44), (52),
% 89.52/13.00 | | | | | | | | | | (53), (81), (82) gives:
% 89.52/13.00 | | | | | | | | | | (83) point_equal(a2, b1) | line_equal(a2c2, b1c1)
% 89.52/13.00 | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | BETA: splitting (56) gives:
% 89.52/13.00 | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | Case 1:
% 89.52/13.00 | | | | | | | | | | |
% 89.52/13.00 | | | | | | | | | | | (84) ~ incident(c1, a2b2)
% 89.52/13.00 | | | | | | | | | | |
% 89.52/13.01 | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (13), (14), (15), (16),
% 89.52/13.01 | | | | | | | | | | | (17), (18), (19), (20), (21), (22), (23), (24),
% 89.52/13.01 | | | | | | | | | | | (25), (26), (27), (29), (30), (31), (32), (33),
% 89.52/13.01 | | | | | | | | | | | (36), (37), (38), (39), (43), (44), (45), (47),
% 89.52/13.01 | | | | | | | | | | | (48), (50), (51), (52), (53), (54), (55), (57),
% 89.52/13.01 | | | | | | | | | | | (59), (60), (61), (62), (63), (64), (66), (69),
% 89.52/13.01 | | | | | | | | | | | (82), (83), (84), (goal_to_be_proved), (lcon),
% 89.52/13.01 | | | | | | | | | | | (pcon), (symmetry_of_point_equal), (unique) are
% 89.52/13.01 | | | | | | | | | | | inconsistent by sub-proof #4.
% 89.52/13.01 | | | | | | | | | | |
% 89.52/13.01 | | | | | | | | | | Case 2:
% 89.52/13.01 | | | | | | | | | | |
% 89.52/13.01 | | | | | | | | | | | (85) incident(c1, a2b2)
% 89.52/13.01 | | | | | | | | | | |
% 89.52/13.02 | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 89.52/13.02 | | | | | | | | | | | (16), (17), (18), (19), (20), (21), (22), (23),
% 89.52/13.02 | | | | | | | | | | | (24), (25), (26), (27), (28), (29), (30), (31),
% 89.52/13.02 | | | | | | | | | | | (32), (33), (34), (35), (36), (37), (38), (39),
% 89.52/13.02 | | | | | | | | | | | (40), (41), (43), (44), (45), (46), (47), (48),
% 89.52/13.02 | | | | | | | | | | | (50), (51), (52), (53), (54), (55), (56), (57),
% 89.52/13.02 | | | | | | | | | | | (58), (59), (60), (61), (62), (63), (64), (65),
% 89.52/13.02 | | | | | | | | | | | (66), (67), (68), (69), (70), (85),
% 89.52/13.02 | | | | | | | | | | | (goal_to_be_proved), (lcon), (pcon),
% 89.52/13.02 | | | | | | | | | | | (symmetry_of_point_equal), (unique) are
% 89.52/13.02 | | | | | | | | | | | inconsistent by sub-proof #2.
% 89.52/13.02 | | | | | | | | | | |
% 89.52/13.02 | | | | | | | | | | End of split
% 89.52/13.02 | | | | | | | | | |
% 89.52/13.02 | | | | | | | | | Case 2:
% 89.52/13.02 | | | | | | | | | |
% 89.52/13.02 | | | | | | | | | | (86) ~ incident(a2, b1c1)
% 89.52/13.02 | | | | | | | | | |
% 89.52/13.02 | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 89.52/13.02 | | | | | | | | | | (16), (17), (18), (19), (20), (21), (22), (23),
% 89.52/13.02 | | | | | | | | | | (24), (25), (26), (27), (28), (29), (30), (31),
% 89.52/13.02 | | | | | | | | | | (32), (33), (34), (35), (36), (37), (38), (39),
% 89.52/13.02 | | | | | | | | | | (40), (41), (43), (44), (45), (46), (47), (48),
% 89.52/13.02 | | | | | | | | | | (50), (51), (52), (53), (54), (55), (56), (57),
% 89.52/13.02 | | | | | | | | | | (58), (59), (60), (61), (62), (63), (64), (65),
% 89.52/13.02 | | | | | | | | | | (66), (67), (68), (69), (70), (86),
% 89.52/13.02 | | | | | | | | | | (goal_to_be_proved), (lcon), (pcon),
% 89.52/13.02 | | | | | | | | | | (symmetry_of_point_equal), (unique) are
% 89.52/13.02 | | | | | | | | | | inconsistent by sub-proof #1.
% 89.52/13.02 | | | | | | | | | |
% 89.52/13.02 | | | | | | | | | End of split
% 89.52/13.02 | | | | | | | | |
% 89.52/13.02 | | | | | | | | End of split
% 89.52/13.02 | | | | | | | |
% 89.52/13.02 | | | | | | | Case 2:
% 89.52/13.02 | | | | | | | |
% 89.52/13.02 | | | | | | | | (87) incident(a1, b2c2)
% 89.52/13.02 | | | | | | | |
% 89.52/13.02 | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 89.52/13.02 | | | | | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 89.52/13.02 | | | | | | | | (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 89.52/13.02 | | | | | | | | (34), (35), (36), (37), (38), (39), (40), (41), (43),
% 89.52/13.02 | | | | | | | | (44), (45), (46), (47), (48), (50), (51), (52), (53),
% 89.52/13.02 | | | | | | | | (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 89.52/13.02 | | | | | | | | (63), (64), (65), (66), (68), (69), (87),
% 89.52/13.02 | | | | | | | | (goal_to_be_proved), (lcon), (pcon),
% 89.52/13.02 | | | | | | | | (symmetry_of_point_equal), (unique) are inconsistent
% 89.52/13.02 | | | | | | | | by sub-proof #3.
% 89.52/13.02 | | | | | | | |
% 89.52/13.02 | | | | | | | End of split
% 89.52/13.02 | | | | | | |
% 89.52/13.02 | | | | | | Case 2:
% 89.52/13.02 | | | | | | |
% 89.52/13.02 | | | | | | | (88) goal
% 89.52/13.02 | | | | | | |
% 89.52/13.02 | | | | | | | PRED_UNIFY: (88), (goal_to_be_proved) imply:
% 89.52/13.02 | | | | | | | (89) $false
% 89.52/13.02 | | | | | | |
% 89.52/13.02 | | | | | | | CLOSE: (89) is inconsistent.
% 89.52/13.02 | | | | | | |
% 89.52/13.02 | | | | | | End of split
% 89.52/13.02 | | | | | |
% 89.52/13.02 | | | | | Case 2:
% 89.52/13.02 | | | | | |
% 89.52/13.02 | | | | | | (90) goal
% 89.52/13.02 | | | | | |
% 89.52/13.02 | | | | | | PRED_UNIFY: (90), (goal_to_be_proved) imply:
% 89.52/13.02 | | | | | | (91) $false
% 89.52/13.02 | | | | | |
% 89.52/13.02 | | | | | | CLOSE: (91) is inconsistent.
% 89.52/13.02 | | | | | |
% 89.52/13.02 | | | | | End of split
% 89.52/13.02 | | | | |
% 89.52/13.02 | | | | Case 2:
% 89.52/13.02 | | | | |
% 89.52/13.02 | | | | | (92) goal
% 89.52/13.02 | | | | |
% 89.52/13.02 | | | | | PRED_UNIFY: (92), (goal_to_be_proved) imply:
% 89.52/13.02 | | | | | (93) $false
% 89.52/13.02 | | | | |
% 89.52/13.02 | | | | | CLOSE: (93) is inconsistent.
% 89.52/13.02 | | | | |
% 89.52/13.02 | | | | End of split
% 89.52/13.02 | | | |
% 89.52/13.02 | | | Case 2:
% 89.52/13.02 | | | |
% 89.52/13.02 | | | | (94) goal
% 89.52/13.02 | | | |
% 89.52/13.02 | | | | PRED_UNIFY: (94), (goal_to_be_proved) imply:
% 89.52/13.02 | | | | (95) $false
% 89.52/13.02 | | | |
% 89.52/13.02 | | | | CLOSE: (95) is inconsistent.
% 89.52/13.02 | | | |
% 89.52/13.02 | | | End of split
% 89.52/13.02 | | |
% 89.52/13.02 | | Case 2:
% 89.52/13.02 | | |
% 89.52/13.02 | | | (96) goal
% 89.52/13.02 | | |
% 89.52/13.02 | | | PRED_UNIFY: (96), (goal_to_be_proved) imply:
% 89.52/13.02 | | | (97) $false
% 89.52/13.02 | | |
% 89.52/13.02 | | | CLOSE: (97) is inconsistent.
% 89.52/13.02 | | |
% 89.52/13.02 | | End of split
% 89.52/13.02 | |
% 89.52/13.02 | Case 2:
% 89.52/13.02 | |
% 89.52/13.02 | | (98) goal
% 89.52/13.02 | |
% 89.52/13.02 | | PRED_UNIFY: (98), (goal_to_be_proved) imply:
% 89.52/13.03 | | (99) $false
% 89.52/13.03 | |
% 89.52/13.03 | | CLOSE: (99) is inconsistent.
% 89.52/13.03 | |
% 89.52/13.03 | End of split
% 89.52/13.03 |
% 89.52/13.03 End of proof
% 89.52/13.03
% 89.52/13.03 Sub-proof #1 shows that the following formulas are inconsistent:
% 89.52/13.03 ----------------------------------------------------------------
% 89.52/13.03 (1) $i(b2c2)
% 89.52/13.03 (2) $i(ob)
% 89.52/13.03 (3) ~ goal
% 89.52/13.03 (4) ~ point_equal(c2, c1)
% 89.52/13.03 (5) ~ point_equal(a2, a1)
% 89.52/13.03 (6) incident(a1, oa)
% 89.52/13.03 (7) incident(a2, a2b2)
% 89.52/13.03 (8) ! [v0: $i] : ( ~ $i(v0) | ~ incident(c2, v0) | ~ incident(b2, v0) | ~
% 89.52/13.03 incident(a2, v0) | goal)
% 89.52/13.03 (9) incident(c2, oc)
% 89.52/13.03 (10) $i(c1)
% 89.52/13.03 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 89.52/13.03 $i(v0) | ~ incident(v0, v1) | ~ line_equal(v1, v2) | incident(v0,
% 89.52/13.03 v2))
% 89.52/13.03 (12) incident(bc, b2c2)
% 89.52/13.03 (13) incident(a2, a2c2)
% 89.52/13.03 (14) $i(oc)
% 89.52/13.03 (15) incident(b2, b2c2)
% 89.52/13.03 (16) $i(b1)
% 89.52/13.03 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 89.52/13.03 $i(v0) | ~ point_equal(v0, v1) | ~ incident(v1, v2) | incident(v0,
% 89.52/13.03 v2))
% 89.52/13.03 (18) incident(ab, a1b1)
% 89.52/13.03 (19) incident(bc, b1c1)
% 89.52/13.03 (20) incident(c1, b1c1)
% 89.52/13.03 (21) ~ line_equal(a1b1, a2b2)
% 89.52/13.03 (22) ~ line_equal(a1c1, a2c2)
% 89.52/13.03 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 89.52/13.03 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ incident(v1, v3) | ~ incident(v1,
% 89.52/13.03 v2) | ~ incident(v0, v3) | ~ incident(v0, v2) | point_equal(v0,
% 89.52/13.03 v1) | line_equal(v2, v3))
% 89.52/13.03 (24) $i(b1c1)
% 89.52/13.03 (25) ! [v0: $i] : ( ~ $i(v0) | ~ incident(c1, v0) | ~ incident(b1, v0) |
% 89.52/13.03 ~ incident(a1, v0) | goal)
% 89.52/13.03 (26) $i(a2)
% 89.52/13.03 (27) incident(c1, a1c1)
% 89.52/13.03 (28) $i(o)
% 89.52/13.03 (29) incident(a1, a1b1)
% 89.52/13.03 (30) incident(ac, a2c2)
% 89.52/13.03 (31) incident(ab, a2b2)
% 89.52/13.03 (32) ~ incident(a2, b1c1)
% 89.52/13.03 (33) $i(a2b2)
% 89.52/13.03 (34) incident(b2, a2b2)
% 89.52/13.03 (35) ~ line_equal(b1c1, b2c2)
% 89.52/13.03 (36) $i(ac)
% 89.52/13.03 (37) incident(o, oc)
% 89.52/13.03 (38) $i(b2)
% 89.52/13.03 (39) incident(b1, b1c1)
% 89.52/13.03 (40) ! [v0: $i] : ( ~ $i(v0) | ~ incident(ab, v0) | ~ incident(ac, v0) |
% 89.52/13.03 ~ incident(bc, v0) | ~ line_equal(v0, v0) | goal)
% 89.52/13.03 (41) line_equal(a2c2, a2c2)
% 89.52/13.03 (42) $i(a1b1)
% 89.52/13.03 (43) incident(c2, a1b1) | incident(b1, a2c2)
% 89.52/13.03 (44) incident(a2, oa)
% 89.52/13.03 (45) incident(o, ob)
% 89.52/13.03 (46) incident(c1, oc)
% 89.52/13.03 (47) $i(a2c2)
% 89.52/13.03 (48) incident(ac, a1c1)
% 89.52/13.03 (49) $i(a1c1)
% 89.52/13.03 (50) incident(b1, ob)
% 89.52/13.03 (51) incident(a2, b1c1) | incident(c1, a2b2)
% 89.52/13.03 (52) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ point_equal(v0,
% 89.52/13.03 v1) | point_equal(v1, v0))
% 89.52/13.04 (53) $i(a1)
% 89.52/13.04 (54) line_equal(b2c2, b2c2)
% 89.52/13.04 (55) incident(a1, a1c1)
% 89.52/13.04 (56) $i(oa)
% 89.52/13.04 (57) incident(b1, a1b1)
% 89.52/13.04 (58) $i(bc)
% 89.52/13.04 (59) $i(c2)
% 89.52/13.04 (60) incident(c2, a2c2)
% 89.52/13.04 (61) incident(o, oa)
% 89.52/13.04 (62) incident(b2, a1c1)
% 89.52/13.04 (63) ~ incident(c1, a2b2) | ~ incident(b1, a2c2) | ~ incident(a1, b2c2) |
% 89.52/13.04 goal
% 89.52/13.04 (64) $i(ab)
% 89.52/13.04 (65) incident(b2, ob)
% 89.52/13.04 (66) incident(c2, b2c2)
% 89.52/13.04 (67) ~ point_equal(b2, b1)
% 89.52/13.04 (68) line_equal(a2b2, a2b2)
% 89.52/13.04
% 89.52/13.04 Begin of proof
% 89.52/13.04 |
% 89.52/13.04 | BETA: splitting (51) gives:
% 89.52/13.04 |
% 89.52/13.04 | Case 1:
% 89.52/13.04 | |
% 89.52/13.04 | | (69) incident(a2, b1c1)
% 89.52/13.04 | |
% 89.52/13.04 | | PRED_UNIFY: (32), (69) imply:
% 89.52/13.04 | | (70) $false
% 89.52/13.04 | |
% 89.52/13.04 | | CLOSE: (70) is inconsistent.
% 89.52/13.04 | |
% 89.52/13.04 | Case 2:
% 89.52/13.04 | |
% 89.52/13.04 | | (71) incident(c1, a2b2)
% 89.52/13.04 | |
% 89.52/13.04 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 89.52/13.04 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 89.52/13.04 | | (24), (25), (26), (27), (28), (29), (30), (31), (33), (34), (35),
% 89.52/13.04 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 89.52/13.04 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 89.52/13.04 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 89.52/13.04 | | (71) are inconsistent by sub-proof #2.
% 89.52/13.04 | |
% 89.52/13.04 | End of split
% 89.52/13.04 |
% 89.52/13.04 End of proof
% 89.52/13.04
% 89.52/13.04 Sub-proof #2 shows that the following formulas are inconsistent:
% 89.52/13.04 ----------------------------------------------------------------
% 89.52/13.04 (1) $i(b2c2)
% 89.52/13.04 (2) $i(ob)
% 89.52/13.04 (3) ~ goal
% 89.52/13.04 (4) ~ point_equal(c2, c1)
% 89.52/13.04 (5) ~ point_equal(a2, a1)
% 89.52/13.04 (6) incident(a1, oa)
% 89.52/13.04 (7) incident(a2, a2b2)
% 89.52/13.04 (8) ! [v0: $i] : ( ~ $i(v0) | ~ incident(c2, v0) | ~ incident(b2, v0) | ~
% 89.52/13.04 incident(a2, v0) | goal)
% 89.52/13.04 (9) incident(c2, oc)
% 89.52/13.04 (10) $i(c1)
% 89.52/13.04 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 89.52/13.04 $i(v0) | ~ incident(v0, v1) | ~ line_equal(v1, v2) | incident(v0,
% 89.52/13.04 v2))
% 89.52/13.04 (12) incident(bc, b2c2)
% 89.52/13.04 (13) incident(a2, a2c2)
% 89.52/13.04 (14) $i(oc)
% 89.52/13.04 (15) incident(b2, b2c2)
% 89.52/13.04 (16) $i(b1)
% 89.52/13.04 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 89.52/13.04 $i(v0) | ~ point_equal(v0, v1) | ~ incident(v1, v2) | incident(v0,
% 89.52/13.04 v2))
% 89.52/13.04 (18) incident(ab, a1b1)
% 89.52/13.04 (19) incident(bc, b1c1)
% 89.52/13.04 (20) incident(c1, b1c1)
% 89.52/13.04 (21) ~ line_equal(a1b1, a2b2)
% 89.52/13.04 (22) ~ line_equal(a1c1, a2c2)
% 89.52/13.04 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 89.52/13.05 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ incident(v1, v3) | ~ incident(v1,
% 89.52/13.05 v2) | ~ incident(v0, v3) | ~ incident(v0, v2) | point_equal(v0,
% 89.52/13.05 v1) | line_equal(v2, v3))
% 89.52/13.05 (24) $i(b1c1)
% 89.52/13.05 (25) ! [v0: $i] : ( ~ $i(v0) | ~ incident(c1, v0) | ~ incident(b1, v0) |
% 89.52/13.05 ~ incident(a1, v0) | goal)
% 89.52/13.05 (26) $i(a2)
% 89.52/13.05 (27) incident(c1, a1c1)
% 89.52/13.05 (28) $i(o)
% 89.52/13.05 (29) incident(a1, a1b1)
% 89.52/13.05 (30) incident(ac, a2c2)
% 89.52/13.05 (31) incident(ab, a2b2)
% 89.52/13.05 (32) $i(a2b2)
% 89.52/13.05 (33) incident(c1, a2b2)
% 89.52/13.05 (34) incident(b2, a2b2)
% 89.52/13.05 (35) ~ line_equal(b1c1, b2c2)
% 89.52/13.05 (36) $i(ac)
% 89.52/13.05 (37) incident(o, oc)
% 89.52/13.05 (38) $i(b2)
% 89.52/13.05 (39) incident(b1, b1c1)
% 89.52/13.05 (40) ! [v0: $i] : ( ~ $i(v0) | ~ incident(ab, v0) | ~ incident(ac, v0) |
% 89.52/13.05 ~ incident(bc, v0) | ~ line_equal(v0, v0) | goal)
% 89.52/13.05 (41) line_equal(a2c2, a2c2)
% 89.52/13.05 (42) $i(a1b1)
% 89.52/13.05 (43) incident(c2, a1b1) | incident(b1, a2c2)
% 89.52/13.05 (44) incident(a2, oa)
% 89.52/13.05 (45) incident(o, ob)
% 89.52/13.05 (46) incident(c1, oc)
% 89.52/13.05 (47) $i(a2c2)
% 89.52/13.05 (48) incident(ac, a1c1)
% 89.52/13.05 (49) $i(a1c1)
% 89.52/13.05 (50) incident(b1, ob)
% 89.52/13.05 (51) incident(a2, b1c1) | incident(c1, a2b2)
% 89.52/13.05 (52) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ point_equal(v0,
% 89.52/13.05 v1) | point_equal(v1, v0))
% 89.52/13.05 (53) $i(a1)
% 89.52/13.05 (54) line_equal(b2c2, b2c2)
% 89.52/13.05 (55) incident(a1, a1c1)
% 89.52/13.05 (56) $i(oa)
% 89.52/13.05 (57) incident(b1, a1b1)
% 89.52/13.05 (58) $i(bc)
% 89.52/13.05 (59) $i(c2)
% 89.52/13.05 (60) incident(c2, a2c2)
% 89.52/13.05 (61) incident(o, oa)
% 89.52/13.05 (62) incident(b2, a1c1)
% 89.52/13.05 (63) ~ incident(c1, a2b2) | ~ incident(b1, a2c2) | ~ incident(a1, b2c2) |
% 89.52/13.05 goal
% 89.52/13.05 (64) $i(ab)
% 89.52/13.05 (65) incident(b2, ob)
% 89.52/13.05 (66) incident(c2, b2c2)
% 89.52/13.05 (67) ~ point_equal(b2, b1)
% 89.52/13.05 (68) line_equal(a2b2, a2b2)
% 89.52/13.05
% 89.52/13.05 Begin of proof
% 89.52/13.05 |
% 89.52/13.05 | GROUND_INST: instantiating (23) with b2, c1, a2b2, a1c1, simplifying with
% 89.52/13.05 | (10), (27), (32), (33), (34), (38), (49), (62) gives:
% 89.52/13.05 | (69) point_equal(b2, c1) | line_equal(a2b2, a1c1)
% 89.52/13.05 |
% 89.52/13.05 | GROUND_INST: instantiating (23) with b2, c1, a1c1, a2b2, simplifying with
% 89.52/13.05 | (10), (27), (32), (33), (34), (38), (49), (62) gives:
% 89.52/13.05 | (70) point_equal(b2, c1) | line_equal(a1c1, a2b2)
% 89.52/13.05 |
% 89.52/13.05 | BETA: splitting (70) gives:
% 89.52/13.05 |
% 89.52/13.05 | Case 1:
% 89.52/13.05 | |
% 89.52/13.05 | | (71) point_equal(b2, c1)
% 89.52/13.05 | |
% 89.52/13.05 | | GROUND_INST: instantiating (17) with b2, c1, b1c1, simplifying with (10),
% 89.52/13.05 | | (20), (24), (38), (71) gives:
% 89.52/13.05 | | (72) incident(b2, b1c1)
% 89.52/13.05 | |
% 89.52/13.05 | | GROUND_INST: instantiating (52) with b2, c1, simplifying with (10), (38),
% 89.52/13.05 | | (71) gives:
% 89.52/13.05 | | (73) point_equal(c1, b2)
% 89.52/13.05 | |
% 89.52/13.06 | | GROUND_INST: instantiating (23) with bc, b2, b1c1, b2c2, simplifying with
% 89.52/13.06 | | (1), (12), (15), (19), (24), (35), (38), (58), (72) gives:
% 89.52/13.06 | | (74) point_equal(bc, b2)
% 89.52/13.06 | |
% 89.52/13.06 | | GROUND_INST: instantiating (23) with b2, b1, ob, b1c1, simplifying with (2),
% 89.52/13.06 | | (16), (24), (38), (39), (50), (65), (67), (72) gives:
% 89.52/13.06 | | (75) line_equal(ob, b1c1)
% 89.52/13.06 | |
% 89.52/13.06 | | GROUND_INST: instantiating (17) with c1, b2, b2c2, simplifying with (1),
% 89.52/13.06 | | (10), (15), (38), (73) gives:
% 89.52/13.06 | | (76) incident(c1, b2c2)
% 89.52/13.06 | |
% 89.52/13.06 | | GROUND_INST: instantiating (11) with o, ob, b1c1, simplifying with (2),
% 89.52/13.06 | | (24), (28), (45), (75) gives:
% 89.52/13.06 | | (77) incident(o, b1c1)
% 89.52/13.06 | |
% 89.52/13.06 | | GROUND_INST: instantiating (23) with c2, c1, oc, b2c2, simplifying with (1),
% 89.52/13.06 | | (4), (9), (10), (14), (46), (59), (66), (76) gives:
% 89.52/13.06 | | (78) line_equal(oc, b2c2)
% 89.52/13.06 | |
% 89.52/13.06 | | GROUND_INST: instantiating (17) with bc, b2, a2b2, simplifying with (32),
% 89.52/13.06 | | (34), (38), (58), (74) gives:
% 89.52/13.06 | | (79) incident(bc, a2b2)
% 89.52/13.06 | |
% 89.52/13.06 | | GROUND_INST: instantiating (11) with o, oc, b2c2, simplifying with (1),
% 89.52/13.06 | | (14), (28), (37), (78) gives:
% 89.52/13.06 | | (80) incident(o, b2c2)
% 89.52/13.06 | |
% 89.52/13.06 | | GROUND_INST: instantiating (23) with o, b2, b1c1, b2c2, simplifying with
% 89.52/13.06 | | (1), (15), (24), (28), (35), (38), (72), (77), (80) gives:
% 89.52/13.06 | | (81) point_equal(o, b2)
% 89.52/13.06 | |
% 89.52/13.06 | | GROUND_INST: instantiating (17) with o, b2, a1c1, simplifying with (28),
% 89.52/13.06 | | (38), (49), (62), (81) gives:
% 89.52/13.06 | | (82) incident(o, a1c1)
% 89.52/13.06 | |
% 89.52/13.06 | | GROUND_INST: instantiating (23) with o, a1, a1c1, oa, simplifying with (6),
% 89.52/13.06 | | (28), (49), (53), (55), (56), (61), (82) gives:
% 89.52/13.06 | | (83) point_equal(o, a1) | line_equal(a1c1, oa)
% 89.52/13.06 | |
% 89.52/13.06 | | GROUND_INST: instantiating (23) with o, a1, oa, a1c1, simplifying with (6),
% 89.52/13.06 | | (28), (49), (53), (55), (56), (61), (82) gives:
% 89.52/13.06 | | (84) point_equal(o, a1) | line_equal(oa, a1c1)
% 89.52/13.06 | |
% 89.52/13.06 | | BETA: splitting (83) gives:
% 89.52/13.06 | |
% 89.52/13.06 | | Case 1:
% 89.52/13.06 | | |
% 89.52/13.06 | | | (85) point_equal(o, a1)
% 89.52/13.06 | | |
% 89.52/13.06 | | | GROUND_INST: instantiating (52) with o, a1, simplifying with (28), (53),
% 89.52/13.06 | | | (85) gives:
% 89.52/13.06 | | | (86) point_equal(a1, o)
% 89.52/13.06 | | |
% 89.52/13.06 | | | GROUND_INST: instantiating (17) with a1, o, b2c2, simplifying with (1),
% 89.52/13.06 | | | (28), (53), (80), (86) gives:
% 89.52/13.06 | | | (87) incident(a1, b2c2)
% 89.52/13.06 | | |
% 89.52/13.06 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 89.52/13.06 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 89.52/13.06 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 89.52/13.06 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 89.52/13.06 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 89.52/13.06 | | | (54), (55), (56), (57), (58), (59), (60), (61), (63), (64),
% 89.52/13.06 | | | (65), (66), (67), (87) are inconsistent by sub-proof #3.
% 89.52/13.06 | | |
% 89.52/13.06 | | Case 2:
% 89.52/13.06 | | |
% 89.52/13.06 | | | (88) ~ point_equal(o, a1)
% 89.52/13.06 | | |
% 89.52/13.06 | | | BETA: splitting (84) gives:
% 89.52/13.06 | | |
% 89.52/13.06 | | | Case 1:
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | (89) point_equal(o, a1)
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | PRED_UNIFY: (88), (89) imply:
% 89.52/13.06 | | | | (90) $false
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | CLOSE: (90) is inconsistent.
% 89.52/13.06 | | | |
% 89.52/13.06 | | | Case 2:
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | (91) line_equal(oa, a1c1)
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | GROUND_INST: instantiating (11) with a2, oa, a1c1, simplifying with
% 89.52/13.06 | | | | (26), (44), (49), (56), (91) gives:
% 89.52/13.06 | | | | (92) incident(a2, a1c1)
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | GROUND_INST: instantiating (23) with ac, a2, a1c1, a2c2, simplifying
% 89.52/13.06 | | | | with (13), (22), (26), (30), (36), (47), (48), (49), (92)
% 89.52/13.06 | | | | gives:
% 89.52/13.06 | | | | (93) point_equal(ac, a2)
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | GROUND_INST: instantiating (17) with ac, a2, a2b2, simplifying with (7),
% 89.52/13.06 | | | | (26), (32), (36), (93) gives:
% 89.52/13.06 | | | | (94) incident(ac, a2b2)
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | GROUND_INST: instantiating (40) with a2b2, simplifying with (3), (31),
% 89.52/13.06 | | | | (32), (68), (79), (94) gives:
% 89.52/13.06 | | | | (95) $false
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | CLOSE: (95) is inconsistent.
% 89.52/13.06 | | | |
% 89.52/13.06 | | | End of split
% 89.52/13.06 | | |
% 89.52/13.06 | | End of split
% 89.52/13.06 | |
% 89.52/13.06 | Case 2:
% 89.52/13.06 | |
% 89.52/13.06 | | (96) ~ point_equal(b2, c1)
% 89.52/13.06 | |
% 89.52/13.06 | | BETA: splitting (69) gives:
% 89.52/13.06 | |
% 89.52/13.06 | | Case 1:
% 89.52/13.06 | | |
% 89.52/13.06 | | | (97) point_equal(b2, c1)
% 89.52/13.06 | | |
% 89.52/13.06 | | | PRED_UNIFY: (96), (97) imply:
% 89.52/13.06 | | | (98) $false
% 89.52/13.06 | | |
% 89.52/13.06 | | | CLOSE: (98) is inconsistent.
% 89.52/13.06 | | |
% 89.52/13.06 | | Case 2:
% 89.52/13.06 | | |
% 89.52/13.06 | | | (99) line_equal(a2b2, a1c1)
% 89.52/13.06 | | |
% 89.52/13.06 | | | GROUND_INST: instantiating (11) with a2, a2b2, a1c1, simplifying with (7),
% 89.52/13.06 | | | (26), (32), (49), (99) gives:
% 89.52/13.06 | | | (100) incident(a2, a1c1)
% 89.52/13.06 | | |
% 89.52/13.06 | | | GROUND_INST: instantiating (23) with a2, a1, a1c1, oa, simplifying with
% 89.52/13.06 | | | (5), (6), (26), (44), (49), (53), (55), (56), (100) gives:
% 89.52/13.06 | | | (101) line_equal(a1c1, oa)
% 89.52/13.06 | | |
% 89.52/13.06 | | | GROUND_INST: instantiating (11) with b2, a1c1, oa, simplifying with (38),
% 89.52/13.06 | | | (49), (56), (62), (101) gives:
% 89.52/13.06 | | | (102) incident(b2, oa)
% 89.52/13.06 | | |
% 89.52/13.06 | | | GROUND_INST: instantiating (11) with c1, a1c1, oa, simplifying with (10),
% 89.52/13.06 | | | (27), (49), (56), (101) gives:
% 89.52/13.06 | | | (103) incident(c1, oa)
% 89.52/13.06 | | |
% 89.52/13.06 | | | GROUND_INST: instantiating (23) with o, c1, oc, oa, simplifying with (10),
% 89.52/13.06 | | | (14), (28), (37), (46), (56), (61), (103) gives:
% 89.52/13.06 | | | (104) point_equal(o, c1) | line_equal(oc, oa)
% 89.52/13.06 | | |
% 89.52/13.06 | | | BETA: splitting (104) gives:
% 89.52/13.06 | | |
% 89.52/13.06 | | | Case 1:
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | (105) point_equal(o, c1)
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | GROUND_INST: instantiating (52) with o, c1, simplifying with (10), (28),
% 89.52/13.06 | | | | (105) gives:
% 89.52/13.06 | | | | (106) point_equal(c1, o)
% 89.52/13.06 | | | |
% 89.52/13.06 | | | | GROUND_INST: instantiating (17) with c1, o, ob, simplifying with (2),
% 89.52/13.06 | | | | (10), (28), (45), (106) gives:
% 89.52/13.07 | | | | (107) incident(c1, ob)
% 89.52/13.07 | | | |
% 89.52/13.07 | | | | GROUND_INST: instantiating (23) with b2, c1, ob, oa, simplifying with
% 89.52/13.07 | | | | (2), (10), (38), (56), (65), (96), (102), (103), (107)
% 89.52/13.07 | | | | gives:
% 89.52/13.07 | | | | (108) line_equal(ob, oa)
% 89.52/13.07 | | | |
% 89.52/13.07 | | | | GROUND_INST: instantiating (11) with b1, ob, oa, simplifying with (2),
% 89.52/13.07 | | | | (16), (50), (56), (108) gives:
% 89.52/13.07 | | | | (109) incident(b1, oa)
% 89.52/13.07 | | | |
% 89.52/13.07 | | | | GROUND_INST: instantiating (25) with oa, simplifying with (3), (6),
% 89.52/13.07 | | | | (56), (103), (109) gives:
% 89.52/13.07 | | | | (110) $false
% 89.52/13.07 | | | |
% 89.52/13.07 | | | | CLOSE: (110) is inconsistent.
% 89.52/13.07 | | | |
% 89.52/13.07 | | | Case 2:
% 89.52/13.07 | | | |
% 89.52/13.07 | | | | (111) line_equal(oc, oa)
% 89.52/13.07 | | | |
% 89.52/13.07 | | | | GROUND_INST: instantiating (11) with c2, oc, oa, simplifying with (9),
% 89.52/13.07 | | | | (14), (56), (59), (111) gives:
% 89.52/13.07 | | | | (112) incident(c2, oa)
% 89.52/13.07 | | | |
% 89.52/13.07 | | | | GROUND_INST: instantiating (8) with oa, simplifying with (3), (44),
% 89.52/13.07 | | | | (56), (102), (112) gives:
% 89.52/13.07 | | | | (113) $false
% 89.52/13.07 | | | |
% 89.52/13.07 | | | | CLOSE: (113) is inconsistent.
% 89.52/13.07 | | | |
% 89.52/13.07 | | | End of split
% 89.52/13.07 | | |
% 89.52/13.07 | | End of split
% 89.52/13.07 | |
% 89.52/13.07 | End of split
% 89.52/13.07 |
% 89.52/13.07 End of proof
% 89.52/13.07
% 89.52/13.07 Sub-proof #3 shows that the following formulas are inconsistent:
% 89.52/13.07 ----------------------------------------------------------------
% 89.52/13.07 (1) $i(b2c2)
% 89.52/13.07 (2) $i(ob)
% 89.52/13.07 (3) ~ goal
% 89.52/13.07 (4) ~ point_equal(c2, c1)
% 89.52/13.07 (5) ~ point_equal(a2, a1)
% 89.52/13.07 (6) incident(a1, oa)
% 89.52/13.07 (7) incident(a2, a2b2)
% 89.52/13.07 (8) ! [v0: $i] : ( ~ $i(v0) | ~ incident(c2, v0) | ~ incident(b2, v0) | ~
% 89.52/13.07 incident(a2, v0) | goal)
% 89.52/13.07 (9) incident(c2, oc)
% 89.52/13.07 (10) $i(c1)
% 89.52/13.07 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 89.52/13.07 $i(v0) | ~ incident(v0, v1) | ~ line_equal(v1, v2) | incident(v0,
% 89.52/13.07 v2))
% 89.52/13.07 (12) incident(bc, b2c2)
% 89.52/13.07 (13) incident(a2, a2c2)
% 89.52/13.07 (14) $i(oc)
% 89.52/13.07 (15) incident(b2, b2c2)
% 89.52/13.07 (16) $i(b1)
% 89.52/13.07 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 89.52/13.07 $i(v0) | ~ point_equal(v0, v1) | ~ incident(v1, v2) | incident(v0,
% 89.52/13.07 v2))
% 89.52/13.07 (18) incident(ab, a1b1)
% 89.52/13.07 (19) incident(bc, b1c1)
% 89.52/13.07 (20) incident(c1, b1c1)
% 89.52/13.07 (21) ~ line_equal(a1b1, a2b2)
% 89.52/13.07 (22) ~ line_equal(a1c1, a2c2)
% 89.52/13.07 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 89.52/13.07 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ incident(v1, v3) | ~ incident(v1,
% 89.52/13.07 v2) | ~ incident(v0, v3) | ~ incident(v0, v2) | point_equal(v0,
% 89.52/13.07 v1) | line_equal(v2, v3))
% 89.52/13.07 (24) $i(b1c1)
% 89.52/13.07 (25) ! [v0: $i] : ( ~ $i(v0) | ~ incident(c1, v0) | ~ incident(b1, v0) |
% 89.52/13.07 ~ incident(a1, v0) | goal)
% 89.52/13.07 (26) $i(a2)
% 89.52/13.07 (27) incident(c1, a1c1)
% 89.52/13.07 (28) $i(o)
% 89.52/13.07 (29) incident(a1, a1b1)
% 89.52/13.07 (30) incident(ac, a2c2)
% 89.52/13.07 (31) incident(ab, a2b2)
% 89.52/13.07 (32) $i(a2b2)
% 89.52/13.07 (33) incident(b2, a2b2)
% 89.52/13.07 (34) ~ line_equal(b1c1, b2c2)
% 89.52/13.07 (35) $i(ac)
% 89.52/13.07 (36) incident(o, oc)
% 89.52/13.07 (37) $i(b2)
% 89.52/13.07 (38) incident(b1, b1c1)
% 89.52/13.07 (39) ! [v0: $i] : ( ~ $i(v0) | ~ incident(ab, v0) | ~ incident(ac, v0) |
% 89.52/13.07 ~ incident(bc, v0) | ~ line_equal(v0, v0) | goal)
% 89.52/13.07 (40) line_equal(a2c2, a2c2)
% 89.52/13.07 (41) $i(a1b1)
% 89.52/13.07 (42) incident(c2, a1b1) | incident(b1, a2c2)
% 89.52/13.07 (43) incident(a2, oa)
% 89.52/13.07 (44) incident(o, ob)
% 89.52/13.07 (45) incident(c1, oc)
% 89.52/13.07 (46) $i(a2c2)
% 89.52/13.07 (47) incident(ac, a1c1)
% 89.52/13.07 (48) $i(a1c1)
% 89.52/13.07 (49) incident(b1, ob)
% 89.52/13.07 (50) incident(a2, b1c1) | incident(c1, a2b2)
% 89.52/13.07 (51) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ point_equal(v0,
% 89.52/13.07 v1) | point_equal(v1, v0))
% 89.52/13.07 (52) $i(a1)
% 89.52/13.07 (53) line_equal(b2c2, b2c2)
% 89.52/13.07 (54) incident(a1, a1c1)
% 89.52/13.08 (55) incident(a1, b2c2)
% 89.52/13.08 (56) $i(oa)
% 89.52/13.08 (57) incident(b1, a1b1)
% 89.52/13.08 (58) $i(bc)
% 89.52/13.08 (59) $i(c2)
% 89.52/13.08 (60) incident(c2, a2c2)
% 89.52/13.08 (61) incident(o, oa)
% 89.52/13.08 (62) ~ incident(c1, a2b2) | ~ incident(b1, a2c2) | ~ incident(a1, b2c2) |
% 89.52/13.08 goal
% 89.52/13.08 (63) $i(ab)
% 89.52/13.08 (64) incident(b2, ob)
% 89.52/13.08 (65) incident(c2, b2c2)
% 89.52/13.08 (66) ~ point_equal(b2, b1)
% 89.52/13.08
% 89.52/13.08 Begin of proof
% 89.52/13.08 |
% 89.52/13.08 | BETA: splitting (42) gives:
% 89.52/13.08 |
% 89.52/13.08 | Case 1:
% 89.52/13.08 | |
% 89.52/13.08 | | (67) incident(c2, a1b1)
% 89.52/13.08 | |
% 89.52/13.08 | | GROUND_INST: instantiating (23) with a1, c2, b2c2, a1b1, simplifying with
% 89.52/13.08 | | (1), (29), (41), (52), (55), (59), (65), (67) gives:
% 89.52/13.08 | | (68) point_equal(a1, c2) | line_equal(b2c2, a1b1)
% 89.52/13.08 | |
% 89.52/13.08 | | GROUND_INST: instantiating (23) with a1, c2, a1b1, b2c2, simplifying with
% 89.52/13.08 | | (1), (29), (41), (52), (55), (59), (65), (67) gives:
% 89.52/13.08 | | (69) point_equal(a1, c2) | line_equal(a1b1, b2c2)
% 89.52/13.08 | |
% 89.52/13.08 | | BETA: splitting (69) gives:
% 89.52/13.08 | |
% 89.52/13.08 | | Case 1:
% 89.52/13.08 | | |
% 89.52/13.08 | | | (70) point_equal(a1, c2)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (17) with a1, c2, oc, simplifying with (9),
% 89.52/13.08 | | | (14), (52), (59), (70) gives:
% 89.52/13.08 | | | (71) incident(a1, oc)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (17) with a1, c2, a2c2, simplifying with (46),
% 89.52/13.08 | | | (52), (59), (60), (70) gives:
% 89.52/13.08 | | | (72) incident(a1, a2c2)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (51) with a1, c2, simplifying with (52), (59),
% 89.52/13.08 | | | (70) gives:
% 89.52/13.08 | | | (73) point_equal(c2, a1)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (23) with a2, a1, oa, a2c2, simplifying with
% 89.52/13.08 | | | (5), (6), (13), (26), (43), (46), (52), (56), (72) gives:
% 89.52/13.08 | | | (74) line_equal(oa, a2c2)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (23) with ac, a1, a1c1, a2c2, simplifying with
% 89.52/13.08 | | | (22), (30), (35), (46), (47), (48), (52), (54), (72) gives:
% 89.52/13.08 | | | (75) point_equal(ac, a1)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (17) with c2, a1, a1c1, simplifying with (48),
% 89.52/13.08 | | | (52), (54), (59), (73) gives:
% 89.52/13.08 | | | (76) incident(c2, a1c1)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (11) with o, oa, a2c2, simplifying with (28),
% 89.52/13.08 | | | (46), (56), (61), (74) gives:
% 89.52/13.08 | | | (77) incident(o, a2c2)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (23) with c2, c1, oc, a1c1, simplifying with
% 89.52/13.08 | | | (4), (9), (10), (14), (27), (45), (48), (59), (76) gives:
% 89.52/13.08 | | | (78) line_equal(oc, a1c1)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (17) with ac, a1, b2c2, simplifying with (1),
% 89.52/13.08 | | | (35), (52), (55), (75) gives:
% 89.52/13.08 | | | (79) incident(ac, b2c2)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (11) with o, oc, a1c1, simplifying with (14),
% 89.52/13.08 | | | (28), (36), (48), (78) gives:
% 89.52/13.08 | | | (80) incident(o, a1c1)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (23) with o, c2, a1c1, a2c2, simplifying with
% 89.52/13.08 | | | (22), (28), (46), (48), (59), (60), (76), (77), (80) gives:
% 89.52/13.08 | | | (81) point_equal(o, c2)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (17) with o, c2, a1b1, simplifying with (28),
% 89.52/13.08 | | | (41), (59), (67), (81) gives:
% 89.52/13.08 | | | (82) incident(o, a1b1)
% 89.52/13.08 | | |
% 89.52/13.08 | | | GROUND_INST: instantiating (23) with o, b1, ob, a1b1, simplifying with
% 89.52/13.08 | | | (2), (16), (28), (41), (44), (49), (57), (82) gives:
% 89.52/13.08 | | | (83) point_equal(o, b1) | line_equal(ob, a1b1)
% 89.52/13.08 | | |
% 89.52/13.08 | | | BETA: splitting (83) gives:
% 89.52/13.08 | | |
% 89.52/13.08 | | | Case 1:
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | (84) point_equal(o, b1)
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | GROUND_INST: instantiating (51) with o, b1, simplifying with (16), (28),
% 89.52/13.08 | | | | (84) gives:
% 89.52/13.08 | | | | (85) point_equal(b1, o)
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | GROUND_INST: instantiating (17) with b1, o, oc, simplifying with (14),
% 89.52/13.08 | | | | (16), (28), (36), (85) gives:
% 89.52/13.08 | | | | (86) incident(b1, oc)
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | GROUND_INST: instantiating (25) with oc, simplifying with (3), (14),
% 89.52/13.08 | | | | (45), (71), (86) gives:
% 89.52/13.08 | | | | (87) $false
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | CLOSE: (87) is inconsistent.
% 89.52/13.08 | | | |
% 89.52/13.08 | | | Case 2:
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | (88) line_equal(ob, a1b1)
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | GROUND_INST: instantiating (11) with b2, ob, a1b1, simplifying with (2),
% 89.52/13.08 | | | | (37), (41), (64), (88) gives:
% 89.52/13.08 | | | | (89) incident(b2, a1b1)
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | GROUND_INST: instantiating (23) with ab, b2, a1b1, a2b2, simplifying
% 89.52/13.08 | | | | with (18), (21), (31), (32), (33), (37), (41), (63), (89)
% 89.52/13.08 | | | | gives:
% 89.52/13.08 | | | | (90) point_equal(ab, b2)
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | GROUND_INST: instantiating (17) with ab, b2, b2c2, simplifying with (1),
% 89.52/13.08 | | | | (15), (37), (63), (90) gives:
% 89.52/13.08 | | | | (91) incident(ab, b2c2)
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | GROUND_INST: instantiating (39) with b2c2, simplifying with (1), (3),
% 89.52/13.08 | | | | (12), (53), (79), (91) gives:
% 89.52/13.08 | | | | (92) $false
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | CLOSE: (92) is inconsistent.
% 89.52/13.08 | | | |
% 89.52/13.08 | | | End of split
% 89.52/13.08 | | |
% 89.52/13.08 | | Case 2:
% 89.52/13.08 | | |
% 89.52/13.08 | | | (93) ~ point_equal(a1, c2)
% 89.52/13.08 | | |
% 89.52/13.08 | | | BETA: splitting (68) gives:
% 89.52/13.08 | | |
% 89.52/13.08 | | | Case 1:
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | (94) point_equal(a1, c2)
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | PRED_UNIFY: (93), (94) imply:
% 89.52/13.08 | | | | (95) $false
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | CLOSE: (95) is inconsistent.
% 89.52/13.08 | | | |
% 89.52/13.08 | | | Case 2:
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | (96) line_equal(b2c2, a1b1)
% 89.52/13.08 | | | |
% 89.52/13.08 | | | | GROUND_INST: instantiating (11) with b2, b2c2, a1b1, simplifying with
% 89.52/13.08 | | | | (1), (15), (37), (41), (96) gives:
% 89.52/13.08 | | | | (97) incident(b2, a1b1)
% 89.52/13.08 | | | |
% 89.52/13.09 | | | | GROUND_INST: instantiating (23) with b2, b1, a1b1, ob, simplifying with
% 89.52/13.09 | | | | (2), (16), (37), (41), (49), (57), (64), (66), (97) gives:
% 89.52/13.09 | | | | (98) line_equal(a1b1, ob)
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | GROUND_INST: instantiating (11) with c2, a1b1, ob, simplifying with (2),
% 89.52/13.09 | | | | (41), (59), (67), (98) gives:
% 89.52/13.09 | | | | (99) incident(c2, ob)
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | GROUND_INST: instantiating (11) with a1, a1b1, ob, simplifying with (2),
% 89.52/13.09 | | | | (29), (41), (52), (98) gives:
% 89.52/13.09 | | | | (100) incident(a1, ob)
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | GROUND_INST: instantiating (23) with o, a1, ob, oa, simplifying with
% 89.52/13.09 | | | | (2), (6), (28), (44), (52), (56), (61), (100) gives:
% 89.52/13.09 | | | | (101) point_equal(o, a1) | line_equal(ob, oa)
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | BETA: splitting (101) gives:
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | Case 1:
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | (102) point_equal(o, a1)
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | GROUND_INST: instantiating (51) with o, a1, simplifying with (28),
% 89.52/13.09 | | | | | (52), (102) gives:
% 89.52/13.09 | | | | | (103) point_equal(a1, o)
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | GROUND_INST: instantiating (17) with a1, o, oc, simplifying with (14),
% 89.52/13.09 | | | | | (28), (36), (52), (103) gives:
% 89.52/13.09 | | | | | (104) incident(a1, oc)
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | GROUND_INST: instantiating (23) with a1, c2, oc, ob, simplifying with
% 89.52/13.09 | | | | | (2), (9), (14), (52), (59), (93), (99), (100), (104)
% 89.52/13.09 | | | | | gives:
% 89.52/13.09 | | | | | (105) line_equal(oc, ob)
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | GROUND_INST: instantiating (11) with c1, oc, ob, simplifying with (2),
% 89.52/13.09 | | | | | (10), (14), (45), (105) gives:
% 89.52/13.09 | | | | | (106) incident(c1, ob)
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | GROUND_INST: instantiating (25) with ob, simplifying with (2), (3),
% 89.52/13.09 | | | | | (49), (100), (106) gives:
% 89.52/13.09 | | | | | (107) $false
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | CLOSE: (107) is inconsistent.
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | Case 2:
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | (108) line_equal(ob, oa)
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | GROUND_INST: instantiating (11) with c2, ob, oa, simplifying with (2),
% 89.52/13.09 | | | | | (56), (59), (99), (108) gives:
% 89.52/13.09 | | | | | (109) incident(c2, oa)
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | GROUND_INST: instantiating (11) with b2, ob, oa, simplifying with (2),
% 89.52/13.09 | | | | | (37), (56), (64), (108) gives:
% 89.52/13.09 | | | | | (110) incident(b2, oa)
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | GROUND_INST: instantiating (8) with oa, simplifying with (3), (43),
% 89.52/13.09 | | | | | (56), (109), (110) gives:
% 89.52/13.09 | | | | | (111) $false
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | CLOSE: (111) is inconsistent.
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | End of split
% 89.52/13.09 | | | |
% 89.52/13.09 | | | End of split
% 89.52/13.09 | | |
% 89.52/13.09 | | End of split
% 89.52/13.09 | |
% 89.52/13.09 | Case 2:
% 89.52/13.09 | |
% 89.52/13.09 | | (112) incident(b1, a2c2)
% 89.52/13.09 | |
% 89.52/13.09 | | BETA: splitting (62) gives:
% 89.52/13.09 | |
% 89.52/13.09 | | Case 1:
% 89.52/13.09 | | |
% 89.52/13.09 | | | (113) ~ incident(c1, a2b2)
% 89.52/13.09 | | |
% 89.52/13.09 | | | BETA: splitting (50) gives:
% 89.52/13.09 | | |
% 89.52/13.09 | | | Case 1:
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | (114) incident(a2, b1c1)
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | GROUND_INST: instantiating (23) with a2, b1, a2c2, b1c1, simplifying
% 89.52/13.09 | | | | with (13), (16), (24), (26), (38), (46), (112), (114)
% 89.52/13.09 | | | | gives:
% 89.52/13.09 | | | | (115) point_equal(a2, b1) | line_equal(a2c2, b1c1)
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 89.52/13.09 | | | | (12), (13), (14), (16), (17), (18), (19), (20), (21), (23),
% 89.52/13.09 | | | | (24), (25), (26), (28), (29), (30), (31), (32), (33), (34),
% 89.52/13.09 | | | | (36), (37), (38), (39), (40), (41), (43), (44), (45), (46),
% 89.52/13.09 | | | | (49), (51), (52), (56), (57), (58), (59), (60), (61), (63),
% 89.52/13.09 | | | | (64), (65), (66), (113), (114), (115) are inconsistent by
% 89.52/13.09 | | | | sub-proof #4.
% 89.52/13.09 | | | |
% 89.52/13.09 | | | Case 2:
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | (116) incident(c1, a2b2)
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | PRED_UNIFY: (113), (116) imply:
% 89.52/13.09 | | | | (117) $false
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | CLOSE: (117) is inconsistent.
% 89.52/13.09 | | | |
% 89.52/13.09 | | | End of split
% 89.52/13.09 | | |
% 89.52/13.09 | | Case 2:
% 89.52/13.09 | | |
% 89.52/13.09 | | | (118) ~ incident(b1, a2c2) | ~ incident(a1, b2c2) | goal
% 89.52/13.09 | | |
% 89.52/13.09 | | | BETA: splitting (118) gives:
% 89.52/13.09 | | |
% 89.52/13.09 | | | Case 1:
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | (119) ~ incident(b1, a2c2)
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | PRED_UNIFY: (112), (119) imply:
% 89.52/13.09 | | | | (120) $false
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | CLOSE: (120) is inconsistent.
% 89.52/13.09 | | | |
% 89.52/13.09 | | | Case 2:
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | (121) ~ incident(a1, b2c2) | goal
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | BETA: splitting (121) gives:
% 89.52/13.09 | | | |
% 89.52/13.09 | | | | Case 1:
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | (122) ~ incident(a1, b2c2)
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | PRED_UNIFY: (55), (122) imply:
% 89.52/13.09 | | | | | (123) $false
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | CLOSE: (123) is inconsistent.
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | Case 2:
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | (124) goal
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | PRED_UNIFY: (3), (124) imply:
% 89.52/13.09 | | | | | (125) $false
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | | CLOSE: (125) is inconsistent.
% 89.52/13.09 | | | | |
% 89.52/13.09 | | | | End of split
% 89.52/13.09 | | | |
% 89.52/13.09 | | | End of split
% 89.52/13.09 | | |
% 89.52/13.09 | | End of split
% 89.52/13.09 | |
% 89.52/13.09 | End of split
% 89.52/13.09 |
% 89.52/13.09 End of proof
% 89.52/13.09
% 89.52/13.09 Sub-proof #4 shows that the following formulas are inconsistent:
% 89.52/13.09 ----------------------------------------------------------------
% 89.52/13.09 (1) $i(b2c2)
% 89.52/13.09 (2) $i(ob)
% 89.52/13.09 (3) ~ goal
% 89.52/13.09 (4) ~ point_equal(c2, c1)
% 89.52/13.09 (5) ~ point_equal(a2, a1)
% 89.52/13.09 (6) incident(a1, oa)
% 89.52/13.09 (7) incident(a2, a2b2)
% 89.52/13.09 (8) ! [v0: $i] : ( ~ $i(v0) | ~ incident(c2, v0) | ~ incident(b2, v0) | ~
% 89.52/13.09 incident(a2, v0) | goal)
% 89.52/13.09 (9) incident(c2, oc)
% 89.52/13.09 (10) $i(c1)
% 89.52/13.09 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 89.52/13.09 $i(v0) | ~ incident(v0, v1) | ~ line_equal(v1, v2) | incident(v0,
% 89.52/13.09 v2))
% 89.52/13.09 (12) incident(bc, b2c2)
% 89.52/13.09 (13) incident(a2, a2c2)
% 89.52/13.09 (14) $i(oc)
% 89.52/13.09 (15) $i(b1)
% 89.52/13.09 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 89.52/13.09 $i(v0) | ~ point_equal(v0, v1) | ~ incident(v1, v2) | incident(v0,
% 89.52/13.09 v2))
% 89.52/13.09 (17) incident(ab, a1b1)
% 89.52/13.09 (18) incident(bc, b1c1)
% 89.52/13.09 (19) point_equal(a2, b1) | line_equal(a2c2, b1c1)
% 89.52/13.09 (20) incident(c1, b1c1)
% 89.52/13.09 (21) ~ line_equal(a1b1, a2b2)
% 89.52/13.09 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 89.52/13.09 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ incident(v1, v3) | ~ incident(v1,
% 89.52/13.09 v2) | ~ incident(v0, v3) | ~ incident(v0, v2) | point_equal(v0,
% 89.52/13.09 v1) | line_equal(v2, v3))
% 89.52/13.09 (23) $i(b1c1)
% 89.52/13.09 (24) ! [v0: $i] : ( ~ $i(v0) | ~ incident(c1, v0) | ~ incident(b1, v0) |
% 89.52/13.09 ~ incident(a1, v0) | goal)
% 89.52/13.09 (25) ~ incident(c1, a2b2)
% 89.52/13.09 (26) $i(a2)
% 89.52/13.09 (27) $i(o)
% 89.52/13.09 (28) incident(a1, a1b1)
% 89.52/13.09 (29) incident(ac, a2c2)
% 89.52/13.09 (30) incident(ab, a2b2)
% 89.52/13.09 (31) $i(a2b2)
% 89.52/13.09 (32) incident(b2, a2b2)
% 89.52/13.09 (33) ~ line_equal(b1c1, b2c2)
% 89.52/13.09 (34) incident(o, oc)
% 89.52/13.09 (35) $i(b2)
% 89.52/13.09 (36) incident(b1, b1c1)
% 89.52/13.10 (37) ! [v0: $i] : ( ~ $i(v0) | ~ incident(ab, v0) | ~ incident(ac, v0) |
% 89.52/13.10 ~ incident(bc, v0) | ~ line_equal(v0, v0) | goal)
% 89.52/13.10 (38) line_equal(a2c2, a2c2)
% 89.52/13.10 (39) $i(a1b1)
% 89.52/13.10 (40) incident(a2, oa)
% 89.52/13.10 (41) incident(o, ob)
% 89.52/13.10 (42) incident(c1, oc)
% 89.52/13.10 (43) $i(a2c2)
% 89.52/13.10 (44) incident(b1, ob)
% 89.52/13.10 (45) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ point_equal(v0,
% 89.52/13.10 v1) | point_equal(v1, v0))
% 89.52/13.10 (46) $i(a1)
% 89.52/13.10 (47) incident(a2, b1c1)
% 89.52/13.10 (48) $i(oa)
% 89.52/13.10 (49) incident(b1, a1b1)
% 89.52/13.10 (50) $i(bc)
% 89.52/13.10 (51) $i(c2)
% 89.52/13.10 (52) incident(c2, a2c2)
% 89.52/13.10 (53) incident(o, oa)
% 89.52/13.10 (54) $i(ab)
% 89.52/13.10 (55) incident(b2, ob)
% 89.52/13.10 (56) incident(c2, b2c2)
% 89.52/13.10 (57) ~ point_equal(b2, b1)
% 89.52/13.10
% 89.52/13.10 Begin of proof
% 89.52/13.10 |
% 89.52/13.10 | BETA: splitting (19) gives:
% 89.52/13.10 |
% 89.52/13.10 | Case 1:
% 89.52/13.10 | |
% 89.52/13.10 | | (58) point_equal(a2, b1)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (16) with a2, b1, a1b1, simplifying with (15),
% 89.52/13.10 | | (26), (39), (49), (58) gives:
% 89.52/13.10 | | (59) incident(a2, a1b1)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (45) with a2, b1, simplifying with (15), (26),
% 89.52/13.10 | | (58) gives:
% 89.52/13.10 | | (60) point_equal(b1, a2)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (22) with ab, a2, a1b1, a2b2, simplifying with
% 89.52/13.10 | | (7), (17), (21), (26), (30), (31), (39), (54), (59) gives:
% 89.52/13.10 | | (61) point_equal(ab, a2)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (22) with a2, a1, oa, a1b1, simplifying with (5),
% 89.52/13.10 | | (6), (26), (28), (39), (40), (46), (48), (59) gives:
% 89.52/13.10 | | (62) line_equal(oa, a1b1)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (16) with b1, a2, a2b2, simplifying with (7),
% 89.52/13.10 | | (15), (26), (31), (60) gives:
% 89.52/13.10 | | (63) incident(b1, a2b2)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (11) with o, oa, a1b1, simplifying with (27),
% 89.52/13.10 | | (39), (48), (53), (62) gives:
% 89.52/13.10 | | (64) incident(o, a1b1)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (22) with b2, b1, ob, a2b2, simplifying with (2),
% 89.52/13.10 | | (15), (31), (32), (35), (44), (55), (57), (63) gives:
% 89.52/13.10 | | (65) line_equal(ob, a2b2)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (16) with ab, a2, a2c2, simplifying with (13),
% 89.52/13.10 | | (26), (43), (54), (61) gives:
% 89.52/13.10 | | (66) incident(ab, a2c2)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (11) with o, ob, a2b2, simplifying with (2),
% 89.52/13.10 | | (27), (31), (41), (65) gives:
% 89.52/13.10 | | (67) incident(o, a2b2)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (22) with o, a2, a1b1, a2b2, simplifying with
% 89.52/13.10 | | (7), (21), (26), (27), (31), (39), (59), (64), (67) gives:
% 89.52/13.10 | | (68) point_equal(o, a2)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (16) with o, a2, b1c1, simplifying with (23),
% 89.52/13.10 | | (26), (27), (47), (68) gives:
% 89.52/13.10 | | (69) incident(o, b1c1)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (22) with o, c1, oc, b1c1, simplifying with (10),
% 89.52/13.10 | | (14), (20), (23), (27), (34), (42), (69) gives:
% 89.52/13.10 | | (70) point_equal(o, c1) | line_equal(oc, b1c1)
% 89.52/13.10 | |
% 89.52/13.10 | | BETA: splitting (70) gives:
% 89.52/13.10 | |
% 89.52/13.10 | | Case 1:
% 89.52/13.10 | | |
% 89.52/13.10 | | | (71) point_equal(o, c1)
% 89.52/13.10 | | |
% 89.52/13.10 | | | GROUND_INST: instantiating (45) with o, c1, simplifying with (10), (27),
% 89.52/13.10 | | | (71) gives:
% 89.52/13.10 | | | (72) point_equal(c1, o)
% 89.52/13.10 | | |
% 89.52/13.10 | | | GROUND_INST: instantiating (16) with c1, o, a2b2, simplifying with (10),
% 89.52/13.10 | | | (25), (27), (31), (67), (72) gives:
% 89.52/13.10 | | | (73) $false
% 89.52/13.10 | | |
% 89.52/13.10 | | | CLOSE: (73) is inconsistent.
% 89.52/13.10 | | |
% 89.52/13.10 | | Case 2:
% 89.52/13.10 | | |
% 89.52/13.10 | | | (74) line_equal(oc, b1c1)
% 89.52/13.10 | | |
% 89.52/13.10 | | | GROUND_INST: instantiating (11) with c2, oc, b1c1, simplifying with (9),
% 89.52/13.10 | | | (14), (23), (51), (74) gives:
% 89.52/13.10 | | | (75) incident(c2, b1c1)
% 89.52/13.10 | | |
% 89.52/13.10 | | | GROUND_INST: instantiating (22) with bc, c2, b1c1, b2c2, simplifying with
% 89.52/13.10 | | | (1), (12), (18), (23), (33), (50), (51), (56), (75) gives:
% 89.52/13.10 | | | (76) point_equal(bc, c2)
% 89.52/13.10 | | |
% 89.52/13.10 | | | GROUND_INST: instantiating (16) with bc, c2, a2c2, simplifying with (43),
% 89.52/13.10 | | | (50), (51), (52), (76) gives:
% 89.52/13.10 | | | (77) incident(bc, a2c2)
% 89.52/13.10 | | |
% 89.52/13.10 | | | GROUND_INST: instantiating (37) with a2c2, simplifying with (3), (29),
% 89.52/13.10 | | | (38), (43), (66), (77) gives:
% 89.52/13.10 | | | (78) $false
% 89.52/13.10 | | |
% 89.52/13.10 | | | CLOSE: (78) is inconsistent.
% 89.52/13.10 | | |
% 89.52/13.10 | | End of split
% 89.52/13.10 | |
% 89.52/13.10 | Case 2:
% 89.52/13.10 | |
% 89.52/13.10 | | (79) ~ point_equal(a2, b1)
% 89.52/13.10 | | (80) line_equal(a2c2, b1c1)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (11) with c2, a2c2, b1c1, simplifying with (23),
% 89.52/13.10 | | (43), (51), (52), (80) gives:
% 89.52/13.10 | | (81) incident(c2, b1c1)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (22) with c2, c1, b1c1, oc, simplifying with (4),
% 89.52/13.10 | | (9), (10), (14), (20), (23), (42), (51), (81) gives:
% 89.52/13.10 | | (82) line_equal(b1c1, oc)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (22) with c2, c1, oc, b1c1, simplifying with (4),
% 89.52/13.10 | | (9), (10), (14), (20), (23), (42), (51), (81) gives:
% 89.52/13.10 | | (83) line_equal(oc, b1c1)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (11) with a2, b1c1, oc, simplifying with (14),
% 89.52/13.10 | | (23), (26), (47), (82) gives:
% 89.52/13.10 | | (84) incident(a2, oc)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (11) with b1, b1c1, oc, simplifying with (14),
% 89.52/13.10 | | (15), (23), (36), (82) gives:
% 89.52/13.10 | | (85) incident(b1, oc)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (11) with o, oc, b1c1, simplifying with (14),
% 89.52/13.10 | | (23), (27), (34), (83) gives:
% 89.52/13.10 | | (86) incident(o, b1c1)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (22) with o, b1, oc, ob, simplifying with (2),
% 89.52/13.10 | | (14), (15), (27), (34), (41), (44), (85) gives:
% 89.52/13.10 | | (87) point_equal(o, b1) | line_equal(oc, ob)
% 89.52/13.10 | |
% 89.52/13.10 | | GROUND_INST: instantiating (22) with o, b1, ob, b1c1, simplifying with (2),
% 89.52/13.10 | | (15), (23), (27), (36), (41), (44), (86) gives:
% 89.52/13.10 | | (88) point_equal(o, b1) | line_equal(ob, b1c1)
% 89.52/13.10 | |
% 89.52/13.10 | | BETA: splitting (88) gives:
% 89.52/13.10 | |
% 89.52/13.10 | | Case 1:
% 89.52/13.10 | | |
% 89.52/13.10 | | | (89) point_equal(o, b1)
% 89.52/13.10 | | |
% 89.52/13.10 | | | GROUND_INST: instantiating (45) with o, b1, simplifying with (15), (27),
% 89.52/13.10 | | | (89) gives:
% 89.52/13.10 | | | (90) point_equal(b1, o)
% 89.52/13.10 | | |
% 89.52/13.10 | | | GROUND_INST: instantiating (16) with b1, o, oa, simplifying with (15),
% 89.52/13.10 | | | (27), (48), (53), (90) gives:
% 89.52/13.10 | | | (91) incident(b1, oa)
% 89.52/13.10 | | |
% 89.52/13.10 | | | GROUND_INST: instantiating (22) with a2, b1, oa, oc, simplifying with
% 89.52/13.10 | | | (14), (15), (26), (40), (48), (79), (84), (85), (91) gives:
% 89.52/13.10 | | | (92) line_equal(oa, oc)
% 89.52/13.10 | | |
% 89.52/13.11 | | | GROUND_INST: instantiating (11) with a1, oa, oc, simplifying with (6),
% 89.52/13.11 | | | (14), (46), (48), (92) gives:
% 89.52/13.11 | | | (93) incident(a1, oc)
% 89.52/13.11 | | |
% 89.52/13.11 | | | GROUND_INST: instantiating (24) with oc, simplifying with (3), (14), (42),
% 89.52/13.11 | | | (85), (93) gives:
% 89.52/13.11 | | | (94) $false
% 89.52/13.11 | | |
% 89.52/13.11 | | | CLOSE: (94) is inconsistent.
% 89.52/13.11 | | |
% 89.52/13.11 | | Case 2:
% 89.52/13.11 | | |
% 89.52/13.11 | | | (95) ~ point_equal(o, b1)
% 89.52/13.11 | | |
% 89.52/13.11 | | | BETA: splitting (87) gives:
% 89.52/13.11 | | |
% 89.52/13.11 | | | Case 1:
% 89.52/13.11 | | | |
% 89.52/13.11 | | | | (96) point_equal(o, b1)
% 89.52/13.11 | | | |
% 89.52/13.11 | | | | PRED_UNIFY: (95), (96) imply:
% 89.52/13.11 | | | | (97) $false
% 89.52/13.11 | | | |
% 89.52/13.11 | | | | CLOSE: (97) is inconsistent.
% 89.52/13.11 | | | |
% 89.52/13.11 | | | Case 2:
% 89.52/13.11 | | | |
% 89.52/13.11 | | | | (98) line_equal(oc, ob)
% 89.52/13.11 | | | |
% 89.52/13.11 | | | | GROUND_INST: instantiating (11) with c2, oc, ob, simplifying with (2),
% 89.52/13.11 | | | | (9), (14), (51), (98) gives:
% 89.52/13.11 | | | | (99) incident(c2, ob)
% 89.52/13.11 | | | |
% 89.52/13.11 | | | | GROUND_INST: instantiating (11) with a2, oc, ob, simplifying with (2),
% 89.52/13.11 | | | | (14), (26), (84), (98) gives:
% 89.52/13.11 | | | | (100) incident(a2, ob)
% 89.52/13.11 | | | |
% 89.52/13.11 | | | | GROUND_INST: instantiating (8) with ob, simplifying with (2), (3), (55),
% 89.52/13.11 | | | | (99), (100) gives:
% 89.52/13.11 | | | | (101) $false
% 89.52/13.11 | | | |
% 89.52/13.11 | | | | CLOSE: (101) is inconsistent.
% 89.52/13.11 | | | |
% 89.52/13.11 | | | End of split
% 89.52/13.11 | | |
% 89.52/13.11 | | End of split
% 89.52/13.11 | |
% 89.52/13.11 | End of split
% 89.52/13.11 |
% 89.52/13.11 End of proof
% 89.52/13.11 % SZS output end Proof for theBenchmark
% 89.52/13.11
% 89.52/13.11 12478ms
%------------------------------------------------------------------------------