TSTP Solution File: GEO085+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO085+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 03:47:30 EDT 2022
% Result : Theorem 2.63s 1.32s
% Output : Proof 3.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO085+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 10:01:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/0.96 Prover 0: Preprocessing ...
% 2.26/1.16 Prover 0: Warning: ignoring some quantifiers
% 2.33/1.18 Prover 0: Constructing countermodel ...
% 2.63/1.32 Prover 0: proved (682ms)
% 2.63/1.32
% 2.63/1.32 No countermodel exists, formula is valid
% 2.63/1.32 % SZS status Theorem for theBenchmark
% 2.63/1.32
% 2.63/1.32 Generating proof ... Warning: ignoring some quantifiers
% 3.74/1.55 found it (size 10)
% 3.74/1.55
% 3.74/1.55 % SZS output start Proof for theBenchmark
% 3.74/1.56 Assumed formulas after preprocessing and simplification:
% 3.83/1.56 | (0) ? [v0] : (open(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sum(v2, v3) = v1) | ~ closed(v1) | ~ meet(v4, v2, v3) | ~ end_point(v5, v2) | meet(v5, v2, v3)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ end_point(v5, v4) | ~ end_point(v5, v3) | ~ end_point(v5, v2) | ~ part_of(v4, v1) | ~ part_of(v3, v1) | ~ part_of(v2, v1) | part_of(v4, v3) | part_of(v4, v2) | part_of(v3, v4) | part_of(v3, v2) | part_of(v2, v4) | part_of(v2, v3)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | v4 = v2 | v3 = v2 | ~ end_point(v4, v1) | ~ end_point(v3, v1) | ~ end_point(v2, v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sum(v4, v3) = v2) | ~ (sum(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v2, v3) = v1) | ~ incident_c(v4, v3) | incident_c(v4, v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v2, v3) = v1) | ~ incident_c(v4, v2) | incident_c(v4, v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v2, v3) = v1) | ~ incident_c(v4, v1) | incident_c(v4, v3) | incident_c(v4, v2)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ meet(v1, v2, v3) | ~ incident_c(v4, v3) | ~ incident_c(v4, v2) | end_point(v4, v3)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ meet(v1, v2, v3) | ~ incident_c(v4, v3) | ~ incident_c(v4, v2) | end_point(v4, v2)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ end_point(v1, v2) | ~ incident_c(v1, v4) | ~ incident_c(v1, v3) | ~ part_of(v4, v2) | ~ part_of(v3, v2) | part_of(v4, v3) | part_of(v3, v4)) & ? [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | ~ (sum(v2, v3) = v4) | ? [v5] : (( ~ incident_c(v5, v1) | ( ~ incident_c(v5, v3) & ~ incident_c(v5, v2))) & (incident_c(v5, v3) | incident_c(v5, v2) | incident_c(v5, v1)))) & ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v1, v2, v3) | incident_c(v1, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v1, v2, v3) | incident_c(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : ( ~ incident_c(v3, v2) | ~ part_of(v2, v1) | incident_c(v3, v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ incident_c(v1, v3) | ~ incident_c(v1, v2) | meet(v1, v2, v3) | ? [v4] : (incident_c(v4, v3) & incident_c(v4, v2) & ( ~ end_point(v4, v3) | ~ end_point(v4, v2)))) & ! [v1] : ! [v2] : (v2 = v1 | ~ end_point(v2, v0) | ~ end_point(v1, v0)) & ! [v1] : ! [v2] : (v2 = v1 | ~ part_of(v2, v1) | open(v2)) & ! [v1] : ! [v2] : ( ~ closed(v1) | ~ end_point(v2, v1)) & ! [v1] : ! [v2] : ( ~ inner_point(v2, v1) | ? [v3] : ? [v4] : (sum(v3, v4) = v1 & meet(v2, v3, v4))) & ! [v1] : ! [v2] : ( ~ inner_point(v1, v2) | ~ end_point(v1, v2)) & ! [v1] : ! [v2] : ( ~ inner_point(v1, v2) | incident_c(v1, v2)) & ! [v1] : ! [v2] : ( ~ end_point(v2, v1) | open(v1)) & ! [v1] : ! [v2] : ( ~ end_point(v2, v1) | ? [v3] : ( ~ (v3 = v2) & end_point(v3, v1))) & ! [v1] : ! [v2] : ( ~ end_point(v1, v2) | incident_c(v1, v2)) & ! [v1] : ! [v2] : ( ~ incident_c(v1, v2) | inner_point(v1, v2) | end_point(v1, v2)) & ! [v1] : ! [v2] : ( ~ incident_c(v1, v2) | end_point(v1, v2) | ? [v3] : ? [v4] : (incident_c(v1, v4) & incident_c(v1, v3) & part_of(v4, v2) & part_of(v3, v2) & ~ part_of(v4, v3) & ~ part_of(v3, v4))) & ! [v1] : ( ~ open(v1) | ? [v2] : end_point(v2, v1)) & ? [v1] : ? [v2] : (v2 = v1 | ? [v3] : (( ~ incident_c(v3, v2) | ~ incident_c(v3, v1)) & (incident_c(v3, v2) | incident_c(v3, v1)))) & ? [v1] : ? [v2] : inner_point(v2, v1) & ? [v1] : ? [v2] : (part_of(v2, v1) | ? [v3] : (incident_c(v3, v2) & ~ incident_c(v3, v1))) & ? [v1] : (closed(v1) | ? [v2] : end_point(v2, v1)))
% 3.83/1.60 | Instantiating (0) with all_0_0_0 yields:
% 3.83/1.60 | (1) open(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v1, v2) = v0) | ~ closed(v0) | ~ meet(v3, v1, v2) | ~ end_point(v4, v1) | meet(v4, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ end_point(v4, v3) | ~ end_point(v4, v2) | ~ end_point(v4, v1) | ~ part_of(v3, v0) | ~ part_of(v2, v0) | ~ part_of(v1, v0) | part_of(v3, v2) | part_of(v3, v1) | part_of(v2, v3) | part_of(v2, v1) | part_of(v1, v3) | part_of(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ end_point(v3, v0) | ~ end_point(v2, v0) | ~ end_point(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v2) | incident_c(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v1) | incident_c(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v0) | incident_c(v3, v2) | incident_c(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ end_point(v0, v1) | ~ incident_c(v0, v3) | ~ incident_c(v0, v2) | ~ part_of(v3, v1) | ~ part_of(v2, v1) | part_of(v3, v2) | part_of(v2, v3)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (sum(v1, v2) = v3) | ? [v4] : (( ~ incident_c(v4, v0) | ( ~ incident_c(v4, v2) & ~ incident_c(v4, v1))) & (incident_c(v4, v2) | incident_c(v4, v1) | incident_c(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ incident_c(v2, v1) | ~ part_of(v1, v0) | incident_c(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ incident_c(v0, v2) | ~ incident_c(v0, v1) | meet(v0, v1, v2) | ? [v3] : (incident_c(v3, v2) & incident_c(v3, v1) & ( ~ end_point(v3, v2) | ~ end_point(v3, v1)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ end_point(v1, all_0_0_0) | ~ end_point(v0, all_0_0_0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ part_of(v1, v0) | open(v1)) & ! [v0] : ! [v1] : ( ~ closed(v0) | ~ end_point(v1, v0)) & ! [v0] : ! [v1] : ( ~ inner_point(v1, v0) | ? [v2] : ? [v3] : (sum(v2, v3) = v0 & meet(v1, v2, v3))) & ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | ~ end_point(v0, v1)) & ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | incident_c(v0, v1)) & ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | open(v0)) & ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0))) & ! [v0] : ! [v1] : ( ~ end_point(v0, v1) | incident_c(v0, v1)) & ! [v0] : ! [v1] : ( ~ incident_c(v0, v1) | inner_point(v0, v1) | end_point(v0, v1)) & ! [v0] : ! [v1] : ( ~ incident_c(v0, v1) | end_point(v0, v1) | ? [v2] : ? [v3] : (incident_c(v0, v3) & incident_c(v0, v2) & part_of(v3, v1) & part_of(v2, v1) & ~ part_of(v3, v2) & ~ part_of(v2, v3))) & ! [v0] : ( ~ open(v0) | ? [v1] : end_point(v1, v0)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ incident_c(v2, v1) | ~ incident_c(v2, v0)) & (incident_c(v2, v1) | incident_c(v2, v0)))) & ? [v0] : ? [v1] : inner_point(v1, v0) & ? [v0] : ? [v1] : (part_of(v1, v0) | ? [v2] : (incident_c(v2, v1) & ~ incident_c(v2, v0))) & ? [v0] : (closed(v0) | ? [v1] : end_point(v1, v0))
% 3.83/1.61 |
% 3.83/1.61 | Applying alpha-rule on (1) yields:
% 3.83/1.61 | (2) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (sum(v1, v2) = v3) | ? [v4] : (( ~ incident_c(v4, v0) | ( ~ incident_c(v4, v2) & ~ incident_c(v4, v1))) & (incident_c(v4, v2) | incident_c(v4, v1) | incident_c(v4, v0))))
% 3.83/1.61 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v2))
% 3.83/1.61 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v0) | incident_c(v3, v2) | incident_c(v3, v1))
% 3.83/1.61 | (5) ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | ~ end_point(v0, v1))
% 3.83/1.61 | (6) ? [v0] : (closed(v0) | ? [v1] : end_point(v1, v0))
% 3.83/1.61 | (7) ! [v0] : ! [v1] : ( ~ incident_c(v0, v1) | inner_point(v0, v1) | end_point(v0, v1))
% 3.83/1.61 | (8) ? [v0] : ? [v1] : (part_of(v1, v0) | ? [v2] : (incident_c(v2, v1) & ~ incident_c(v2, v0)))
% 3.83/1.61 | (9) ! [v0] : ! [v1] : ( ~ incident_c(v0, v1) | end_point(v0, v1) | ? [v2] : ? [v3] : (incident_c(v0, v3) & incident_c(v0, v2) & part_of(v3, v1) & part_of(v2, v1) & ~ part_of(v3, v2) & ~ part_of(v2, v3)))
% 3.83/1.61 | (10) ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | incident_c(v0, v1))
% 3.83/1.61 | (11) open(all_0_0_0)
% 3.83/1.61 | (12) ! [v0] : ! [v1] : ( ~ closed(v0) | ~ end_point(v1, v0))
% 3.83/1.61 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v1) | incident_c(v3, v0))
% 3.83/1.61 | (14) ! [v0] : ! [v1] : ( ~ end_point(v0, v1) | incident_c(v0, v1))
% 3.83/1.61 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ end_point(v4, v3) | ~ end_point(v4, v2) | ~ end_point(v4, v1) | ~ part_of(v3, v0) | ~ part_of(v2, v0) | ~ part_of(v1, v0) | part_of(v3, v2) | part_of(v3, v1) | part_of(v2, v3) | part_of(v2, v1) | part_of(v1, v3) | part_of(v1, v2))
% 3.83/1.61 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ incident_c(v2, v1) | ~ part_of(v1, v0) | incident_c(v2, v0))
% 3.83/1.61 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 3.83/1.61 | (18) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ incident_c(v2, v1) | ~ incident_c(v2, v0)) & (incident_c(v2, v1) | incident_c(v2, v0))))
% 3.83/1.62 | (19) ! [v0] : ! [v1] : ( ~ inner_point(v1, v0) | ? [v2] : ? [v3] : (sum(v2, v3) = v0 & meet(v1, v2, v3)))
% 3.83/1.62 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v2))
% 3.83/1.62 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v1))
% 3.83/1.62 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ end_point(v1, all_0_0_0) | ~ end_point(v0, all_0_0_0))
% 3.83/1.62 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v1))
% 3.83/1.62 | (24) ! [v0] : ( ~ open(v0) | ? [v1] : end_point(v1, v0))
% 3.83/1.62 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ end_point(v3, v0) | ~ end_point(v2, v0) | ~ end_point(v1, v0))
% 3.83/1.62 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ part_of(v1, v0) | open(v1))
% 3.83/1.62 | (27) ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0)))
% 3.83/1.62 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v1, v2) = v0) | ~ closed(v0) | ~ meet(v3, v1, v2) | ~ end_point(v4, v1) | meet(v4, v1, v2))
% 3.83/1.62 | (29) ? [v0] : ? [v1] : inner_point(v1, v0)
% 3.83/1.62 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ incident_c(v0, v2) | ~ incident_c(v0, v1) | meet(v0, v1, v2) | ? [v3] : (incident_c(v3, v2) & incident_c(v3, v1) & ( ~ end_point(v3, v2) | ~ end_point(v3, v1))))
% 3.83/1.62 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ end_point(v0, v1) | ~ incident_c(v0, v3) | ~ incident_c(v0, v2) | ~ part_of(v3, v1) | ~ part_of(v2, v1) | part_of(v3, v2) | part_of(v2, v3))
% 3.83/1.62 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v2) | incident_c(v3, v0))
% 3.83/1.62 | (33) ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | open(v0))
% 3.83/1.62 |
% 3.83/1.62 | Instantiating formula (24) with all_0_0_0 and discharging atoms open(all_0_0_0), yields:
% 3.83/1.62 | (34) ? [v0] : end_point(v0, all_0_0_0)
% 3.83/1.62 |
% 3.83/1.62 | Instantiating (34) with all_18_0_11 yields:
% 3.83/1.62 | (35) end_point(all_18_0_11, all_0_0_0)
% 3.83/1.62 |
% 3.83/1.62 | Instantiating formula (27) with all_18_0_11, all_0_0_0 and discharging atoms end_point(all_18_0_11, all_0_0_0), yields:
% 3.83/1.62 | (36) ? [v0] : ( ~ (v0 = all_18_0_11) & end_point(v0, all_0_0_0))
% 3.83/1.62 |
% 3.83/1.62 | Instantiating (36) with all_26_0_12 yields:
% 3.83/1.62 | (37) ~ (all_26_0_12 = all_18_0_11) & end_point(all_26_0_12, all_0_0_0)
% 3.83/1.62 |
% 3.83/1.62 | Applying alpha-rule on (37) yields:
% 3.83/1.62 | (38) ~ (all_26_0_12 = all_18_0_11)
% 3.83/1.62 | (39) end_point(all_26_0_12, all_0_0_0)
% 3.83/1.62 |
% 3.83/1.62 | Instantiating formula (22) with all_26_0_12, all_18_0_11 and discharging atoms end_point(all_26_0_12, all_0_0_0), end_point(all_18_0_11, all_0_0_0), yields:
% 3.83/1.62 | (40) all_26_0_12 = all_18_0_11
% 3.83/1.62 |
% 3.83/1.62 | Equations (40) can reduce 38 to:
% 3.83/1.62 | (41) $false
% 3.83/1.62 |
% 3.83/1.62 |-The branch is then unsatisfiable
% 3.83/1.62 % SZS output end Proof for theBenchmark
% 3.83/1.62
% 3.83/1.62 1031ms
%------------------------------------------------------------------------------