TSTP Solution File: NUN062+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUN062+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.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 : Mon Jul 18 16:25:07 EDT 2022
% Result : Theorem 10.68s 3.10s
% Output : Proof 14.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN062+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n017.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jun 2 02:03:27 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.50/0.56 ____ _
% 0.50/0.56 ___ / __ \_____(_)___ ________ __________
% 0.50/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.56
% 0.50/0.57 A Theorem Prover for First-Order Logic
% 0.50/0.57 (ePrincess v.1.0)
% 0.50/0.57
% 0.50/0.57 (c) Philipp Rümmer, 2009-2015
% 0.50/0.57 (c) Peter Backeman, 2014-2015
% 0.50/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.57 Bug reports to peter@backeman.se
% 0.50/0.57
% 0.50/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.57
% 0.50/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.50/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.93 Prover 0: Preprocessing ...
% 2.04/1.07 Prover 0: Warning: ignoring some quantifiers
% 2.11/1.08 Prover 0: Constructing countermodel ...
% 3.01/1.35 Prover 0: gave up
% 3.01/1.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.09/1.38 Prover 1: Preprocessing ...
% 3.31/1.45 Prover 1: Warning: ignoring some quantifiers
% 3.31/1.45 Prover 1: Constructing countermodel ...
% 3.91/1.61 Prover 1: gave up
% 3.91/1.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.91/1.63 Prover 2: Preprocessing ...
% 4.35/1.68 Prover 2: Warning: ignoring some quantifiers
% 4.35/1.68 Prover 2: Constructing countermodel ...
% 4.69/1.79 Prover 2: gave up
% 4.69/1.79 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.69/1.81 Prover 3: Preprocessing ...
% 4.98/1.83 Prover 3: Warning: ignoring some quantifiers
% 4.98/1.83 Prover 3: Constructing countermodel ...
% 5.17/1.91 Prover 3: gave up
% 5.17/1.91 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.17/1.93 Prover 4: Preprocessing ...
% 5.52/1.97 Prover 4: Warning: ignoring some quantifiers
% 5.70/1.98 Prover 4: Constructing countermodel ...
% 6.09/2.11 Prover 4: gave up
% 6.09/2.11 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.38/2.13 Prover 5: Preprocessing ...
% 6.38/2.15 Prover 5: Warning: ignoring some quantifiers
% 6.38/2.15 Prover 5: Constructing countermodel ...
% 6.64/2.22 Prover 5: gave up
% 6.64/2.22 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.64/2.23 Prover 6: Preprocessing ...
% 7.00/2.25 Prover 6: Warning: ignoring some quantifiers
% 7.00/2.26 Prover 6: Constructing countermodel ...
% 7.16/2.33 Prover 6: gave up
% 7.16/2.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 7.40/2.34 Prover 7: Preprocessing ...
% 7.40/2.36 Prover 7: Proving ...
% 10.68/3.09 Prover 7: proved (764ms)
% 10.68/3.10
% 10.68/3.10 % SZS status Theorem for theBenchmark
% 10.68/3.10
% 10.68/3.10 Generating proof ... found it (size 15)
% 14.65/4.04
% 14.65/4.04 % SZS output start Proof for theBenchmark
% 14.65/4.04 Assumed formulas after preprocessing and simplification:
% 14.65/4.04 | (0) ? [v0] : ! [v1] : ! [v2] : ( ~ r3(v0, v2, v1) | r1(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ! [v2] : ( ~ r2(v1, v2) | ~ r2(v0, v2))) & ! [v0] : ! [v1] : ( ~ r2(v0, v1) | ~ r1(v1)) & ! [v0] : ! [v1] : ? [v2] : ! [v3] : ((v3 = v2 & r4(v0, v1, v2)) | ( ~ (v3 = v2) & ~ r4(v0, v1, v3))) & ! [v0] : ! [v1] : ? [v2] : ! [v3] : ((v3 = v2 & r3(v0, v1, v2)) | ( ~ (v3 = v2) & ~ r3(v0, v1, v3))) & ! [v0] : ? [v1] : ! [v2] : ((v2 = v1 & r2(v0, v1)) | ( ~ (v2 = v1) & ~ r2(v0, v2))) & ? [v0] : ! [v1] : ((v1 = v0 & r1(v0)) | ( ~ (v1 = v0) & ~ r1(v1))) & ! [v0] : (r1(v0) | ? [v1] : r2(v1, v0)) & ! [v0] : ! [v1] : ? [v2] : ( ? [v3] : (r4(v0, v3, v2) & r2(v1, v3)) & ? [v3] : (r4(v0, v1, v3) & r3(v3, v0, v2))) & ! [v0] : ! [v1] : ? [v2] : ( ? [v3] : (r3(v0, v3, v2) & r2(v1, v3)) & ? [v3] : (r3(v0, v1, v3) & r2(v3, v2))) & ! [v0] : ? [v1] : (r3(v0, v1, v0) & r1(v1)) & ! [v0] : ? [v1] : (r1(v1) & ? [v2] : (r4(v0, v2, v1) & r1(v2)))
% 14.65/4.04 | Applying alpha-rule on (0) yields:
% 14.65/4.04 | (1) ? [v0] : ! [v1] : ! [v2] : ( ~ r3(v0, v2, v1) | r1(v2))
% 14.65/4.04 | (2) ! [v0] : ? [v1] : ! [v2] : ((v2 = v1 & r2(v0, v1)) | ( ~ (v2 = v1) & ~ r2(v0, v2)))
% 14.65/4.04 | (3) ! [v0] : (r1(v0) | ? [v1] : r2(v1, v0))
% 14.65/4.04 | (4) ! [v0] : ! [v1] : ? [v2] : ! [v3] : ((v3 = v2 & r4(v0, v1, v2)) | ( ~ (v3 = v2) & ~ r4(v0, v1, v3)))
% 14.65/4.04 | (5) ! [v0] : ! [v1] : (v1 = v0 | ! [v2] : ( ~ r2(v1, v2) | ~ r2(v0, v2)))
% 14.65/4.04 | (6) ! [v0] : ! [v1] : ? [v2] : ! [v3] : ((v3 = v2 & r3(v0, v1, v2)) | ( ~ (v3 = v2) & ~ r3(v0, v1, v3)))
% 14.65/4.04 | (7) ! [v0] : ! [v1] : ? [v2] : ( ? [v3] : (r4(v0, v3, v2) & r2(v1, v3)) & ? [v3] : (r4(v0, v1, v3) & r3(v3, v0, v2)))
% 14.65/4.04 | (8) ! [v0] : ? [v1] : (r3(v0, v1, v0) & r1(v1))
% 14.65/4.04 | (9) ! [v0] : ! [v1] : ? [v2] : ( ? [v3] : (r3(v0, v3, v2) & r2(v1, v3)) & ? [v3] : (r3(v0, v1, v3) & r2(v3, v2)))
% 14.65/4.04 | (10) ! [v0] : ? [v1] : (r1(v1) & ? [v2] : (r4(v0, v2, v1) & r1(v2)))
% 14.65/4.05 | (11) ? [v0] : ! [v1] : ((v1 = v0 & r1(v0)) | ( ~ (v1 = v0) & ~ r1(v1)))
% 14.65/4.05 | (12) ! [v0] : ! [v1] : ( ~ r2(v0, v1) | ~ r1(v1))
% 14.65/4.05 |
% 14.65/4.05 | Instantiating (1) with all_2_0_1 yields:
% 14.65/4.05 | (13) ! [v0] : ! [v1] : ( ~ r3(all_2_0_1, v1, v0) | r1(v1))
% 14.65/4.05 |
% 14.65/4.05 | Introducing new symbol ex_36_1_11 defined by:
% 14.65/4.05 | (14) ex_36_1_11 = all_2_0_1
% 14.65/4.05 |
% 14.65/4.05 | Instantiating formula (9) with ex_36_0_10, ex_36_1_11 yields:
% 14.65/4.05 | (15) ? [v0] : ( ? [v1] : (r3(ex_36_1_11, v1, v0) & r2(ex_36_0_10, v1)) & ? [v1] : (r3(ex_36_1_11, ex_36_0_10, v1) & r2(v1, v0)))
% 14.65/4.05 |
% 14.65/4.05 | Instantiating (15) with all_37_0_12 yields:
% 14.65/4.05 | (16) ? [v0] : (r3(ex_36_1_11, v0, all_37_0_12) & r2(ex_36_0_10, v0)) & ? [v0] : (r3(ex_36_1_11, ex_36_0_10, v0) & r2(v0, all_37_0_12))
% 14.65/4.05 |
% 14.65/4.05 | Applying alpha-rule on (16) yields:
% 14.65/4.05 | (17) ? [v0] : (r3(ex_36_1_11, v0, all_37_0_12) & r2(ex_36_0_10, v0))
% 14.65/4.05 | (18) ? [v0] : (r3(ex_36_1_11, ex_36_0_10, v0) & r2(v0, all_37_0_12))
% 14.65/4.05 |
% 14.65/4.05 | Instantiating (17) with all_40_0_14 yields:
% 14.65/4.05 | (19) r3(ex_36_1_11, all_40_0_14, all_37_0_12) & r2(ex_36_0_10, all_40_0_14)
% 14.65/4.05 |
% 14.65/4.05 | Applying alpha-rule on (19) yields:
% 14.65/4.05 | (20) r3(ex_36_1_11, all_40_0_14, all_37_0_12)
% 14.65/4.05 | (21) r2(ex_36_0_10, all_40_0_14)
% 14.65/4.05 |
% 14.65/4.05 | Instantiating formula (13) with all_40_0_14, all_37_0_12 yields:
% 14.65/4.05 | (22) ~ r3(all_2_0_1, all_40_0_14, all_37_0_12) | r1(all_40_0_14)
% 14.65/4.05 |
% 14.65/4.05 +-Applying beta-rule and splitting (22), into two cases.
% 14.65/4.05 |-Branch one:
% 14.65/4.05 | (23) r1(all_40_0_14)
% 14.65/4.05 |
% 14.65/4.05 | Instantiating formula (12) with all_40_0_14, ex_36_0_10 and discharging atoms r2(ex_36_0_10, all_40_0_14), r1(all_40_0_14), yields:
% 14.65/4.05 | (24) $false
% 14.65/4.05 |
% 14.65/4.05 |-The branch is then unsatisfiable
% 14.65/4.05 |-Branch two:
% 14.65/4.05 | (25) ~ r3(all_2_0_1, all_40_0_14, all_37_0_12)
% 14.65/4.05 |
% 14.65/4.05 | From (14) and (20) follows:
% 14.65/4.05 | (26) r3(all_2_0_1, all_40_0_14, all_37_0_12)
% 14.65/4.05 |
% 14.65/4.05 | Using (26) and (25) yields:
% 14.65/4.05 | (24) $false
% 14.65/4.05 |
% 14.65/4.05 |-The branch is then unsatisfiable
% 14.65/4.05 % SZS output end Proof for theBenchmark
% 14.65/4.05
% 14.65/4.05 3473ms
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