TSTP Solution File: SYN986+1.001 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN986+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 : Thu Jul 21 05:06:18 EDT 2022
% Result : Theorem 6.46s 2.36s
% Output : Proof 12.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN986+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n012.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 : 600
% 0.14/0.35 % DateTime : Mon Jul 11 23:20:27 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.59 ____ _
% 0.20/0.59 ___ / __ \_____(_)___ ________ __________
% 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic
% 0.20/0.59 (ePrincess v.1.0)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2015
% 0.20/0.59 (c) Peter Backeman, 2014-2015
% 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.59 Bug reports to peter@backeman.se
% 0.20/0.59
% 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.37/0.90 Prover 0: Preprocessing ...
% 1.45/0.98 Prover 0: Constructing countermodel ...
% 1.60/1.03 Prover 0: gave up
% 1.60/1.03 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.60/1.04 Prover 1: Preprocessing ...
% 1.80/1.10 Prover 1: Constructing countermodel ...
% 1.80/1.10 Prover 1: gave up
% 1.80/1.10 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.80/1.11 Prover 2: Preprocessing ...
% 1.80/1.16 Prover 2: Warning: ignoring some quantifiers
% 1.80/1.16 Prover 2: Constructing countermodel ...
% 2.27/1.20 Prover 2: gave up
% 2.27/1.20 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.27/1.21 Prover 3: Preprocessing ...
% 2.27/1.22 Prover 3: Constructing countermodel ...
% 2.45/1.23 Prover 3: gave up
% 2.45/1.23 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.45/1.24 Prover 4: Preprocessing ...
% 2.56/1.28 Prover 4: Warning: ignoring some quantifiers
% 2.56/1.28 Prover 4: Constructing countermodel ...
% 4.21/1.74 Prover 4: gave up
% 4.21/1.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.21/1.75 Prover 5: Preprocessing ...
% 4.53/1.76 Prover 5: Constructing countermodel ...
% 4.53/1.77 Prover 5: gave up
% 4.53/1.77 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.53/1.77 Prover 6: Preprocessing ...
% 4.66/1.79 Prover 6: Warning: ignoring some quantifiers
% 4.66/1.79 Prover 6: Constructing countermodel ...
% 4.66/1.79 Prover 6: gave up
% 4.66/1.79 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 4.66/1.80 Prover 7: Preprocessing ...
% 4.66/1.81 Prover 7: Constructing countermodel ...
% 4.66/1.81 Prover 7: gave up
% 4.66/1.81 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 4.66/1.82 Prover 8: Preprocessing ...
% 4.66/1.82 Prover 8: Constructing countermodel ...
% 4.66/1.83 Prover 8: gave up
% 4.66/1.83 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal
% 4.66/1.83 Prover 9: Preprocessing ...
% 4.66/1.84 Prover 9: Proving ...
% 6.46/2.36 Prover 9: proved (528ms)
% 6.46/2.36
% 6.46/2.36 % SZS status Theorem for theBenchmark
% 6.46/2.36
% 6.46/2.36 Generating proof ... found it (size 26)
% 12.30/3.88
% 12.30/3.88 % SZS output start Proof for theBenchmark
% 12.30/3.88 Assumed formulas after preprocessing and simplification:
% 12.30/3.88 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (succ(v2) = v5) | ~ r(v3, v2, v4) | ~ r(v1, v2, v3) | r(v1, v5, v4)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (succ(v3) = v2) | ~ (succ(v3) = v1)) & ! [v1] : ! [v2] : ( ~ r(v0, v1, v2) | ~ r(v0, v0, v1)) & ! [v1] : ? [v2] : (succ(v1) = v2 & r(v1, v0, v2)))
% 12.64/3.90 | Instantiating (0) with all_0_0_0 yields:
% 12.64/3.90 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (succ(v1) = v4) | ~ r(v2, v1, v3) | ~ r(v0, v1, v2) | r(v0, v4, v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ( ~ r(all_0_0_0, v0, v1) | ~ r(all_0_0_0, all_0_0_0, v0)) & ! [v0] : ? [v1] : (succ(v0) = v1 & r(v0, all_0_0_0, v1))
% 12.64/3.90 |
% 12.64/3.90 | Applying alpha-rule on (1) yields:
% 12.64/3.90 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (succ(v1) = v4) | ~ r(v2, v1, v3) | ~ r(v0, v1, v2) | r(v0, v4, v3))
% 12.64/3.90 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 12.64/3.91 | (4) ! [v0] : ! [v1] : ( ~ r(all_0_0_0, v0, v1) | ~ r(all_0_0_0, all_0_0_0, v0))
% 12.64/3.91 | (5) ! [v0] : ? [v1] : (succ(v0) = v1 & r(v0, all_0_0_0, v1))
% 12.64/3.91 |
% 12.64/3.91 | Introducing new symbol ex_4_0_1 defined by:
% 12.64/3.91 | (6) ex_4_0_1 = all_0_0_0
% 12.64/3.91 |
% 12.64/3.91 | Instantiating formula (5) with ex_4_0_1 yields:
% 12.64/3.91 | (7) ? [v0] : (succ(ex_4_0_1) = v0 & r(ex_4_0_1, all_0_0_0, v0))
% 12.64/3.91 |
% 12.64/3.91 | Instantiating (7) with all_5_0_2 yields:
% 12.64/3.91 | (8) succ(ex_4_0_1) = all_5_0_2 & r(ex_4_0_1, all_0_0_0, all_5_0_2)
% 12.64/3.91 |
% 12.64/3.91 | Applying alpha-rule on (8) yields:
% 12.64/3.91 | (9) succ(ex_4_0_1) = all_5_0_2
% 12.64/3.91 | (10) r(ex_4_0_1, all_0_0_0, all_5_0_2)
% 12.64/3.91 |
% 12.64/3.91 | Introducing new symbol ex_13_0_3 defined by:
% 12.64/3.91 | (11) ex_13_0_3 = all_5_0_2
% 12.64/3.91 |
% 12.64/3.91 | Instantiating formula (5) with ex_13_0_3 yields:
% 12.64/3.91 | (12) ? [v0] : (succ(ex_13_0_3) = v0 & r(ex_13_0_3, all_0_0_0, v0))
% 12.64/3.91 |
% 12.64/3.91 | Instantiating (12) with all_14_0_4 yields:
% 12.64/3.91 | (13) succ(ex_13_0_3) = all_14_0_4 & r(ex_13_0_3, all_0_0_0, all_14_0_4)
% 12.64/3.91 |
% 12.64/3.91 | Applying alpha-rule on (13) yields:
% 12.64/3.91 | (14) succ(ex_13_0_3) = all_14_0_4
% 12.64/3.91 | (15) r(ex_13_0_3, all_0_0_0, all_14_0_4)
% 12.64/3.91 |
% 12.64/3.91 | Instantiating formula (2) with all_5_0_2, all_14_0_4, all_5_0_2, all_0_0_0, all_0_0_0 yields:
% 12.64/3.91 | (16) ~ (succ(all_0_0_0) = all_5_0_2) | ~ r(all_5_0_2, all_0_0_0, all_14_0_4) | ~ r(all_0_0_0, all_0_0_0, all_5_0_2) | r(all_0_0_0, all_5_0_2, all_14_0_4)
% 12.64/3.91 |
% 12.64/3.91 +-Applying beta-rule and splitting (16), into two cases.
% 12.64/3.91 |-Branch one:
% 12.64/3.91 | (17) ~ r(all_5_0_2, all_0_0_0, all_14_0_4)
% 12.64/3.91 |
% 12.64/3.91 | From (11) and (15) follows:
% 12.64/3.91 | (18) r(all_5_0_2, all_0_0_0, all_14_0_4)
% 12.64/3.91 |
% 12.64/3.91 | Using (18) and (17) yields:
% 12.64/3.91 | (19) $false
% 12.64/3.91 |
% 12.64/3.91 |-The branch is then unsatisfiable
% 12.64/3.91 |-Branch two:
% 12.64/3.91 | (20) ~ (succ(all_0_0_0) = all_5_0_2) | ~ r(all_0_0_0, all_0_0_0, all_5_0_2) | r(all_0_0_0, all_5_0_2, all_14_0_4)
% 12.64/3.91 |
% 12.64/3.91 +-Applying beta-rule and splitting (20), into two cases.
% 12.64/3.91 |-Branch one:
% 12.64/3.91 | (21) ~ r(all_0_0_0, all_0_0_0, all_5_0_2)
% 12.64/3.91 |
% 12.64/3.91 | From (6) and (10) follows:
% 12.64/3.91 | (22) r(all_0_0_0, all_0_0_0, all_5_0_2)
% 12.64/3.91 |
% 12.64/3.91 | Using (22) and (21) yields:
% 12.64/3.91 | (19) $false
% 12.64/3.91 |
% 12.64/3.91 |-The branch is then unsatisfiable
% 12.64/3.91 |-Branch two:
% 12.64/3.91 | (22) r(all_0_0_0, all_0_0_0, all_5_0_2)
% 12.64/3.91 | (25) ~ (succ(all_0_0_0) = all_5_0_2) | r(all_0_0_0, all_5_0_2, all_14_0_4)
% 12.64/3.91 |
% 12.64/3.91 +-Applying beta-rule and splitting (25), into two cases.
% 12.64/3.91 |-Branch one:
% 12.64/3.91 | (26) r(all_0_0_0, all_5_0_2, all_14_0_4)
% 12.64/3.91 |
% 12.64/3.91 | Instantiating formula (4) with all_14_0_4, all_5_0_2 and discharging atoms r(all_0_0_0, all_5_0_2, all_14_0_4), yields:
% 12.64/3.91 | (21) ~ r(all_0_0_0, all_0_0_0, all_5_0_2)
% 12.64/3.91 |
% 12.64/3.91 | Using (22) and (21) yields:
% 12.64/3.91 | (19) $false
% 12.64/3.91 |
% 12.64/3.91 |-The branch is then unsatisfiable
% 12.64/3.91 |-Branch two:
% 12.64/3.91 | (29) ~ (succ(all_0_0_0) = all_5_0_2)
% 12.64/3.91 |
% 12.64/3.91 | From (6) and (9) follows:
% 12.64/3.91 | (30) succ(all_0_0_0) = all_5_0_2
% 12.64/3.91 |
% 12.64/3.91 | Using (30) and (29) yields:
% 12.64/3.91 | (19) $false
% 12.64/3.91 |
% 12.64/3.91 |-The branch is then unsatisfiable
% 12.64/3.91 % SZS output end Proof for theBenchmark
% 12.64/3.91
% 12.64/3.91 3312ms
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