TSTP Solution File: GEO169+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO169+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 : 600s
% DateTime : Sat Jul 16 03:48:06 EDT 2022
% Result : Theorem 13.12s 3.79s
% Output : Proof 17.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO169+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n024.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 : 600
% 0.12/0.33 % DateTime : Sat Jun 18 15:39:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.56 ____ _
% 0.54/0.56 ___ / __ \_____(_)___ ________ __________
% 0.54/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.56
% 0.54/0.56 A Theorem Prover for First-Order Logic
% 0.54/0.57 (ePrincess v.1.0)
% 0.54/0.57
% 0.54/0.57 (c) Philipp Rümmer, 2009-2015
% 0.54/0.57 (c) Peter Backeman, 2014-2015
% 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.57 Bug reports to peter@backeman.se
% 0.54/0.57
% 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.57
% 0.54/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.60/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.59/0.94 Prover 0: Preprocessing ...
% 1.98/1.08 Prover 0: Constructing countermodel ...
% 13.12/3.79 Prover 0: proved (3176ms)
% 13.12/3.79
% 13.12/3.79 No countermodel exists, formula is valid
% 13.12/3.79 % SZS status Theorem for theBenchmark
% 13.12/3.79
% 13.12/3.79 Generating proof ... found it (size 244)
% 17.65/4.95
% 17.65/4.95 % SZS output start Proof for theBenchmark
% 17.65/4.95 Assumed formulas after preprocessing and simplification:
% 17.65/4.95 | (0) incident(o, oc) & incident(o, ob) & incident(o, oa) & incident(c2, oc) & incident(c2, a2c2) & incident(c2, b2c2) & incident(b2, ob) & incident(b2, a2b2) & incident(b2, b2c2) & incident(a2, oa) & incident(a2, a2b2) & incident(a2, a2c2) & incident(c1, oc) & incident(c1, a1c1) & incident(c1, b1c1) & incident(b1, ob) & incident(b1, a1b1) & incident(b1, b1c1) & incident(a1, oa) & incident(a1, a1b1) & incident(a1, a1c1) & incident(ab, a1b1) & incident(ab, a2b2) & incident(ac, a1c1) & incident(ac, a2c2) & incident(bc, b1c1) & incident(bc, b2c2) & ~ point_equal(c2, c1) & ~ point_equal(b2, b1) & ~ point_equal(a2, a1) & ~ goal & ~ line_equal(a1b1, a2b2) & ~ line_equal(a1c1, a2c2) & ~ line_equal(b1c1, b2c2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ incident(v1, v3) | ~ incident(v1, v2) | ~ incident(v0, v3) | ~ incident(v0, v2) | point_equal(v0, v1) | line_equal(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ point_equal(v1, v2) | ~ point_equal(v0, v1) | point_equal(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ point_equal(v0, v1) | ~ incident(v1, v2) | incident(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ incident(v0, v1) | ~ line_equal(v1, v2) | incident(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ line_equal(v1, v2) | ~ line_equal(v0, v1) | line_equal(v0, v2)) & ! [v0] : ! [v1] : ( ~ point_equal(v0, v1) | point_equal(v1, v0)) & ! [v0] : ! [v1] : ( ~ incident(v0, v1) | point_equal(v0, v0)) & ! [v0] : ! [v1] : ( ~ incident(v0, v1) | line_equal(v1, v1)) & ! [v0] : ! [v1] : ( ~ line_equal(v0, v1) | line_equal(v1, v0)) & ! [v0] : ( ~ incident(c2, v0) | ~ incident(b2, v0) | ~ incident(a2, v0)) & ! [v0] : ( ~ incident(c1, v0) | ~ incident(b1, v0) | ~ incident(a1, v0)) & ! [v0] : ( ~ incident(ab, v0) | ~ incident(ac, v0) | ~ incident(bc, v0) | ~ line_equal(v0, v0)) & ( ~ incident(c2, a1b1) | ~ incident(b2, a1c1) | ~ incident(a2, b1c1)) & ( ~ incident(c1, a2b2) | ~ incident(b1, a2c2) | ~ incident(a1, b2c2)) & (incident(c2, a1b1) | incident(b1, a2c2)) & (incident(b2, a1c1) | incident(a1, b2c2)) & (incident(a2, b1c1) | incident(c1, a2b2))
% 17.65/4.96 | Applying alpha-rule on (0) yields:
% 17.65/4.96 | (1) incident(b1, b1c1)
% 17.65/4.96 | (2) incident(b2, a1c1) | incident(a1, b2c2)
% 17.65/4.96 | (3) incident(b1, ob)
% 17.65/4.96 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ point_equal(v0, v1) | ~ incident(v1, v2) | incident(v0, v2))
% 17.65/4.96 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ incident(v1, v3) | ~ incident(v1, v2) | ~ incident(v0, v3) | ~ incident(v0, v2) | point_equal(v0, v1) | line_equal(v2, v3))
% 17.65/4.96 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ line_equal(v1, v2) | ~ line_equal(v0, v1) | line_equal(v0, v2))
% 17.65/4.96 | (7) ! [v0] : ! [v1] : ( ~ incident(v0, v1) | point_equal(v0, v0))
% 17.65/4.96 | (8) incident(c1, b1c1)
% 17.65/4.96 | (9) incident(ab, a1b1)
% 17.65/4.97 | (10) ~ goal
% 17.65/4.97 | (11) incident(o, oa)
% 17.65/4.97 | (12) incident(a2, b1c1) | incident(c1, a2b2)
% 17.65/4.97 | (13) ! [v0] : ! [v1] : ( ~ incident(v0, v1) | line_equal(v1, v1))
% 17.65/4.97 | (14) ! [v0] : ( ~ incident(ab, v0) | ~ incident(ac, v0) | ~ incident(bc, v0) | ~ line_equal(v0, v0))
% 17.65/4.97 | (15) incident(ac, a1c1)
% 17.65/4.97 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ incident(v0, v1) | ~ line_equal(v1, v2) | incident(v0, v2))
% 17.65/4.97 | (17) incident(c2, a1b1) | incident(b1, a2c2)
% 17.65/4.97 | (18) incident(o, ob)
% 17.65/4.97 | (19) ~ incident(c2, a1b1) | ~ incident(b2, a1c1) | ~ incident(a2, b1c1)
% 17.65/4.97 | (20) incident(b2, a2b2)
% 17.65/4.97 | (21) incident(ab, a2b2)
% 17.65/4.97 | (22) incident(c2, a2c2)
% 17.65/4.97 | (23) incident(a2, oa)
% 17.65/4.97 | (24) incident(b2, b2c2)
% 17.65/4.97 | (25) ~ point_equal(a2, a1)
% 17.65/4.97 | (26) incident(c1, oc)
% 17.65/4.97 | (27) incident(a1, oa)
% 17.65/4.97 | (28) incident(ac, a2c2)
% 17.65/4.97 | (29) incident(c2, b2c2)
% 17.65/4.97 | (30) ~ point_equal(c2, c1)
% 17.65/4.97 | (31) incident(b1, a1b1)
% 17.65/4.97 | (32) ! [v0] : ! [v1] : ( ~ point_equal(v0, v1) | point_equal(v1, v0))
% 17.65/4.97 | (33) incident(bc, b1c1)
% 17.65/4.97 | (34) incident(a1, a1b1)
% 17.65/4.97 | (35) ~ point_equal(b2, b1)
% 17.65/4.97 | (36) incident(o, oc)
% 17.65/4.97 | (37) ~ line_equal(a1c1, a2c2)
% 17.65/4.97 | (38) incident(a1, a1c1)
% 17.65/4.97 | (39) ! [v0] : ( ~ incident(c1, v0) | ~ incident(b1, v0) | ~ incident(a1, v0))
% 17.65/4.97 | (40) incident(a2, a2b2)
% 17.65/4.97 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ point_equal(v1, v2) | ~ point_equal(v0, v1) | point_equal(v0, v2))
% 17.65/4.97 | (42) ~ line_equal(b1c1, b2c2)
% 17.65/4.97 | (43) ~ incident(c1, a2b2) | ~ incident(b1, a2c2) | ~ incident(a1, b2c2)
% 17.65/4.97 | (44) incident(c1, a1c1)
% 17.65/4.97 | (45) ~ line_equal(a1b1, a2b2)
% 17.65/4.97 | (46) ! [v0] : ( ~ incident(c2, v0) | ~ incident(b2, v0) | ~ incident(a2, v0))
% 17.65/4.97 | (47) incident(c2, oc)
% 17.65/4.97 | (48) ! [v0] : ! [v1] : ( ~ line_equal(v0, v1) | line_equal(v1, v0))
% 17.65/4.97 | (49) incident(bc, b2c2)
% 17.65/4.97 | (50) incident(a2, a2c2)
% 17.65/4.97 | (51) incident(b2, ob)
% 17.65/4.97 |
% 17.65/4.98 | Instantiating formula (13) with a1b1, ab and discharging atoms incident(ab, a1b1), yields:
% 17.65/4.98 | (52) line_equal(a1b1, a1b1)
% 17.65/4.98 |
% 17.65/4.98 | Instantiating formula (13) with a2b2, ab and discharging atoms incident(ab, a2b2), yields:
% 17.65/4.98 | (53) line_equal(a2b2, a2b2)
% 17.65/4.98 |
% 17.65/4.98 | Instantiating formula (13) with b1c1, bc and discharging atoms incident(bc, b1c1), yields:
% 17.65/4.98 | (54) line_equal(b1c1, b1c1)
% 17.92/4.98 |
% 17.92/4.98 +-Applying beta-rule and splitting (2), into two cases.
% 17.92/4.98 |-Branch one:
% 17.92/4.98 | (55) incident(b2, a1c1)
% 17.92/4.98 |
% 17.92/4.98 +-Applying beta-rule and splitting (12), into two cases.
% 17.92/4.98 |-Branch one:
% 17.92/4.98 | (56) incident(a2, b1c1)
% 17.92/4.98 |
% 17.92/4.98 +-Applying beta-rule and splitting (19), into two cases.
% 17.92/4.98 |-Branch one:
% 17.92/4.98 | (57) ~ incident(c2, a1b1)
% 17.92/4.98 |
% 17.92/4.98 +-Applying beta-rule and splitting (17), into two cases.
% 17.92/4.98 |-Branch one:
% 17.92/4.98 | (58) incident(c2, a1b1)
% 17.92/4.98 |
% 17.92/4.98 | Using (58) and (57) yields:
% 17.92/4.98 | (59) $false
% 17.92/4.98 |
% 17.92/4.98 |-The branch is then unsatisfiable
% 17.92/4.98 |-Branch two:
% 17.92/4.98 | (57) ~ incident(c2, a1b1)
% 17.92/4.98 | (61) incident(b1, a2c2)
% 17.92/4.98 |
% 17.92/4.98 | Instantiating formula (5) with a2c2, b1c1, b1, a2 and discharging atoms incident(a2, b1c1), incident(a2, a2c2), incident(b1, b1c1), incident(b1, a2c2), yields:
% 17.92/4.98 | (62) point_equal(a2, b1) | line_equal(b1c1, a2c2)
% 17.92/4.98 |
% 17.92/4.98 | Instantiating formula (5) with b1c1, a2c2, b1, a2 and discharging atoms incident(a2, b1c1), incident(a2, a2c2), incident(b1, b1c1), incident(b1, a2c2), yields:
% 17.92/4.98 | (63) point_equal(a2, b1) | line_equal(a2c2, b1c1)
% 17.92/4.98 |
% 17.92/4.98 +-Applying beta-rule and splitting (62), into two cases.
% 17.92/4.98 |-Branch one:
% 17.92/4.98 | (64) point_equal(a2, b1)
% 17.92/4.98 |
% 17.92/4.98 | Instantiating formula (4) with a1b1, b1, a2 and discharging atoms point_equal(a2, b1), incident(b1, a1b1), yields:
% 17.92/4.98 | (65) incident(a2, a1b1)
% 17.92/4.98 |
% 17.92/4.98 | Instantiating formula (32) with b1, a2 and discharging atoms point_equal(a2, b1), yields:
% 17.92/4.98 | (66) point_equal(b1, a2)
% 17.92/4.98 |
% 17.92/4.98 | Instantiating formula (4) with a2b2, a2, b1 and discharging atoms point_equal(b1, a2), incident(a2, a2b2), yields:
% 17.92/4.98 | (67) incident(b1, a2b2)
% 17.92/4.98 |
% 17.92/4.98 | Instantiating formula (5) with a2b2, a1b1, a2, ab and discharging atoms incident(a2, a1b1), incident(a2, a2b2), incident(ab, a1b1), incident(ab, a2b2), ~ line_equal(a1b1, a2b2), yields:
% 17.92/4.98 | (68) point_equal(ab, a2)
% 17.92/4.98 |
% 17.92/4.98 | Instantiating formula (5) with a1b1, oa, a1, a2 and discharging atoms incident(a2, oa), incident(a2, a1b1), incident(a1, oa), incident(a1, a1b1), ~ point_equal(a2, a1), yields:
% 17.92/4.98 | (69) line_equal(oa, a1b1)
% 17.92/4.98 |
% 17.92/4.98 | Instantiating formula (4) with b1c1, a2, ab and discharging atoms point_equal(ab, a2), incident(a2, b1c1), yields:
% 17.92/4.98 | (70) incident(ab, b1c1)
% 17.92/4.98 |
% 17.92/4.98 | Instantiating formula (4) with a2c2, a2, ab and discharging atoms point_equal(ab, a2), incident(a2, a2c2), yields:
% 17.92/4.99 | (71) incident(ab, a2c2)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (5) with a2b2, ob, b1, b2 and discharging atoms incident(b2, ob), incident(b2, a2b2), incident(b1, ob), incident(b1, a2b2), ~ point_equal(b2, b1), yields:
% 17.92/4.99 | (72) line_equal(ob, a2b2)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (16) with a1b1, oa, o and discharging atoms incident(o, oa), line_equal(oa, a1b1), yields:
% 17.92/4.99 | (73) incident(o, a1b1)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (16) with a2b2, ob, o and discharging atoms incident(o, ob), line_equal(ob, a2b2), yields:
% 17.92/4.99 | (74) incident(o, a2b2)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (5) with a2b2, a1b1, o, ab and discharging atoms incident(o, a1b1), incident(o, a2b2), incident(ab, a1b1), incident(ab, a2b2), ~ line_equal(a1b1, a2b2), yields:
% 17.92/4.99 | (75) point_equal(ab, o)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (4) with oc, o, ab and discharging atoms point_equal(ab, o), incident(o, oc), yields:
% 17.92/4.99 | (76) incident(ab, oc)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (5) with a2c2, oc, ab, c2 and discharging atoms incident(c2, oc), incident(c2, a2c2), incident(ab, oc), incident(ab, a2c2), yields:
% 17.92/4.99 | (77) point_equal(c2, ab) | line_equal(oc, a2c2)
% 17.92/4.99 |
% 17.92/4.99 +-Applying beta-rule and splitting (77), into two cases.
% 17.92/4.99 |-Branch one:
% 17.92/4.99 | (78) point_equal(c2, ab)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (4) with a1b1, ab, c2 and discharging atoms point_equal(c2, ab), incident(ab, a1b1), ~ incident(c2, a1b1), yields:
% 17.92/4.99 | (59) $false
% 17.92/4.99 |
% 17.92/4.99 |-The branch is then unsatisfiable
% 17.92/4.99 |-Branch two:
% 17.92/4.99 | (80) ~ point_equal(c2, ab)
% 17.92/4.99 | (81) line_equal(oc, a2c2)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (16) with a2c2, oc, c1 and discharging atoms incident(c1, oc), line_equal(oc, a2c2), yields:
% 17.92/4.99 | (82) incident(c1, a2c2)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (5) with a2c2, a1c1, c1, ac and discharging atoms incident(c1, a1c1), incident(c1, a2c2), incident(ac, a1c1), incident(ac, a2c2), ~ line_equal(a1c1, a2c2), yields:
% 17.92/4.99 | (83) point_equal(ac, c1)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (4) with b1c1, c1, ac and discharging atoms point_equal(ac, c1), incident(c1, b1c1), yields:
% 17.92/4.99 | (84) incident(ac, b1c1)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (14) with b1c1 and discharging atoms incident(ab, b1c1), incident(ac, b1c1), incident(bc, b1c1), line_equal(b1c1, b1c1), yields:
% 17.92/4.99 | (59) $false
% 17.92/4.99 |
% 17.92/4.99 |-The branch is then unsatisfiable
% 17.92/4.99 |-Branch two:
% 17.92/4.99 | (86) ~ point_equal(a2, b1)
% 17.92/4.99 | (87) line_equal(b1c1, a2c2)
% 17.92/4.99 |
% 17.92/4.99 +-Applying beta-rule and splitting (63), into two cases.
% 17.92/4.99 |-Branch one:
% 17.92/4.99 | (64) point_equal(a2, b1)
% 17.92/4.99 |
% 17.92/4.99 | Using (64) and (86) yields:
% 17.92/4.99 | (59) $false
% 17.92/4.99 |
% 17.92/4.99 |-The branch is then unsatisfiable
% 17.92/4.99 |-Branch two:
% 17.92/4.99 | (86) ~ point_equal(a2, b1)
% 17.92/4.99 | (91) line_equal(a2c2, b1c1)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (16) with a2c2, b1c1, c1 and discharging atoms incident(c1, b1c1), line_equal(b1c1, a2c2), yields:
% 17.92/4.99 | (82) incident(c1, a2c2)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (5) with oc, a2c2, c1, c2 and discharging atoms incident(c2, oc), incident(c2, a2c2), incident(c1, oc), incident(c1, a2c2), ~ point_equal(c2, c1), yields:
% 17.92/4.99 | (93) line_equal(a2c2, oc)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (5) with a2c2, oc, c1, c2 and discharging atoms incident(c2, oc), incident(c2, a2c2), incident(c1, oc), incident(c1, a2c2), ~ point_equal(c2, c1), yields:
% 17.92/4.99 | (81) line_equal(oc, a2c2)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (16) with a2c2, oc, o and discharging atoms incident(o, oc), line_equal(oc, a2c2), yields:
% 17.92/4.99 | (95) incident(o, a2c2)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (16) with oc, a2c2, b1 and discharging atoms incident(b1, a2c2), line_equal(a2c2, oc), yields:
% 17.92/4.99 | (96) incident(b1, oc)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (5) with ob, a2c2, b1, o and discharging atoms incident(o, ob), incident(o, a2c2), incident(b1, ob), incident(b1, a2c2), yields:
% 17.92/4.99 | (97) point_equal(o, b1) | line_equal(a2c2, ob)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (5) with a2c2, ob, b1, o and discharging atoms incident(o, ob), incident(o, a2c2), incident(b1, ob), incident(b1, a2c2), yields:
% 17.92/4.99 | (98) point_equal(o, b1) | line_equal(ob, a2c2)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (5) with oc, ob, b1, o and discharging atoms incident(o, oc), incident(o, ob), incident(b1, oc), incident(b1, ob), yields:
% 17.92/4.99 | (99) point_equal(o, b1) | line_equal(ob, oc)
% 17.92/4.99 |
% 17.92/4.99 | Instantiating formula (5) with ob, oc, b1, o and discharging atoms incident(o, oc), incident(o, ob), incident(b1, oc), incident(b1, ob), yields:
% 17.92/4.99 | (100) point_equal(o, b1) | line_equal(oc, ob)
% 17.92/5.00 |
% 17.92/5.00 +-Applying beta-rule and splitting (100), into two cases.
% 17.92/5.00 |-Branch one:
% 17.92/5.00 | (101) point_equal(o, b1)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (32) with b1, o and discharging atoms point_equal(o, b1), yields:
% 17.92/5.00 | (102) point_equal(b1, o)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (4) with oa, o, b1 and discharging atoms point_equal(b1, o), incident(o, oa), yields:
% 17.92/5.00 | (103) incident(b1, oa)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (5) with a2c2, oa, b1, a2 and discharging atoms incident(a2, oa), incident(a2, a2c2), incident(b1, oa), incident(b1, a2c2), ~ point_equal(a2, b1), yields:
% 17.92/5.00 | (104) line_equal(oa, a2c2)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (16) with a2c2, oa, a1 and discharging atoms incident(a1, oa), line_equal(oa, a2c2), yields:
% 17.92/5.00 | (105) incident(a1, a2c2)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (39) with a2c2 and discharging atoms incident(c1, a2c2), incident(b1, a2c2), incident(a1, a2c2), yields:
% 17.92/5.00 | (59) $false
% 17.92/5.00 |
% 17.92/5.00 |-The branch is then unsatisfiable
% 17.92/5.00 |-Branch two:
% 17.92/5.00 | (107) ~ point_equal(o, b1)
% 17.92/5.00 | (108) line_equal(oc, ob)
% 17.92/5.00 |
% 17.92/5.00 +-Applying beta-rule and splitting (99), into two cases.
% 17.92/5.00 |-Branch one:
% 17.92/5.00 | (101) point_equal(o, b1)
% 17.92/5.00 |
% 17.92/5.00 | Using (101) and (107) yields:
% 17.92/5.00 | (59) $false
% 17.92/5.00 |
% 17.92/5.00 |-The branch is then unsatisfiable
% 17.92/5.00 |-Branch two:
% 17.92/5.00 | (107) ~ point_equal(o, b1)
% 17.92/5.00 | (112) line_equal(ob, oc)
% 17.92/5.00 |
% 17.92/5.00 +-Applying beta-rule and splitting (98), into two cases.
% 17.92/5.00 |-Branch one:
% 17.92/5.00 | (101) point_equal(o, b1)
% 17.92/5.00 |
% 17.92/5.00 | Using (101) and (107) yields:
% 17.92/5.00 | (59) $false
% 17.92/5.00 |
% 17.92/5.00 |-The branch is then unsatisfiable
% 17.92/5.00 |-Branch two:
% 17.92/5.00 | (107) ~ point_equal(o, b1)
% 17.92/5.00 | (116) line_equal(ob, a2c2)
% 17.92/5.00 |
% 17.92/5.00 +-Applying beta-rule and splitting (97), into two cases.
% 17.92/5.00 |-Branch one:
% 17.92/5.00 | (101) point_equal(o, b1)
% 17.92/5.00 |
% 17.92/5.00 | Using (101) and (107) yields:
% 17.92/5.00 | (59) $false
% 17.92/5.00 |
% 17.92/5.00 |-The branch is then unsatisfiable
% 17.92/5.00 |-Branch two:
% 17.92/5.00 | (107) ~ point_equal(o, b1)
% 17.92/5.00 | (120) line_equal(a2c2, ob)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (16) with ob, a2c2, c2 and discharging atoms incident(c2, a2c2), line_equal(a2c2, ob), yields:
% 17.92/5.00 | (121) incident(c2, ob)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (16) with ob, a2c2, a2 and discharging atoms incident(a2, a2c2), line_equal(a2c2, ob), yields:
% 17.92/5.00 | (122) incident(a2, ob)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (46) with ob and discharging atoms incident(c2, ob), incident(b2, ob), incident(a2, ob), yields:
% 17.92/5.00 | (59) $false
% 17.92/5.00 |
% 17.92/5.00 |-The branch is then unsatisfiable
% 17.92/5.00 |-Branch two:
% 17.92/5.00 | (58) incident(c2, a1b1)
% 17.92/5.00 | (125) ~ incident(b2, a1c1) | ~ incident(a2, b1c1)
% 17.92/5.00 |
% 17.92/5.00 +-Applying beta-rule and splitting (125), into two cases.
% 17.92/5.00 |-Branch one:
% 17.92/5.00 | (126) ~ incident(b2, a1c1)
% 17.92/5.00 |
% 17.92/5.00 | Using (55) and (126) yields:
% 17.92/5.00 | (59) $false
% 17.92/5.00 |
% 17.92/5.00 |-The branch is then unsatisfiable
% 17.92/5.00 |-Branch two:
% 17.92/5.00 | (55) incident(b2, a1c1)
% 17.92/5.00 | (129) ~ incident(a2, b1c1)
% 17.92/5.00 |
% 17.92/5.00 | Using (56) and (129) yields:
% 17.92/5.00 | (59) $false
% 17.92/5.00 |
% 17.92/5.00 |-The branch is then unsatisfiable
% 17.92/5.00 |-Branch two:
% 17.92/5.00 | (129) ~ incident(a2, b1c1)
% 17.92/5.00 | (132) incident(c1, a2b2)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (5) with a1c1, a2b2, b2, c1 and discharging atoms incident(b2, a1c1), incident(b2, a2b2), incident(c1, a1c1), incident(c1, a2b2), yields:
% 17.92/5.00 | (133) point_equal(c1, b2) | line_equal(a2b2, a1c1)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (5) with a2b2, a1c1, b2, c1 and discharging atoms incident(b2, a1c1), incident(b2, a2b2), incident(c1, a1c1), incident(c1, a2b2), yields:
% 17.92/5.00 | (134) point_equal(c1, b2) | line_equal(a1c1, a2b2)
% 17.92/5.00 |
% 17.92/5.00 +-Applying beta-rule and splitting (43), into two cases.
% 17.92/5.00 |-Branch one:
% 17.92/5.00 | (135) ~ incident(c1, a2b2)
% 17.92/5.00 |
% 17.92/5.00 | Using (132) and (135) yields:
% 17.92/5.00 | (59) $false
% 17.92/5.00 |
% 17.92/5.00 |-The branch is then unsatisfiable
% 17.92/5.00 |-Branch two:
% 17.92/5.00 | (132) incident(c1, a2b2)
% 17.92/5.00 | (138) ~ incident(b1, a2c2) | ~ incident(a1, b2c2)
% 17.92/5.00 |
% 17.92/5.00 +-Applying beta-rule and splitting (134), into two cases.
% 17.92/5.00 |-Branch one:
% 17.92/5.00 | (139) point_equal(c1, b2)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (4) with b2c2, b2, c1 and discharging atoms point_equal(c1, b2), incident(b2, b2c2), yields:
% 17.92/5.00 | (140) incident(c1, b2c2)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (32) with b2, c1 and discharging atoms point_equal(c1, b2), yields:
% 17.92/5.00 | (141) point_equal(b2, c1)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (4) with b1c1, c1, b2 and discharging atoms point_equal(b2, c1), incident(c1, b1c1), yields:
% 17.92/5.00 | (142) incident(b2, b1c1)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (5) with b2c2, oc, c1, c2 and discharging atoms incident(c2, oc), incident(c2, b2c2), incident(c1, oc), incident(c1, b2c2), ~ point_equal(c2, c1), yields:
% 17.92/5.00 | (143) line_equal(oc, b2c2)
% 17.92/5.00 |
% 17.92/5.00 | Instantiating formula (5) with b2c2, b1c1, c1, bc and discharging atoms incident(c1, b1c1), incident(c1, b2c2), incident(bc, b1c1), incident(bc, b2c2), ~ line_equal(b1c1, b2c2), yields:
% 17.92/5.01 | (144) point_equal(bc, c1)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (4) with a1c1, c1, bc and discharging atoms point_equal(bc, c1), incident(c1, a1c1), yields:
% 17.92/5.01 | (145) incident(bc, a1c1)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (4) with a2b2, c1, bc and discharging atoms point_equal(bc, c1), incident(c1, a2b2), yields:
% 17.92/5.01 | (146) incident(bc, a2b2)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (5) with b1c1, ob, b1, b2 and discharging atoms incident(b2, ob), incident(b2, b1c1), incident(b1, ob), incident(b1, b1c1), ~ point_equal(b2, b1), yields:
% 17.92/5.01 | (147) line_equal(ob, b1c1)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (16) with b2c2, oc, o and discharging atoms incident(o, oc), line_equal(oc, b2c2), yields:
% 17.92/5.01 | (148) incident(o, b2c2)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (16) with b1c1, ob, o and discharging atoms incident(o, ob), line_equal(ob, b1c1), yields:
% 17.92/5.01 | (149) incident(o, b1c1)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (5) with b2c2, b1c1, bc, o and discharging atoms incident(o, b1c1), incident(o, b2c2), incident(bc, b1c1), incident(bc, b2c2), ~ line_equal(b1c1, b2c2), yields:
% 17.92/5.01 | (150) point_equal(o, bc)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (4) with a1c1, bc, o and discharging atoms point_equal(o, bc), incident(bc, a1c1), yields:
% 17.92/5.01 | (151) incident(o, a1c1)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (5) with oa, a1c1, o, a1 and discharging atoms incident(o, oa), incident(o, a1c1), incident(a1, oa), incident(a1, a1c1), yields:
% 17.92/5.01 | (152) point_equal(a1, o) | line_equal(a1c1, oa)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (5) with a1c1, oa, o, a1 and discharging atoms incident(o, oa), incident(o, a1c1), incident(a1, oa), incident(a1, a1c1), yields:
% 17.92/5.01 | (153) point_equal(a1, o) | line_equal(oa, a1c1)
% 17.92/5.01 |
% 17.92/5.01 +-Applying beta-rule and splitting (152), into two cases.
% 17.92/5.01 |-Branch one:
% 17.92/5.01 | (154) point_equal(a1, o)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (4) with b1c1, o, a1 and discharging atoms point_equal(a1, o), incident(o, b1c1), yields:
% 17.92/5.01 | (155) incident(a1, b1c1)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (39) with b1c1 and discharging atoms incident(c1, b1c1), incident(b1, b1c1), incident(a1, b1c1), yields:
% 17.92/5.01 | (59) $false
% 17.92/5.01 |
% 17.92/5.01 |-The branch is then unsatisfiable
% 17.92/5.01 |-Branch two:
% 17.92/5.01 | (157) ~ point_equal(a1, o)
% 17.92/5.01 | (158) line_equal(a1c1, oa)
% 17.92/5.01 |
% 17.92/5.01 +-Applying beta-rule and splitting (153), into two cases.
% 17.92/5.01 |-Branch one:
% 17.92/5.01 | (154) point_equal(a1, o)
% 17.92/5.01 |
% 17.92/5.01 | Using (154) and (157) yields:
% 17.92/5.01 | (59) $false
% 17.92/5.01 |
% 17.92/5.01 |-The branch is then unsatisfiable
% 17.92/5.01 |-Branch two:
% 17.92/5.01 | (157) ~ point_equal(a1, o)
% 17.92/5.01 | (162) line_equal(oa, a1c1)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (16) with a1c1, oa, a2 and discharging atoms incident(a2, oa), line_equal(oa, a1c1), yields:
% 17.92/5.01 | (163) incident(a2, a1c1)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (5) with a2c2, a1c1, a2, ac and discharging atoms incident(a2, a1c1), incident(a2, a2c2), incident(ac, a1c1), incident(ac, a2c2), ~ line_equal(a1c1, a2c2), yields:
% 17.92/5.01 | (164) point_equal(ac, a2)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (4) with a2b2, a2, ac and discharging atoms point_equal(ac, a2), incident(a2, a2b2), yields:
% 17.92/5.01 | (165) incident(ac, a2b2)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (14) with a2b2 and discharging atoms incident(ab, a2b2), incident(ac, a2b2), incident(bc, a2b2), line_equal(a2b2, a2b2), yields:
% 17.92/5.01 | (59) $false
% 17.92/5.01 |
% 17.92/5.01 |-The branch is then unsatisfiable
% 17.92/5.01 |-Branch two:
% 17.92/5.01 | (167) ~ point_equal(c1, b2)
% 17.92/5.01 | (168) line_equal(a1c1, a2b2)
% 17.92/5.01 |
% 17.92/5.01 +-Applying beta-rule and splitting (133), into two cases.
% 17.92/5.01 |-Branch one:
% 17.92/5.01 | (139) point_equal(c1, b2)
% 17.92/5.01 |
% 17.92/5.01 | Using (139) and (167) yields:
% 17.92/5.01 | (59) $false
% 17.92/5.01 |
% 17.92/5.01 |-The branch is then unsatisfiable
% 17.92/5.01 |-Branch two:
% 17.92/5.01 | (167) ~ point_equal(c1, b2)
% 17.92/5.01 | (172) line_equal(a2b2, a1c1)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (16) with a2b2, a1c1, a1 and discharging atoms incident(a1, a1c1), line_equal(a1c1, a2b2), yields:
% 17.92/5.01 | (173) incident(a1, a2b2)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (16) with a1c1, a2b2, a2 and discharging atoms incident(a2, a2b2), line_equal(a2b2, a1c1), yields:
% 17.92/5.01 | (163) incident(a2, a1c1)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (5) with a1c1, oa, a1, a2 and discharging atoms incident(a2, oa), incident(a2, a1c1), incident(a1, oa), incident(a1, a1c1), ~ point_equal(a2, a1), yields:
% 17.92/5.01 | (162) line_equal(oa, a1c1)
% 17.92/5.01 |
% 17.92/5.01 | Instantiating formula (5) with a2b2, oa, a1, a2 and discharging atoms incident(a2, oa), incident(a2, a2b2), incident(a1, oa), incident(a1, a2b2), ~ point_equal(a2, a1), yields:
% 17.92/5.02 | (176) line_equal(oa, a2b2)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (16) with a1c1, oa, o and discharging atoms incident(o, oa), line_equal(oa, a1c1), yields:
% 17.92/5.02 | (151) incident(o, a1c1)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (16) with a2b2, oa, o and discharging atoms incident(o, oa), line_equal(oa, a2b2), yields:
% 17.92/5.02 | (74) incident(o, a2b2)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (5) with a1c1, oc, o, c1 and discharging atoms incident(o, oc), incident(o, a1c1), incident(c1, oc), incident(c1, a1c1), yields:
% 17.92/5.02 | (179) point_equal(c1, o) | line_equal(oc, a1c1)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (5) with oc, a2b2, o, c1 and discharging atoms incident(o, oc), incident(o, a2b2), incident(c1, oc), incident(c1, a2b2), yields:
% 17.92/5.02 | (180) point_equal(c1, o) | line_equal(a2b2, oc)
% 17.92/5.02 |
% 17.92/5.02 +-Applying beta-rule and splitting (179), into two cases.
% 17.92/5.02 |-Branch one:
% 17.92/5.02 | (181) point_equal(c1, o)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (4) with ob, o, c1 and discharging atoms point_equal(c1, o), incident(o, ob), yields:
% 17.92/5.02 | (182) incident(c1, ob)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (5) with ob, a2b2, b2, c1 and discharging atoms incident(b2, ob), incident(b2, a2b2), incident(c1, ob), incident(c1, a2b2), ~ point_equal(c1, b2), yields:
% 17.92/5.02 | (183) line_equal(a2b2, ob)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (16) with ob, a2b2, a1 and discharging atoms incident(a1, a2b2), line_equal(a2b2, ob), yields:
% 17.92/5.02 | (184) incident(a1, ob)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (39) with ob and discharging atoms incident(c1, ob), incident(b1, ob), incident(a1, ob), yields:
% 17.92/5.02 | (59) $false
% 17.92/5.02 |
% 17.92/5.02 |-The branch is then unsatisfiable
% 17.92/5.02 |-Branch two:
% 17.92/5.02 | (186) ~ point_equal(c1, o)
% 17.92/5.02 | (187) line_equal(oc, a1c1)
% 17.92/5.02 |
% 17.92/5.02 +-Applying beta-rule and splitting (180), into two cases.
% 17.92/5.02 |-Branch one:
% 17.92/5.02 | (181) point_equal(c1, o)
% 17.92/5.02 |
% 17.92/5.02 | Using (181) and (186) yields:
% 17.92/5.02 | (59) $false
% 17.92/5.02 |
% 17.92/5.02 |-The branch is then unsatisfiable
% 17.92/5.02 |-Branch two:
% 17.92/5.02 | (186) ~ point_equal(c1, o)
% 17.92/5.02 | (191) line_equal(a2b2, oc)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (16) with oc, a2b2, b2 and discharging atoms incident(b2, a2b2), line_equal(a2b2, oc), yields:
% 17.92/5.02 | (192) incident(b2, oc)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (16) with oc, a2b2, a2 and discharging atoms incident(a2, a2b2), line_equal(a2b2, oc), yields:
% 17.92/5.02 | (193) incident(a2, oc)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (46) with oc and discharging atoms incident(c2, oc), incident(b2, oc), incident(a2, oc), yields:
% 17.92/5.02 | (59) $false
% 17.92/5.02 |
% 17.92/5.02 |-The branch is then unsatisfiable
% 17.92/5.02 |-Branch two:
% 17.92/5.02 | (126) ~ incident(b2, a1c1)
% 17.92/5.02 | (196) incident(a1, b2c2)
% 17.92/5.02 |
% 17.92/5.02 +-Applying beta-rule and splitting (17), into two cases.
% 17.92/5.02 |-Branch one:
% 17.92/5.02 | (58) incident(c2, a1b1)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (5) with a1b1, b2c2, c2, a1 and discharging atoms incident(c2, a1b1), incident(c2, b2c2), incident(a1, a1b1), incident(a1, b2c2), yields:
% 17.92/5.02 | (198) point_equal(a1, c2) | line_equal(b2c2, a1b1)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (5) with b2c2, a1b1, c2, a1 and discharging atoms incident(c2, a1b1), incident(c2, b2c2), incident(a1, a1b1), incident(a1, b2c2), yields:
% 17.92/5.02 | (199) point_equal(a1, c2) | line_equal(a1b1, b2c2)
% 17.92/5.02 |
% 17.92/5.02 +-Applying beta-rule and splitting (198), into two cases.
% 17.92/5.02 |-Branch one:
% 17.92/5.02 | (200) point_equal(a1, c2)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (4) with a2c2, c2, a1 and discharging atoms point_equal(a1, c2), incident(c2, a2c2), yields:
% 17.92/5.02 | (105) incident(a1, a2c2)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (32) with c2, a1 and discharging atoms point_equal(a1, c2), yields:
% 17.92/5.02 | (202) point_equal(c2, a1)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (4) with a1c1, a1, c2 and discharging atoms point_equal(c2, a1), incident(a1, a1c1), yields:
% 17.92/5.02 | (203) incident(c2, a1c1)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (5) with a2c2, oa, a1, a2 and discharging atoms incident(a2, oa), incident(a2, a2c2), incident(a1, oa), incident(a1, a2c2), ~ point_equal(a2, a1), yields:
% 17.92/5.02 | (104) line_equal(oa, a2c2)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (5) with a2c2, a1c1, a1, ac and discharging atoms incident(a1, a1c1), incident(a1, a2c2), incident(ac, a1c1), incident(ac, a2c2), ~ line_equal(a1c1, a2c2), yields:
% 17.92/5.02 | (205) point_equal(ac, a1)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (4) with a1b1, a1, ac and discharging atoms point_equal(ac, a1), incident(a1, a1b1), yields:
% 17.92/5.02 | (206) incident(ac, a1b1)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (4) with b2c2, a1, ac and discharging atoms point_equal(ac, a1), incident(a1, b2c2), yields:
% 17.92/5.02 | (207) incident(ac, b2c2)
% 17.92/5.02 |
% 17.92/5.02 | Instantiating formula (5) with a1c1, oc, c1, c2 and discharging atoms incident(c2, oc), incident(c2, a1c1), incident(c1, oc), incident(c1, a1c1), ~ point_equal(c2, c1), yields:
% 17.92/5.03 | (187) line_equal(oc, a1c1)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (16) with a2c2, oa, o and discharging atoms incident(o, oa), line_equal(oa, a2c2), yields:
% 17.92/5.03 | (95) incident(o, a2c2)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (16) with a1c1, oc, o and discharging atoms incident(o, oc), line_equal(oc, a1c1), yields:
% 17.92/5.03 | (151) incident(o, a1c1)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (5) with a2c2, a1c1, o, ac and discharging atoms incident(o, a1c1), incident(o, a2c2), incident(ac, a1c1), incident(ac, a2c2), ~ line_equal(a1c1, a2c2), yields:
% 17.92/5.03 | (211) point_equal(ac, o)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (4) with ob, o, ac and discharging atoms point_equal(ac, o), incident(o, ob), yields:
% 17.92/5.03 | (212) incident(ac, ob)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (5) with b2c2, ob, ac, b2 and discharging atoms incident(b2, ob), incident(b2, b2c2), incident(ac, ob), incident(ac, b2c2), yields:
% 17.92/5.03 | (213) point_equal(b2, ac) | line_equal(ob, b2c2)
% 17.92/5.03 |
% 17.92/5.03 +-Applying beta-rule and splitting (213), into two cases.
% 17.92/5.03 |-Branch one:
% 17.92/5.03 | (214) point_equal(b2, ac)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (4) with a1c1, ac, b2 and discharging atoms point_equal(b2, ac), incident(ac, a1c1), ~ incident(b2, a1c1), yields:
% 17.92/5.03 | (59) $false
% 17.92/5.03 |
% 17.92/5.03 |-The branch is then unsatisfiable
% 17.92/5.03 |-Branch two:
% 17.92/5.03 | (216) ~ point_equal(b2, ac)
% 17.92/5.03 | (217) line_equal(ob, b2c2)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (16) with b2c2, ob, b1 and discharging atoms incident(b1, ob), line_equal(ob, b2c2), yields:
% 17.92/5.03 | (218) incident(b1, b2c2)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (5) with b2c2, b1c1, b1, bc and discharging atoms incident(b1, b1c1), incident(b1, b2c2), incident(bc, b1c1), incident(bc, b2c2), ~ line_equal(b1c1, b2c2), yields:
% 17.92/5.03 | (219) point_equal(bc, b1)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (4) with a1b1, b1, bc and discharging atoms point_equal(bc, b1), incident(b1, a1b1), yields:
% 17.92/5.03 | (220) incident(bc, a1b1)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (14) with a1b1 and discharging atoms incident(ab, a1b1), incident(ac, a1b1), incident(bc, a1b1), line_equal(a1b1, a1b1), yields:
% 17.92/5.03 | (59) $false
% 17.92/5.03 |
% 17.92/5.03 |-The branch is then unsatisfiable
% 17.92/5.03 |-Branch two:
% 17.92/5.03 | (222) ~ point_equal(a1, c2)
% 17.92/5.03 | (223) line_equal(b2c2, a1b1)
% 17.92/5.03 |
% 17.92/5.03 +-Applying beta-rule and splitting (199), into two cases.
% 17.92/5.03 |-Branch one:
% 17.92/5.03 | (200) point_equal(a1, c2)
% 17.92/5.03 |
% 17.92/5.03 | Using (200) and (222) yields:
% 17.92/5.03 | (59) $false
% 17.92/5.03 |
% 17.92/5.03 |-The branch is then unsatisfiable
% 17.92/5.03 |-Branch two:
% 17.92/5.03 | (222) ~ point_equal(a1, c2)
% 17.92/5.03 | (227) line_equal(a1b1, b2c2)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (16) with b2c2, a1b1, b1 and discharging atoms incident(b1, a1b1), line_equal(a1b1, b2c2), yields:
% 17.92/5.03 | (218) incident(b1, b2c2)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (5) with ob, b2c2, b1, b2 and discharging atoms incident(b2, ob), incident(b2, b2c2), incident(b1, ob), incident(b1, b2c2), ~ point_equal(b2, b1), yields:
% 17.92/5.03 | (229) line_equal(b2c2, ob)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (5) with b2c2, ob, b1, b2 and discharging atoms incident(b2, ob), incident(b2, b2c2), incident(b1, ob), incident(b1, b2c2), ~ point_equal(b2, b1), yields:
% 17.92/5.03 | (217) line_equal(ob, b2c2)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (16) with b2c2, ob, o and discharging atoms incident(o, ob), line_equal(ob, b2c2), yields:
% 17.92/5.03 | (148) incident(o, b2c2)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (16) with ob, b2c2, a1 and discharging atoms incident(a1, b2c2), line_equal(b2c2, ob), yields:
% 17.92/5.03 | (184) incident(a1, ob)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (5) with b2c2, oa, a1, o and discharging atoms incident(o, oa), incident(o, b2c2), incident(a1, oa), incident(a1, b2c2), yields:
% 17.92/5.03 | (233) point_equal(o, a1) | line_equal(oa, b2c2)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (5) with ob, oa, a1, o and discharging atoms incident(o, ob), incident(o, oa), incident(a1, ob), incident(a1, oa), yields:
% 17.92/5.03 | (234) point_equal(o, a1) | line_equal(oa, ob)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (5) with oa, ob, a1, o and discharging atoms incident(o, ob), incident(o, oa), incident(a1, ob), incident(a1, oa), yields:
% 17.92/5.03 | (235) point_equal(o, a1) | line_equal(ob, oa)
% 17.92/5.03 |
% 17.92/5.03 +-Applying beta-rule and splitting (235), into two cases.
% 17.92/5.03 |-Branch one:
% 17.92/5.03 | (236) point_equal(o, a1)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (32) with a1, o and discharging atoms point_equal(o, a1), yields:
% 17.92/5.03 | (154) point_equal(a1, o)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (4) with oc, o, a1 and discharging atoms point_equal(a1, o), incident(o, oc), yields:
% 17.92/5.03 | (238) incident(a1, oc)
% 17.92/5.03 |
% 17.92/5.03 | Instantiating formula (5) with oc, b2c2, c2, a1 and discharging atoms incident(c2, oc), incident(c2, b2c2), incident(a1, oc), incident(a1, b2c2), ~ point_equal(a1, c2), yields:
% 17.92/5.03 | (239) line_equal(b2c2, oc)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (16) with oc, b2c2, b1 and discharging atoms incident(b1, b2c2), line_equal(b2c2, oc), yields:
% 17.92/5.04 | (96) incident(b1, oc)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (39) with oc and discharging atoms incident(c1, oc), incident(b1, oc), incident(a1, oc), yields:
% 17.92/5.04 | (59) $false
% 17.92/5.04 |
% 17.92/5.04 |-The branch is then unsatisfiable
% 17.92/5.04 |-Branch two:
% 17.92/5.04 | (242) ~ point_equal(o, a1)
% 17.92/5.04 | (243) line_equal(ob, oa)
% 17.92/5.04 |
% 17.92/5.04 +-Applying beta-rule and splitting (234), into two cases.
% 17.92/5.04 |-Branch one:
% 17.92/5.04 | (236) point_equal(o, a1)
% 17.92/5.04 |
% 17.92/5.04 | Using (236) and (242) yields:
% 17.92/5.04 | (59) $false
% 17.92/5.04 |
% 17.92/5.04 |-The branch is then unsatisfiable
% 17.92/5.04 |-Branch two:
% 17.92/5.04 | (242) ~ point_equal(o, a1)
% 17.92/5.04 | (247) line_equal(oa, ob)
% 17.92/5.04 |
% 17.92/5.04 +-Applying beta-rule and splitting (233), into two cases.
% 17.92/5.04 |-Branch one:
% 17.92/5.04 | (236) point_equal(o, a1)
% 17.92/5.04 |
% 17.92/5.04 | Using (236) and (242) yields:
% 17.92/5.04 | (59) $false
% 17.92/5.04 |
% 17.92/5.04 |-The branch is then unsatisfiable
% 17.92/5.04 |-Branch two:
% 17.92/5.04 | (242) ~ point_equal(o, a1)
% 17.92/5.04 | (251) line_equal(oa, b2c2)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (16) with b2c2, oa, a2 and discharging atoms incident(a2, oa), line_equal(oa, b2c2), yields:
% 17.92/5.04 | (252) incident(a2, b2c2)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (46) with b2c2 and discharging atoms incident(c2, b2c2), incident(b2, b2c2), incident(a2, b2c2), yields:
% 17.92/5.04 | (59) $false
% 17.92/5.04 |
% 17.92/5.04 |-The branch is then unsatisfiable
% 17.92/5.04 |-Branch two:
% 17.92/5.04 | (57) ~ incident(c2, a1b1)
% 17.92/5.04 | (61) incident(b1, a2c2)
% 17.92/5.04 |
% 17.92/5.04 +-Applying beta-rule and splitting (43), into two cases.
% 17.92/5.04 |-Branch one:
% 17.92/5.04 | (135) ~ incident(c1, a2b2)
% 17.92/5.04 |
% 17.92/5.04 +-Applying beta-rule and splitting (12), into two cases.
% 17.92/5.04 |-Branch one:
% 17.92/5.04 | (56) incident(a2, b1c1)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (5) with a2c2, b1c1, a2, b1 and discharging atoms incident(a2, b1c1), incident(a2, a2c2), incident(b1, b1c1), incident(b1, a2c2), yields:
% 17.92/5.04 | (258) point_equal(b1, a2) | line_equal(b1c1, a2c2)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (5) with b1c1, a2c2, a2, b1 and discharging atoms incident(a2, b1c1), incident(a2, a2c2), incident(b1, b1c1), incident(b1, a2c2), yields:
% 17.92/5.04 | (259) point_equal(b1, a2) | line_equal(a2c2, b1c1)
% 17.92/5.04 |
% 17.92/5.04 +-Applying beta-rule and splitting (259), into two cases.
% 17.92/5.04 |-Branch one:
% 17.92/5.04 | (66) point_equal(b1, a2)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (4) with a2b2, a2, b1 and discharging atoms point_equal(b1, a2), incident(a2, a2b2), yields:
% 17.92/5.04 | (67) incident(b1, a2b2)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (32) with a2, b1 and discharging atoms point_equal(b1, a2), yields:
% 17.92/5.04 | (64) point_equal(a2, b1)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (4) with a1b1, b1, a2 and discharging atoms point_equal(a2, b1), incident(b1, a1b1), yields:
% 17.92/5.04 | (65) incident(a2, a1b1)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (5) with a2b2, ob, b1, b2 and discharging atoms incident(b2, ob), incident(b2, a2b2), incident(b1, ob), incident(b1, a2b2), ~ point_equal(b2, b1), yields:
% 17.92/5.04 | (72) line_equal(ob, a2b2)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (5) with a2b2, a1b1, b1, ab and discharging atoms incident(b1, a1b1), incident(b1, a2b2), incident(ab, a1b1), incident(ab, a2b2), ~ line_equal(a1b1, a2b2), yields:
% 17.92/5.04 | (265) point_equal(ab, b1)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (4) with b1c1, b1, ab and discharging atoms point_equal(ab, b1), incident(b1, b1c1), yields:
% 17.92/5.04 | (70) incident(ab, b1c1)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (4) with a2c2, b1, ab and discharging atoms point_equal(ab, b1), incident(b1, a2c2), yields:
% 17.92/5.04 | (71) incident(ab, a2c2)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (5) with a1b1, oa, a1, a2 and discharging atoms incident(a2, oa), incident(a2, a1b1), incident(a1, oa), incident(a1, a1b1), ~ point_equal(a2, a1), yields:
% 17.92/5.04 | (69) line_equal(oa, a1b1)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (16) with a2b2, ob, o and discharging atoms incident(o, ob), line_equal(ob, a2b2), yields:
% 17.92/5.04 | (74) incident(o, a2b2)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (16) with a1b1, oa, o and discharging atoms incident(o, oa), line_equal(oa, a1b1), yields:
% 17.92/5.04 | (73) incident(o, a1b1)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (5) with a2b2, a1b1, o, ab and discharging atoms incident(o, a1b1), incident(o, a2b2), incident(ab, a1b1), incident(ab, a2b2), ~ line_equal(a1b1, a2b2), yields:
% 17.92/5.04 | (75) point_equal(ab, o)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (4) with oc, o, ab and discharging atoms point_equal(ab, o), incident(o, oc), yields:
% 17.92/5.04 | (76) incident(ab, oc)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (5) with a2c2, oc, ab, c2 and discharging atoms incident(c2, oc), incident(c2, a2c2), incident(ab, oc), incident(ab, a2c2), yields:
% 17.92/5.04 | (77) point_equal(c2, ab) | line_equal(oc, a2c2)
% 17.92/5.04 |
% 17.92/5.04 +-Applying beta-rule and splitting (77), into two cases.
% 17.92/5.04 |-Branch one:
% 17.92/5.04 | (78) point_equal(c2, ab)
% 17.92/5.04 |
% 17.92/5.04 | Instantiating formula (4) with a1b1, ab, c2 and discharging atoms point_equal(c2, ab), incident(ab, a1b1), ~ incident(c2, a1b1), yields:
% 17.92/5.04 | (59) $false
% 17.92/5.05 |
% 17.92/5.05 |-The branch is then unsatisfiable
% 17.92/5.05 |-Branch two:
% 17.92/5.05 | (80) ~ point_equal(c2, ab)
% 17.92/5.05 | (81) line_equal(oc, a2c2)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (16) with a2c2, oc, c1 and discharging atoms incident(c1, oc), line_equal(oc, a2c2), yields:
% 17.92/5.05 | (82) incident(c1, a2c2)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (5) with a2c2, a1c1, c1, ac and discharging atoms incident(c1, a1c1), incident(c1, a2c2), incident(ac, a1c1), incident(ac, a2c2), ~ line_equal(a1c1, a2c2), yields:
% 17.92/5.05 | (83) point_equal(ac, c1)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (4) with b1c1, c1, ac and discharging atoms point_equal(ac, c1), incident(c1, b1c1), yields:
% 17.92/5.05 | (84) incident(ac, b1c1)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (14) with b1c1 and discharging atoms incident(ab, b1c1), incident(ac, b1c1), incident(bc, b1c1), line_equal(b1c1, b1c1), yields:
% 17.92/5.05 | (59) $false
% 17.92/5.05 |
% 17.92/5.05 |-The branch is then unsatisfiable
% 17.92/5.05 |-Branch two:
% 17.92/5.05 | (282) ~ point_equal(b1, a2)
% 17.92/5.05 | (91) line_equal(a2c2, b1c1)
% 17.92/5.05 |
% 17.92/5.05 +-Applying beta-rule and splitting (258), into two cases.
% 17.92/5.05 |-Branch one:
% 17.92/5.05 | (66) point_equal(b1, a2)
% 17.92/5.05 |
% 17.92/5.05 | Using (66) and (282) yields:
% 17.92/5.05 | (59) $false
% 17.92/5.05 |
% 17.92/5.05 |-The branch is then unsatisfiable
% 17.92/5.05 |-Branch two:
% 17.92/5.05 | (282) ~ point_equal(b1, a2)
% 17.92/5.05 | (87) line_equal(b1c1, a2c2)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (16) with a2c2, b1c1, c1 and discharging atoms incident(c1, b1c1), line_equal(b1c1, a2c2), yields:
% 17.92/5.05 | (82) incident(c1, a2c2)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (5) with oc, a2c2, c1, c2 and discharging atoms incident(c2, oc), incident(c2, a2c2), incident(c1, oc), incident(c1, a2c2), ~ point_equal(c2, c1), yields:
% 17.92/5.05 | (93) line_equal(a2c2, oc)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (5) with a2c2, oc, c1, c2 and discharging atoms incident(c2, oc), incident(c2, a2c2), incident(c1, oc), incident(c1, a2c2), ~ point_equal(c2, c1), yields:
% 17.92/5.05 | (81) line_equal(oc, a2c2)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (16) with a2c2, oc, o and discharging atoms incident(o, oc), line_equal(oc, a2c2), yields:
% 17.92/5.05 | (95) incident(o, a2c2)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (16) with oc, a2c2, b1 and discharging atoms incident(b1, a2c2), line_equal(a2c2, oc), yields:
% 17.92/5.05 | (96) incident(b1, oc)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (5) with ob, a2c2, b1, o and discharging atoms incident(o, ob), incident(o, a2c2), incident(b1, ob), incident(b1, a2c2), yields:
% 17.92/5.05 | (97) point_equal(o, b1) | line_equal(a2c2, ob)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (5) with a2c2, ob, b1, o and discharging atoms incident(o, ob), incident(o, a2c2), incident(b1, ob), incident(b1, a2c2), yields:
% 17.92/5.05 | (98) point_equal(o, b1) | line_equal(ob, a2c2)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (5) with oc, ob, b1, o and discharging atoms incident(o, oc), incident(o, ob), incident(b1, oc), incident(b1, ob), yields:
% 17.92/5.05 | (99) point_equal(o, b1) | line_equal(ob, oc)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (5) with ob, oc, b1, o and discharging atoms incident(o, oc), incident(o, ob), incident(b1, oc), incident(b1, ob), yields:
% 17.92/5.05 | (100) point_equal(o, b1) | line_equal(oc, ob)
% 17.92/5.05 |
% 17.92/5.05 +-Applying beta-rule and splitting (100), into two cases.
% 17.92/5.05 |-Branch one:
% 17.92/5.05 | (101) point_equal(o, b1)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (32) with b1, o and discharging atoms point_equal(o, b1), yields:
% 17.92/5.05 | (102) point_equal(b1, o)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (4) with oa, o, b1 and discharging atoms point_equal(b1, o), incident(o, oa), yields:
% 17.92/5.05 | (103) incident(b1, oa)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (5) with a2c2, oa, a2, b1 and discharging atoms incident(a2, oa), incident(a2, a2c2), incident(b1, oa), incident(b1, a2c2), ~ point_equal(b1, a2), yields:
% 17.92/5.05 | (104) line_equal(oa, a2c2)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (16) with a2c2, oa, a1 and discharging atoms incident(a1, oa), line_equal(oa, a2c2), yields:
% 17.92/5.05 | (105) incident(a1, a2c2)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (39) with a2c2 and discharging atoms incident(c1, a2c2), incident(b1, a2c2), incident(a1, a2c2), yields:
% 17.92/5.05 | (59) $false
% 17.92/5.05 |
% 17.92/5.05 |-The branch is then unsatisfiable
% 17.92/5.05 |-Branch two:
% 17.92/5.05 | (107) ~ point_equal(o, b1)
% 17.92/5.05 | (108) line_equal(oc, ob)
% 17.92/5.05 |
% 17.92/5.05 +-Applying beta-rule and splitting (99), into two cases.
% 17.92/5.05 |-Branch one:
% 17.92/5.05 | (101) point_equal(o, b1)
% 17.92/5.05 |
% 17.92/5.05 | Using (101) and (107) yields:
% 17.92/5.05 | (59) $false
% 17.92/5.05 |
% 17.92/5.05 |-The branch is then unsatisfiable
% 17.92/5.05 |-Branch two:
% 17.92/5.05 | (107) ~ point_equal(o, b1)
% 17.92/5.05 | (112) line_equal(ob, oc)
% 17.92/5.05 |
% 17.92/5.05 +-Applying beta-rule and splitting (98), into two cases.
% 17.92/5.05 |-Branch one:
% 17.92/5.05 | (101) point_equal(o, b1)
% 17.92/5.05 |
% 17.92/5.05 | Using (101) and (107) yields:
% 17.92/5.05 | (59) $false
% 17.92/5.05 |
% 17.92/5.05 |-The branch is then unsatisfiable
% 17.92/5.05 |-Branch two:
% 17.92/5.05 | (107) ~ point_equal(o, b1)
% 17.92/5.05 | (116) line_equal(ob, a2c2)
% 17.92/5.05 |
% 17.92/5.05 +-Applying beta-rule and splitting (97), into two cases.
% 17.92/5.05 |-Branch one:
% 17.92/5.05 | (101) point_equal(o, b1)
% 17.92/5.05 |
% 17.92/5.05 | Using (101) and (107) yields:
% 17.92/5.05 | (59) $false
% 17.92/5.05 |
% 17.92/5.05 |-The branch is then unsatisfiable
% 17.92/5.05 |-Branch two:
% 17.92/5.05 | (107) ~ point_equal(o, b1)
% 17.92/5.05 | (120) line_equal(a2c2, ob)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (16) with ob, a2c2, c2 and discharging atoms incident(c2, a2c2), line_equal(a2c2, ob), yields:
% 17.92/5.05 | (121) incident(c2, ob)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (16) with ob, a2c2, a2 and discharging atoms incident(a2, a2c2), line_equal(a2c2, ob), yields:
% 17.92/5.05 | (122) incident(a2, ob)
% 17.92/5.05 |
% 17.92/5.05 | Instantiating formula (46) with ob and discharging atoms incident(c2, ob), incident(b2, ob), incident(a2, ob), yields:
% 17.92/5.06 | (59) $false
% 17.92/5.06 |
% 17.92/5.06 |-The branch is then unsatisfiable
% 17.92/5.06 |-Branch two:
% 17.92/5.06 | (129) ~ incident(a2, b1c1)
% 17.92/5.06 | (132) incident(c1, a2b2)
% 17.92/5.06 |
% 17.92/5.06 | Using (132) and (135) yields:
% 17.92/5.06 | (59) $false
% 17.92/5.06 |
% 17.92/5.06 |-The branch is then unsatisfiable
% 17.92/5.06 |-Branch two:
% 17.92/5.06 | (132) incident(c1, a2b2)
% 17.92/5.06 | (138) ~ incident(b1, a2c2) | ~ incident(a1, b2c2)
% 17.92/5.06 |
% 17.92/5.06 +-Applying beta-rule and splitting (138), into two cases.
% 17.92/5.06 |-Branch one:
% 17.92/5.06 | (325) ~ incident(b1, a2c2)
% 17.92/5.06 |
% 17.92/5.06 | Using (61) and (325) yields:
% 17.92/5.06 | (59) $false
% 17.92/5.06 |
% 17.92/5.06 |-The branch is then unsatisfiable
% 17.92/5.06 |-Branch two:
% 17.92/5.06 | (61) incident(b1, a2c2)
% 17.92/5.06 | (328) ~ incident(a1, b2c2)
% 17.92/5.06 |
% 17.92/5.06 | Using (196) and (328) yields:
% 17.92/5.06 | (59) $false
% 17.92/5.06 |
% 17.92/5.06 |-The branch is then unsatisfiable
% 17.92/5.06 % SZS output end Proof for theBenchmark
% 17.92/5.06
% 17.92/5.06 4481ms
%------------------------------------------------------------------------------