TSTP Solution File: LCL642+1.005 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL642+1.005 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n013.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 : Thu Aug 31 08:11:54 EDT 2023
% Result : Theorem 133.22s 18.39s
% Output : Proof 133.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL642+1.005 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 23:53:32 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.39/1.24 Prover 1: Preprocessing ...
% 3.39/1.24 Prover 4: Preprocessing ...
% 3.76/1.29 Prover 2: Preprocessing ...
% 3.76/1.29 Prover 3: Preprocessing ...
% 3.76/1.29 Prover 5: Preprocessing ...
% 3.76/1.29 Prover 6: Preprocessing ...
% 3.76/1.29 Prover 0: Preprocessing ...
% 6.96/1.72 Prover 5: Constructing countermodel ...
% 6.96/1.74 Prover 2: Constructing countermodel ...
% 8.74/1.97 Prover 3: Constructing countermodel ...
% 8.74/1.97 Prover 6: Proving ...
% 8.74/1.99 Prover 1: Constructing countermodel ...
% 51.67/7.61 Prover 0: Proving ...
% 55.80/8.20 Prover 4: Constructing countermodel ...
% 72.99/10.49 Prover 2: stopped
% 73.66/10.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.35/10.59 Prover 7: Preprocessing ...
% 74.35/10.68 Prover 7: Constructing countermodel ...
% 99.77/13.97 Prover 5: stopped
% 99.77/13.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 101.19/14.08 Prover 8: Preprocessing ...
% 102.27/14.21 Prover 8: Warning: ignoring some quantifiers
% 102.27/14.21 Prover 8: Constructing countermodel ...
% 115.74/16.00 Prover 1: stopped
% 115.74/16.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 115.74/16.07 Prover 9: Preprocessing ...
% 117.76/16.29 Prover 9: Constructing countermodel ...
% 130.39/17.89 Prover 6: stopped
% 130.39/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 130.39/17.98 Prover 10: Preprocessing ...
% 130.39/18.01 Prover 10: Constructing countermodel ...
% 132.82/18.20 Prover 10: Found proof (size 49)
% 132.82/18.20 Prover 10: proved (306ms)
% 132.82/18.20 Prover 3: stopped
% 132.82/18.20 Prover 4: stopped
% 132.82/18.20 Prover 0: stopped
% 132.82/18.20 Prover 9: stopped
% 132.82/18.20 Prover 8: stopped
% 133.22/18.39 Prover 7: stopped
% 133.22/18.39
% 133.22/18.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 133.22/18.39
% 133.22/18.40 % SZS output start Proof for theBenchmark
% 133.22/18.40 Assumptions after simplification:
% 133.22/18.40 ---------------------------------
% 133.22/18.40
% 133.22/18.40 (main)
% 133.22/18.46 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 133.22/18.46 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 133.22/18.46 ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ($i(v14) & $i(v13)
% 133.22/18.46 & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 133.22/18.46 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & r1(v0, v14) & r1(v0, v13) &
% 133.22/18.46 r1(v0, v12) & ~ p1(v12) & ~ p2(v13) & ~ p3(v14) & ! [v15: $i] : ( ~
% 133.22/18.46 $i(v15) | ~ r1(v0, v15) | p1(v15) | ? [v16: $i] : ? [v17: $i] :
% 133.22/18.46 ($i(v17) & $i(v16) & p1(v16) & r1(v16, v17) & r1(v15, v16) & ~ p1(v17)))
% 133.22/18.46 & ! [v15: $i] : ( ~ $i(v15) | ~ r1(v0, v15) | p2(v15) | ? [v16: $i] : ?
% 133.22/18.46 [v17: $i] : ($i(v17) & $i(v16) & p2(v16) & r1(v16, v17) & r1(v15, v16) &
% 133.22/18.46 ~ p2(v17))) & ! [v15: $i] : ( ~ $i(v15) | ~ r1(v0, v15) | p2(v15) | ?
% 133.22/18.46 [v16: $i] : ($i(v16) & r1(v15, v16) & ~ p2(v16) & ! [v17: $i] : ! [v18:
% 133.22/18.46 $i] : ( ~ $i(v18) | ~ $i(v17) | ~ p2(v17) | ~ r1(v17, v18) | ~
% 133.22/18.46 r1(v16, v17) | p2(v18)))) & ! [v15: $i] : ( ~ $i(v15) | ~ r1(v0,
% 133.22/18.46 v15) | p3(v15) | ? [v16: $i] : ? [v17: $i] : ($i(v17) & $i(v16) &
% 133.22/18.46 p3(v16) & r1(v16, v17) & r1(v15, v16) & ~ p3(v17))) & (p4(v0) | p1(v0)
% 133.22/18.46 | p2(v0) | p3(v0) | ! [v15: $i] : ( ~ $i(v15) | ~ r1(v0, v15)) | (r1(v7,
% 133.22/18.46 v8) & r1(v0, v7) & ~ p4(v7) & ~ p1(v7) & ~ p2(v7) & ~ p3(v7) & !
% 133.22/18.46 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~
% 133.22/18.46 $i(v15) | ~ p4(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v7,
% 133.22/18.46 v15) | p4(v16) | p1(v16) | p2(v16) | p3(v16)) & ! [v15: $i] : !
% 133.22/18.46 [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~
% 133.22/18.46 p1(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v7, v15) | p4(v16)
% 133.22/18.46 | p1(v16) | p2(v16) | p3(v16)) & ! [v15: $i] : ! [v16: $i] : !
% 133.22/18.46 [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~
% 133.22/18.46 r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v7, v15) | p4(v16) | p1(v16) |
% 133.22/18.46 p2(v16) | p3(v16)) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~
% 133.22/18.46 $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p3(v15) | ~ r1(v16, v17) | ~
% 133.22/18.46 r1(v15, v16) | ~ r1(v7, v15) | p4(v16) | p1(v16) | p2(v16) | p3(v16))
% 133.22/18.46 & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16)
% 133.22/18.46 | ~ $i(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v7, v15) |
% 133.22/18.46 p4(v16) | p1(v16) | p2(v16) | p3(v16) | ? [v18: $i] : ($i(v18) &
% 133.22/18.46 r1(v15, v18))))) & (p1(v0) | p2(v0) | p3(v0) | ! [v15: $i] : ( ~
% 133.22/18.46 $i(v15) | ~ r1(v0, v15)) | (r1(v5, v6) & r1(v0, v5) & ~ p1(v5) & ~
% 133.22/18.46 p2(v5) & ~ p3(v5) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~
% 133.22/18.46 $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p1(v15) | ~ r1(v16, v17) | ~
% 133.22/18.46 r1(v15, v16) | ~ r1(v5, v15) | p1(v16) | p2(v16) | p3(v16)) & !
% 133.22/18.46 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~
% 133.22/18.46 $i(v15) | ~ p2(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v5,
% 133.22/18.46 v15) | p1(v16) | p2(v16) | p3(v16)) & ! [v15: $i] : ! [v16: $i] :
% 133.22/18.46 ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p3(v15) | ~
% 133.22/18.46 r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v5, v15) | p1(v16) | p2(v16) |
% 133.22/18.46 p3(v16)) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) |
% 133.22/18.46 ~ $i(v16) | ~ $i(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v5,
% 133.22/18.46 v15) | p1(v16) | p2(v16) | p3(v16) | ? [v18: $i] : ($i(v18) &
% 133.22/18.46 r1(v15, v18))))) & (p1(v0) | p2(v0) | ! [v15: $i] : ( ~ $i(v15) |
% 133.22/18.46 ~ r1(v0, v15)) | (r1(v3, v4) & r1(v0, v3) & ~ p1(v3) & ~ p2(v3) & !
% 133.22/18.46 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~
% 133.22/18.46 $i(v15) | ~ p1(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v3,
% 133.22/18.46 v15) | p1(v16) | p2(v16)) & ! [v15: $i] : ! [v16: $i] : ! [v17:
% 133.22/18.46 $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v16,
% 133.22/18.46 v17) | ~ r1(v15, v16) | ~ r1(v3, v15) | p1(v16) | p2(v16)) & !
% 133.22/18.46 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~
% 133.22/18.46 $i(v15) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v3, v15) | p1(v16)
% 133.22/18.46 | p2(v16) | ? [v18: $i] : ($i(v18) & r1(v15, v18))))) & (p1(v0) | !
% 133.22/18.46 [v15: $i] : ( ~ $i(v15) | ~ r1(v0, v15)) | (r1(v1, v2) & r1(v0, v1) & ~
% 133.22/18.46 p1(v1) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~
% 133.22/18.46 $i(v16) | ~ $i(v15) | ~ p1(v15) | ~ r1(v16, v17) | ~ r1(v15, v16)
% 133.22/18.46 | ~ r1(v1, v15) | p1(v16)) & ! [v15: $i] : ! [v16: $i] : ! [v17:
% 133.22/18.46 $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ r1(v16, v17) | ~
% 133.22/18.46 r1(v15, v16) | ~ r1(v1, v15) | p1(v16) | ? [v18: $i] : ($i(v18) &
% 133.22/18.46 r1(v15, v18))))) & ((r1(v0, v9) & ! [v15: $i] : ! [v16: $i] : !
% 133.22/18.46 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] :
% 133.22/18.46 ( ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~
% 133.22/18.46 $i(v16) | ~ $i(v15) | ~ p2(v16) | ~ r1(v20, v21) | ~ r1(v19, v20)
% 133.22/18.46 | ~ r1(v16, v17) | ~ r1(v15, v19) | ~ r1(v15, v18) | ~ r1(v15,
% 133.22/18.46 v16) | ~ r1(v9, v15) | p2(v21) | p2(v18) | p2(v17) | ? [v22: $i] :
% 133.22/18.46 ? [v23: $i] : ($i(v23) & $i(v22) & ((p2(v22) & r1(v22, v23) & r1(v21,
% 133.22/18.46 v22) & ~ p2(v23)) | (p2(v22) & r1(v22, v23) & r1(v18, v22) &
% 133.52/18.46 ~ p2(v23)) | (r1(v19, v22) & ~ p2(v22) & ! [v24: $i] : !
% 133.52/18.46 [v25: $i] : ( ~ $i(v25) | ~ $i(v24) | ~ p2(v24) | ~ r1(v24,
% 133.52/18.46 v25) | ~ r1(v22, v24) | p2(v25)))))) & ! [v15: $i] : !
% 133.52/18.46 [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] :
% 133.52/18.46 ( ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~
% 133.52/18.46 $i(v15) | ~ p2(v16) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v16,
% 133.52/18.47 v17) | ~ r1(v15, v18) | ~ r1(v15, v16) | ~ r1(v9, v15) | p2(v20)
% 133.52/18.47 | p2(v17) | ? [v21: $i] : ? [v22: $i] : ($i(v22) & $i(v21) &
% 133.52/18.47 ((p2(v21) & r1(v21, v22) & r1(v20, v21) & ~ p2(v22)) | (r1(v21,
% 133.52/18.47 v22) & r1(v15, v21) & ~ p2(v22) & ! [v23: $i] : ! [v24: $i]
% 133.52/18.47 : ( ~ $i(v24) | ~ $i(v23) | ~ p2(v23) | ~ r1(v23, v24) | ~
% 133.52/18.47 r1(v22, v23) | p2(v24))) | (r1(v18, v21) & ~ p2(v21) & !
% 133.52/18.47 [v23: $i] : ! [v24: $i] : ( ~ $i(v24) | ~ $i(v23) | ~ p2(v23)
% 133.52/18.47 | ~ r1(v23, v24) | ~ r1(v21, v23) | p2(v24)))))) & ! [v15:
% 133.52/18.47 $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ( ~
% 133.52/18.47 $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~
% 133.52/18.47 p2(v16) | ~ r1(v16, v17) | ~ r1(v15, v19) | ~ r1(v15, v18) | ~
% 133.52/18.47 r1(v15, v16) | ~ r1(v9, v15) | p2(v19) | p2(v18) | p2(v17) | ? [v20:
% 133.52/18.47 $i] : ? [v21: $i] : ($i(v21) & $i(v20) & ((p2(v20) & r1(v20, v21) &
% 133.52/18.47 r1(v19, v20) & ~ p2(v21)) | (p2(v20) & r1(v20, v21) & r1(v18,
% 133.52/18.47 v20) & ~ p2(v21))))) & ! [v15: $i] : ! [v16: $i] : ! [v17:
% 133.52/18.47 $i] : ! [v18: $i] : ! [v19: $i] : ( ~ $i(v19) | ~ $i(v18) | ~
% 133.52/18.47 $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v18, v19) | ~
% 133.52/18.47 r1(v17, v18) | ~ r1(v15, v17) | ~ r1(v15, v16) | ~ r1(v9, v15) |
% 133.52/18.47 p2(v19) | p2(v16) | ? [v20: $i] : ? [v21: $i] : ($i(v21) & $i(v20) &
% 133.52/18.47 ((p2(v20) & r1(v20, v21) & r1(v19, v20) & ~ p2(v21)) | (p2(v20) &
% 133.52/18.47 r1(v20, v21) & r1(v16, v20) & ~ p2(v21)) | (r1(v17, v20) & ~
% 133.52/18.47 p2(v20) & ! [v22: $i] : ! [v23: $i] : ( ~ $i(v23) | ~ $i(v22)
% 133.52/18.47 | ~ p2(v22) | ~ r1(v22, v23) | ~ r1(v20, v22) |
% 133.52/18.47 p2(v23)))))) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : !
% 133.52/18.47 [v18: $i] : ( ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~
% 133.52/18.47 p2(v16) | ~ r1(v16, v17) | ~ r1(v15, v18) | ~ r1(v15, v16) | ~
% 133.52/18.47 r1(v9, v15) | p2(v18) | p2(v17) | ? [v19: $i] : ? [v20: $i] :
% 133.52/18.47 ($i(v20) & $i(v19) & ((p2(v19) & r1(v19, v20) & r1(v18, v19) & ~
% 133.52/18.47 p2(v20)) | (r1(v19, v20) & r1(v15, v19) & ~ p2(v20) & ! [v21:
% 133.52/18.47 $i] : ! [v22: $i] : ( ~ $i(v22) | ~ $i(v21) | ~ p2(v21) |
% 133.52/18.47 ~ r1(v21, v22) | ~ r1(v20, v21) | p2(v22)))))) & ! [v15: $i]
% 133.52/18.47 : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ( ~ $i(v18) | ~ $i(v17)
% 133.52/18.47 | ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v17, v18) | ~ r1(v16,
% 133.52/18.47 v17) | ~ r1(v15, v16) | ~ r1(v9, v15) | p2(v18) | ? [v19: $i] :
% 133.52/18.47 ? [v20: $i] : ($i(v20) & $i(v19) & ((p2(v19) & r1(v19, v20) & r1(v18,
% 133.52/18.47 v19) & ~ p2(v20)) | (r1(v19, v20) & r1(v15, v19) & ~ p2(v20)
% 133.52/18.47 & ! [v21: $i] : ! [v22: $i] : ( ~ $i(v22) | ~ $i(v21) | ~
% 133.52/18.47 p2(v21) | ~ r1(v21, v22) | ~ r1(v20, v21) | p2(v22))) |
% 133.52/18.47 (r1(v16, v19) & ~ p2(v19) & ! [v21: $i] : ! [v22: $i] : ( ~
% 133.52/18.47 $i(v22) | ~ $i(v21) | ~ p2(v21) | ~ r1(v21, v22) | ~
% 133.52/18.47 r1(v19, v21) | p2(v22)))))) & ! [v15: $i] : ! [v16: $i] : !
% 133.52/18.47 [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~
% 133.52/18.47 r1(v15, v17) | ~ r1(v15, v16) | ~ r1(v9, v15) | p2(v17) | p2(v16) |
% 133.52/18.47 ? [v18: $i] : ? [v19: $i] : ($i(v19) & $i(v18) & ((p2(v18) & r1(v18,
% 133.52/18.47 v19) & r1(v17, v18) & ~ p2(v19)) | (p2(v18) & r1(v18, v19) &
% 133.52/18.47 r1(v16, v18) & ~ p2(v19))))) & ! [v15: $i] : ! [v16: $i] : (
% 133.52/18.47 ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v15, v16) | ~ r1(v9, v15)
% 133.52/18.47 | p2(v16) | ? [v17: $i] : ? [v18: $i] : ($i(v18) & $i(v17) &
% 133.52/18.47 ((p2(v17) & r1(v17, v18) & r1(v16, v17) & ~ p2(v18)) | (r1(v17,
% 133.52/18.47 v18) & r1(v15, v17) & ~ p2(v18) & ! [v19: $i] : ! [v20: $i]
% 133.52/18.47 : ( ~ $i(v20) | ~ $i(v19) | ~ p2(v19) | ~ r1(v19, v20) | ~
% 133.52/18.47 r1(v18, v19) | p2(v20)))))) & ((r1(v10, v11) & r1(v9, v10) &
% 133.52/18.47 ~ p2(v11) & ! [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~ $i(v15) |
% 133.52/18.47 ~ p2(v15) | ~ r1(v15, v16) | ~ r1(v11, v15) | p2(v16)) & !
% 133.52/18.47 [v15: $i] : ( ~ $i(v15) | ~ r1(v9, v15) | p2(v15) | ? [v16: $i] :
% 133.52/18.47 ? [v17: $i] : ($i(v17) & $i(v16) & p2(v16) & r1(v16, v17) &
% 133.52/18.47 r1(v15, v16) & ~ p2(v17)))) | ( ~ p2(v9) & ! [v15: $i] : !
% 133.52/18.47 [v16: $i] : ( ~ $i(v16) | ~ $i(v15) | ~ p2(v15) | ~ r1(v15, v16)
% 133.52/18.47 | ~ r1(v9, v15) | p2(v16))))) | ((p2(v0) | (p2(v9) & r1(v9, v10)
% 133.52/18.47 & r1(v0, v9) & ~ p2(v10))) & ( ! [v15: $i] : ! [v16: $i] : ( ~
% 133.52/18.47 $i(v16) | ~ $i(v15) | ~ r1(v15, v16) | ~ r1(v0, v15) | p2(v16) |
% 133.52/18.47 ? [v17: $i] : ? [v18: $i] : ($i(v18) & $i(v17) & p2(v17) & r1(v17,
% 133.52/18.47 v18) & r1(v16, v17) & ~ p2(v18))) | (r1(v0, v11) & ~ p2(v11) &
% 133.52/18.47 ! [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~ $i(v15) | ~ p2(v15)
% 133.52/18.47 | ~ r1(v15, v16) | ~ r1(v11, v15) | p2(v16)))))))
% 133.52/18.47
% 133.52/18.47 Those formulas are unsatisfiable:
% 133.52/18.47 ---------------------------------
% 133.52/18.47
% 133.52/18.47 Begin of proof
% 133.52/18.47 |
% 133.52/18.47 | DELTA: instantiating (main) with fresh symbols all_2_0, all_2_1, all_2_2,
% 133.52/18.47 | all_2_3, all_2_4, all_2_5, all_2_6, all_2_7, all_2_8, all_2_9,
% 133.52/18.47 | all_2_10, all_2_11, all_2_12, all_2_13, all_2_14 gives:
% 133.64/18.50 | (1) $i(all_2_0) & $i(all_2_1) & $i(all_2_2) & $i(all_2_3) & $i(all_2_4) &
% 133.64/18.50 | $i(all_2_5) & $i(all_2_6) & $i(all_2_7) & $i(all_2_8) & $i(all_2_9) &
% 133.64/18.50 | $i(all_2_10) & $i(all_2_11) & $i(all_2_12) & $i(all_2_13) &
% 133.64/18.50 | $i(all_2_14) & r1(all_2_14, all_2_0) & r1(all_2_14, all_2_1) &
% 133.64/18.50 | r1(all_2_14, all_2_2) & ~ p1(all_2_2) & ~ p2(all_2_1) & ~
% 133.64/18.50 | p3(all_2_0) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0) | p1(v0) |
% 133.64/18.50 | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) &
% 133.64/18.50 | r1(v0, v1) & ~ p1(v2))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 133.64/18.50 | r1(all_2_14, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) &
% 133.64/18.50 | $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2))) & ! [v0:
% 133.64/18.50 | $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0) | p2(v0) | ? [v1: $i] :
% 133.64/18.50 | ($i(v1) & r1(v0, v1) & ~ p2(v1) & ! [v2: $i] : ! [v3: $i] : ( ~
% 133.64/18.50 | $i(v3) | ~ $i(v2) | ~ p2(v2) | ~ r1(v2, v3) | ~ r1(v1, v2) |
% 133.64/18.50 | p2(v3)))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0) |
% 133.64/18.50 | p3(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p3(v1) &
% 133.64/18.50 | r1(v1, v2) & r1(v0, v1) & ~ p3(v2))) & (p4(all_2_14) |
% 133.64/18.50 | p1(all_2_14) | p2(all_2_14) | p3(all_2_14) | ! [v0: $i] : ( ~ $i(v0)
% 133.64/18.50 | | ~ r1(all_2_14, v0)) | (r1(all_2_7, all_2_6) & r1(all_2_14,
% 133.64/18.50 | all_2_7) & ~ p4(all_2_7) & ~ p1(all_2_7) & ~ p2(all_2_7) & ~
% 133.64/18.50 | p3(all_2_7) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2)
% 133.64/18.50 | | ~ $i(v1) | ~ $i(v0) | ~ p4(v0) | ~ r1(v1, v2) | ~ r1(v0,
% 133.64/18.50 | v1) | ~ r1(all_2_7, v0) | p4(v1) | p1(v1) | p2(v1) | p3(v1)) &
% 133.64/18.50 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) |
% 133.64/18.50 | ~ $i(v0) | ~ p1(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 133.64/18.50 | r1(all_2_7, v0) | p4(v1) | p1(v1) | p2(v1) | p3(v1)) & ! [v0:
% 133.64/18.50 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 133.64/18.50 | $i(v0) | ~ p2(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 133.64/18.50 | r1(all_2_7, v0) | p4(v1) | p1(v1) | p2(v1) | p3(v1)) & ! [v0:
% 133.64/18.50 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 133.64/18.50 | $i(v0) | ~ p3(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 133.64/18.50 | r1(all_2_7, v0) | p4(v1) | p1(v1) | p2(v1) | p3(v1)) & ! [v0:
% 133.64/18.50 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 133.64/18.50 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_7, v0) |
% 133.64/18.50 | p4(v1) | p1(v1) | p2(v1) | p3(v1) | ? [v3: $i] : ($i(v3) &
% 133.64/18.50 | r1(v0, v3))))) & (p1(all_2_14) | p2(all_2_14) | p3(all_2_14) |
% 133.64/18.50 | ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0)) | (r1(all_2_9,
% 133.64/18.50 | all_2_8) & r1(all_2_14, all_2_9) & ~ p1(all_2_9) & ~
% 133.64/18.50 | p2(all_2_9) & ~ p3(all_2_9) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 133.64/18.50 | $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v1,
% 133.64/18.50 | v2) | ~ r1(v0, v1) | ~ r1(all_2_9, v0) | p1(v1) | p2(v1) |
% 133.64/18.50 | p3(v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) |
% 133.64/18.50 | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v1, v2) | ~ r1(v0, v1)
% 133.64/18.50 | | ~ r1(all_2_9, v0) | p1(v1) | p2(v1) | p3(v1)) & ! [v0: $i] :
% 133.64/18.50 | ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 133.64/18.50 | p3(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_9, v0) |
% 133.64/18.50 | p1(v1) | p2(v1) | p3(v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 133.64/18.50 | $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~
% 133.64/18.50 | r1(v0, v1) | ~ r1(all_2_9, v0) | p1(v1) | p2(v1) | p3(v1) | ?
% 133.64/18.50 | [v3: $i] : ($i(v3) & r1(v0, v3))))) & (p1(all_2_14) |
% 133.64/18.50 | p2(all_2_14) | ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0)) |
% 133.64/18.50 | (r1(all_2_11, all_2_10) & r1(all_2_14, all_2_11) & ~ p1(all_2_11) &
% 133.64/18.50 | ~ p2(all_2_11) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 133.64/18.50 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v1, v2) | ~
% 133.64/18.50 | r1(v0, v1) | ~ r1(all_2_11, v0) | p1(v1) | p2(v1)) & ! [v0: $i]
% 133.64/18.50 | : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 133.64/18.50 | ~ p2(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_11, v0) |
% 133.64/18.50 | p1(v1) | p2(v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 133.64/18.50 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) |
% 133.64/18.50 | ~ r1(all_2_11, v0) | p1(v1) | p2(v1) | ? [v3: $i] : ($i(v3) &
% 133.64/18.50 | r1(v0, v3))))) & (p1(all_2_14) | ! [v0: $i] : ( ~ $i(v0) | ~
% 133.64/18.50 | r1(all_2_14, v0)) | (r1(all_2_13, all_2_12) & r1(all_2_14,
% 133.64/18.50 | all_2_13) & ~ p1(all_2_13) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 133.64/18.50 | $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v1,
% 133.64/18.50 | v2) | ~ r1(v0, v1) | ~ r1(all_2_13, v0) | p1(v1)) & ! [v0:
% 133.64/18.50 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 133.64/18.50 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_13, v0) |
% 133.64/18.50 | p1(v1) | ? [v3: $i] : ($i(v3) & r1(v0, v3))))) & ((r1(all_2_14,
% 133.64/18.50 | all_2_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 133.64/18.50 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5)
% 133.64/18.50 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 133.64/18.50 | p2(v1) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~
% 133.64/18.50 | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.64/18.50 | p2(v6) | p2(v3) | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) &
% 133.64/18.50 | $i(v7) & ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) |
% 133.64/18.50 | (p2(v7) & r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7)
% 133.64/18.50 | & ~ p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~
% 133.64/18.50 | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) |
% 133.64/18.50 | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 133.64/18.50 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) |
% 133.64/18.50 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~
% 133.64/18.50 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~
% 133.64/18.50 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] :
% 133.64/18.50 | ? [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5,
% 133.64/18.50 | v6) & ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) &
% 133.64/18.50 | ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~
% 133.64/18.50 | p2(v8) | ~ r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) |
% 133.64/18.50 | (r1(v3, v6) & ~ p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~
% 133.64/18.51 | $i(v9) | ~ $i(v8) | ~ p2(v8) | ~ r1(v8, v9) | ~
% 133.64/18.51 | r1(v6, v8) | p2(v9)))))) & ! [v0: $i] : ! [v1: $i] : !
% 133.64/18.51 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~
% 133.64/18.51 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~
% 133.64/18.51 | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.64/18.51 | p2(v4) | p2(v3) | p2(v2) | ? [v5: $i] : ? [v6: $i] : ($i(v6) &
% 133.64/18.51 | $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4, v5) & ~ p2(v6)) |
% 133.64/18.51 | (p2(v5) & r1(v5, v6) & r1(v3, v5) & ~ p2(v6))))) & ! [v0:
% 133.64/18.51 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 133.64/18.51 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 133.64/18.51 | p2(v0) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | ~
% 133.64/18.51 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v1) | ? [v5: $i] :
% 133.64/18.51 | ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4,
% 133.64/18.51 | v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v1, v5) & ~
% 133.64/18.51 | p2(v6)) | (r1(v2, v5) & ~ p2(v5) & ! [v7: $i] : ! [v8:
% 133.64/18.51 | $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~ r1(v7, v8)
% 133.64/18.51 | | ~ r1(v5, v7) | p2(v8)))))) & ! [v0: $i] : ! [v1: $i]
% 133.64/18.51 | : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 133.64/18.51 | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0,
% 133.64/18.51 | v1) | ~ r1(all_2_5, v0) | p2(v3) | p2(v2) | ? [v4: $i] : ?
% 133.64/18.51 | [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4)
% 133.64/18.51 | & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & !
% 133.64/18.51 | [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6)
% 133.64/18.51 | | ~ r1(v6, v7) | ~ r1(v5, v6) | p2(v7)))))) & ! [v0:
% 133.64/18.51 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 133.64/18.51 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v2, v3) | ~
% 133.64/18.51 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | ?
% 133.64/18.51 | [v4: $i] : ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5)
% 133.64/18.51 | & r1(v3, v4) & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~
% 133.64/18.51 | p2(v5) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6)
% 133.64/18.51 | | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | p2(v7))) |
% 133.64/18.51 | (r1(v1, v4) & ~ p2(v4) & ! [v6: $i] : ! [v7: $i] : ( ~
% 133.64/18.51 | $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) | ~
% 133.64/18.51 | r1(v4, v6) | p2(v7)))))) & ! [v0: $i] : ! [v1: $i] : !
% 133.64/18.51 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~
% 133.64/18.51 | r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v2) | p2(v1)
% 133.64/18.51 | | ? [v3: $i] : ? [v4: $i] : ($i(v4) & $i(v3) & ((p2(v3) &
% 133.64/18.51 | r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) | (p2(v3) & r1(v3, v4)
% 133.64/18.51 | & r1(v1, v3) & ~ p2(v4))))) & ! [v0: $i] : ! [v1: $i] :
% 133.64/18.51 | ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5,
% 133.64/18.51 | v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) &
% 133.64/18.51 | ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3)) | (r1(v2, v3) &
% 133.64/18.51 | r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5: $i] : ( ~
% 133.64/18.51 | $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) | ~
% 133.64/18.51 | r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) &
% 133.64/18.51 | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1:
% 133.64/18.51 | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.64/18.51 | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 133.64/18.51 | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] :
% 133.64/18.51 | ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~
% 133.64/18.51 | p2(v2)))) | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : (
% 133.64/18.51 | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.64/18.51 | r1(all_2_5, v0) | p2(v1))))) | ((p2(all_2_14) | (p2(all_2_5)
% 133.64/18.51 | & r1(all_2_5, all_2_4) & r1(all_2_14, all_2_5) & ~
% 133.64/18.51 | p2(all_2_4))) & ( ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 133.64/18.51 | $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_14, v0) | p2(v1) | ? [v2:
% 133.64/18.51 | $i] : ? [v3: $i] : ($i(v3) & $i(v2) & p2(v2) & r1(v2, v3) &
% 133.64/18.51 | r1(v1, v2) & ~ p2(v3))) | (r1(all_2_14, all_2_3) & ~
% 133.64/18.51 | p2(all_2_3) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 133.64/18.51 | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_3, v0) |
% 133.64/18.51 | p2(v1))))))
% 133.64/18.51 |
% 133.64/18.51 | ALPHA: (1) implies:
% 133.64/18.51 | (2) ~ p2(all_2_1)
% 133.64/18.51 | (3) r1(all_2_14, all_2_1)
% 133.64/18.51 | (4) $i(all_2_5)
% 133.64/18.51 | (5) $i(all_2_4)
% 133.64/18.51 | (6) $i(all_2_3)
% 133.64/18.51 | (7) $i(all_2_1)
% 133.80/18.52 | (8) (r1(all_2_14, all_2_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 133.80/18.52 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~
% 133.80/18.52 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 133.80/18.52 | | ~ p2(v1) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~
% 133.80/18.52 | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.80/18.52 | p2(v6) | p2(v3) | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) &
% 133.80/18.52 | $i(v7) & ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) |
% 133.80/18.52 | (p2(v7) & r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7) &
% 133.80/18.52 | ~ p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~
% 133.80/18.52 | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) |
% 133.80/18.52 | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 133.80/18.52 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~
% 133.80/18.52 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v4,
% 133.80/18.52 | v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0,
% 133.80/18.52 | v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] : ?
% 133.80/18.52 | [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5, v6) &
% 133.80/18.52 | ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) & ! [v8:
% 133.80/18.52 | $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ p2(v8) | ~
% 133.80/18.52 | r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) | (r1(v3, v6) & ~
% 133.80/18.52 | p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) |
% 133.80/18.52 | ~ p2(v8) | ~ r1(v8, v9) | ~ r1(v6, v8) | p2(v9)))))) &
% 133.80/18.52 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 133.80/18.52 | ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 133.80/18.52 | p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0,
% 133.80/18.52 | v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ? [v5: $i]
% 133.80/18.52 | : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) & r1(v4,
% 133.80/18.52 | v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3, v5) & ~
% 133.80/18.52 | p2(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 133.80/18.52 | [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 133.80/18.52 | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~
% 133.80/18.52 | r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v1) |
% 133.80/18.52 | ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5,
% 133.80/18.52 | v6) & r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) &
% 133.80/18.52 | r1(v1, v5) & ~ p2(v6)) | (r1(v2, v5) & ~ p2(v5) & ! [v7:
% 133.80/18.52 | $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ p2(v7) | ~
% 133.80/18.52 | r1(v7, v8) | ~ r1(v5, v7) | p2(v8)))))) & ! [v0: $i] : !
% 133.80/18.52 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 133.80/18.52 | $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~
% 133.80/18.52 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | p2(v2) | ? [v4: $i] :
% 133.80/18.52 | ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4)
% 133.80/18.52 | & ~ p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6:
% 133.80/18.53 | $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~
% 133.80/18.53 | r1(v6, v7) | ~ r1(v5, v6) | p2(v7)))))) & ! [v0: $i] : !
% 133.80/18.53 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 133.80/18.53 | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 133.80/18.53 | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) | ? [v4: $i] : ? [v5:
% 133.80/18.53 | $i] : ($i(v5) & $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) & ~
% 133.80/18.53 | p2(v5)) | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6: $i]
% 133.80/18.53 | : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~
% 133.80/18.53 | r1(v6, v7) | ~ r1(v5, v6) | p2(v7))) | (r1(v1, v4) & ~
% 133.80/18.53 | p2(v4) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) |
% 133.80/18.53 | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v4, v6) | p2(v7)))))) &
% 133.80/18.53 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 133.80/18.53 | $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5,
% 133.80/18.53 | v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] : ($i(v4) &
% 133.80/18.53 | $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4)) |
% 133.80/18.53 | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4))))) & ! [v0: $i]
% 133.80/18.53 | : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) |
% 133.80/18.53 | ~ r1(all_2_5, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) &
% 133.80/18.53 | $i(v2) & ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3)) |
% 133.80/18.53 | (r1(v2, v3) & r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5:
% 133.80/18.53 | $i] : ( ~ $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) |
% 133.80/18.53 | ~ r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) &
% 133.80/18.53 | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i]
% 133.80/18.53 | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.80/18.53 | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 133.80/18.53 | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2)
% 133.80/18.53 | & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2)))) |
% 133.80/18.53 | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 133.80/18.53 | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.80/18.53 | p2(v1))))) | ((p2(all_2_14) | (p2(all_2_5) & r1(all_2_5,
% 133.80/18.53 | all_2_4) & r1(all_2_14, all_2_5) & ~ p2(all_2_4))) & ( ! [v0:
% 133.80/18.53 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~
% 133.80/18.53 | r1(all_2_14, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) &
% 133.80/18.53 | $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3))) |
% 133.80/18.53 | (r1(all_2_14, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i]
% 133.80/18.53 | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.80/18.53 | r1(all_2_3, v0) | p2(v1)))))
% 133.80/18.53 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0) | p2(v0) | ? [v1: $i] :
% 133.80/18.53 | ($i(v1) & r1(v0, v1) & ~ p2(v1) & ! [v2: $i] : ! [v3: $i] : ( ~
% 133.80/18.53 | $i(v3) | ~ $i(v2) | ~ p2(v2) | ~ r1(v2, v3) | ~ r1(v1, v2) |
% 133.80/18.53 | p2(v3))))
% 133.80/18.53 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_14, v0) | p2(v0) | ? [v1: $i]
% 133.80/18.53 | : ? [v2: $i] : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1)
% 133.80/18.53 | & ~ p2(v2)))
% 133.80/18.53 |
% 133.80/18.53 | GROUND_INST: instantiating (9) with all_2_1, simplifying with (2), (3), (7)
% 133.80/18.53 | gives:
% 133.80/18.53 | (11) ? [v0: $i] : ($i(v0) & r1(all_2_1, v0) & ~ p2(v0) & ! [v1: $i] : !
% 133.80/18.53 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ p2(v1) | ~ r1(v1, v2) | ~
% 133.80/18.53 | r1(v0, v1) | p2(v2)))
% 133.80/18.53 |
% 133.80/18.53 | DELTA: instantiating (11) with fresh symbol all_16_0 gives:
% 133.80/18.53 | (12) $i(all_16_0) & r1(all_2_1, all_16_0) & ~ p2(all_16_0) & ! [v0: $i] :
% 133.80/18.53 | ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.80/18.53 | r1(all_16_0, v0) | p2(v1))
% 133.80/18.53 |
% 133.80/18.53 | ALPHA: (12) implies:
% 133.80/18.53 | (13) ~ p2(all_16_0)
% 133.80/18.53 | (14) r1(all_2_1, all_16_0)
% 133.80/18.53 | (15) $i(all_16_0)
% 133.80/18.53 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~
% 133.80/18.53 | r1(v0, v1) | ~ r1(all_16_0, v0) | p2(v1))
% 133.80/18.53 |
% 133.80/18.53 | BETA: splitting (8) gives:
% 133.80/18.53 |
% 133.80/18.53 | Case 1:
% 133.80/18.53 | |
% 133.80/18.54 | | (17) r1(all_2_14, all_2_5) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 133.80/18.54 | | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~
% 133.80/18.54 | | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 133.80/18.54 | | | ~ p2(v1) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v1, v2) | ~
% 133.80/18.54 | | r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.80/18.54 | | p2(v6) | p2(v3) | p2(v2) | ? [v7: $i] : ? [v8: $i] : ($i(v8) &
% 133.80/18.54 | | $i(v7) & ((p2(v7) & r1(v7, v8) & r1(v6, v7) & ~ p2(v8)) |
% 133.80/18.54 | | (p2(v7) & r1(v7, v8) & r1(v3, v7) & ~ p2(v8)) | (r1(v4, v7) &
% 133.80/18.54 | | ~ p2(v7) & ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~
% 133.80/18.54 | | $i(v9) | ~ p2(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) |
% 133.80/18.54 | | p2(v10)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 133.80/18.54 | | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~
% 133.80/18.54 | | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v4,
% 133.80/18.54 | | v5) | ~ r1(v3, v4) | ~ r1(v1, v2) | ~ r1(v0, v3) | ~ r1(v0,
% 133.80/18.54 | | v1) | ~ r1(all_2_5, v0) | p2(v5) | p2(v2) | ? [v6: $i] : ?
% 133.80/18.54 | | [v7: $i] : ($i(v7) & $i(v6) & ((p2(v6) & r1(v6, v7) & r1(v5, v6) &
% 133.80/18.54 | | ~ p2(v7)) | (r1(v6, v7) & r1(v0, v6) & ~ p2(v7) & ! [v8:
% 133.80/18.54 | | $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ p2(v8) |
% 133.80/18.54 | | ~ r1(v8, v9) | ~ r1(v7, v8) | p2(v9))) | (r1(v3, v6) & ~
% 133.80/18.54 | | p2(v6) & ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8)
% 133.80/18.54 | | | ~ p2(v8) | ~ r1(v8, v9) | ~ r1(v6, v8) | p2(v9))))))
% 133.80/18.54 | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 133.80/18.54 | | $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 133.80/18.54 | | ~ p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~
% 133.80/18.54 | | r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ?
% 133.80/18.54 | | [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6)
% 133.80/18.54 | | & r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3,
% 133.80/18.54 | | v5) & ~ p2(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 133.80/18.54 | | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~
% 133.80/18.54 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v3, v4) | ~
% 133.80/18.54 | | r1(v2, v3) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.80/18.54 | | p2(v4) | p2(v1) | ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v5) &
% 133.80/18.54 | | ((p2(v5) & r1(v5, v6) & r1(v4, v5) & ~ p2(v6)) | (p2(v5) &
% 133.80/18.54 | | r1(v5, v6) & r1(v1, v5) & ~ p2(v6)) | (r1(v2, v5) & ~
% 133.80/18.54 | | p2(v5) & ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7)
% 133.80/18.54 | | | ~ p2(v7) | ~ r1(v7, v8) | ~ r1(v5, v7) | p2(v8))))))
% 133.80/18.54 | | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3)
% 133.80/18.54 | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p2(v1) | ~ r1(v1, v2) |
% 133.80/18.54 | | ~ r1(v0, v3) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v3) |
% 133.80/18.54 | | p2(v2) | ? [v4: $i] : ? [v5: $i] : ($i(v5) & $i(v4) & ((p2(v4) &
% 133.80/18.54 | | r1(v4, v5) & r1(v3, v4) & ~ p2(v5)) | (r1(v4, v5) & r1(v0,
% 133.80/18.54 | | v4) & ~ p2(v5) & ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) |
% 133.80/18.54 | | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) |
% 133.80/18.54 | | p2(v7)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 133.80/18.54 | | [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 133.80/18.54 | | p2(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 133.80/18.54 | | r1(all_2_5, v0) | p2(v3) | ? [v4: $i] : ? [v5: $i] : ($i(v5) &
% 133.80/18.54 | | $i(v4) & ((p2(v4) & r1(v4, v5) & r1(v3, v4) & ~ p2(v5)) |
% 133.80/18.54 | | (r1(v4, v5) & r1(v0, v4) & ~ p2(v5) & ! [v6: $i] : ! [v7:
% 133.80/18.54 | | $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6) | ~ r1(v6, v7) |
% 133.80/18.54 | | ~ r1(v5, v6) | p2(v7))) | (r1(v1, v4) & ~ p2(v4) & !
% 133.80/18.54 | | [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ p2(v6)
% 133.80/18.54 | | | ~ r1(v6, v7) | ~ r1(v4, v6) | p2(v7)))))) & ! [v0:
% 133.80/18.54 | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 133.80/18.54 | | $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~
% 133.80/18.54 | | r1(all_2_5, v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] :
% 133.80/18.54 | | ($i(v4) & $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4))
% 133.80/18.54 | | | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4))))) & ! [v0:
% 133.80/18.54 | | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0,
% 133.80/18.54 | | v1) | ~ r1(all_2_5, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] :
% 133.80/18.54 | | ($i(v3) & $i(v2) & ((p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3))
% 133.80/18.54 | | | (r1(v2, v3) & r1(v0, v2) & ~ p2(v3) & ! [v4: $i] : ! [v5:
% 133.80/18.54 | | $i] : ( ~ $i(v5) | ~ $i(v4) | ~ p2(v4) | ~ r1(v4, v5) |
% 133.80/18.54 | | ~ r1(v3, v4) | p2(v5)))))) & ((r1(all_2_4, all_2_3) &
% 133.80/18.54 | | r1(all_2_5, all_2_4) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1:
% 133.80/18.54 | | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.80/18.54 | | r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 133.80/18.54 | | r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2)
% 133.80/18.54 | | & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~ p2(v2)))) |
% 133.80/18.54 | | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 133.80/18.54 | | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.80/18.54 | | p2(v1))))
% 133.80/18.54 | |
% 133.80/18.54 | | ALPHA: (17) implies:
% 133.80/18.54 | | (18) r1(all_2_14, all_2_5)
% 133.80/18.54 | | (19) (r1(all_2_4, all_2_3) & r1(all_2_5, all_2_4) & ~ p2(all_2_3) & !
% 133.80/18.54 | | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~
% 133.80/18.54 | | r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~
% 133.80/18.54 | | $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i]
% 133.80/18.54 | | : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~
% 133.80/18.54 | | p2(v2)))) | ( ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~
% 133.80/18.54 | | $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5,
% 133.80/18.54 | | v0) | p2(v1)))
% 133.80/18.54 | | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) |
% 133.80/18.54 | | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~
% 133.80/18.54 | | r1(all_2_5, v0) | p2(v2) | p2(v1) | ? [v3: $i] : ? [v4: $i] :
% 133.80/18.54 | | ($i(v4) & $i(v3) & ((p2(v3) & r1(v3, v4) & r1(v2, v3) & ~ p2(v4))
% 133.80/18.54 | | | (p2(v3) & r1(v3, v4) & r1(v1, v3) & ~ p2(v4)))))
% 133.80/18.54 | | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 133.80/18.54 | | : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 133.80/18.54 | | p2(v1) | ~ r1(v1, v2) | ~ r1(v0, v4) | ~ r1(v0, v3) | ~ r1(v0,
% 133.80/18.54 | | v1) | ~ r1(all_2_5, v0) | p2(v4) | p2(v3) | p2(v2) | ? [v5:
% 133.80/18.54 | | $i] : ? [v6: $i] : ($i(v6) & $i(v5) & ((p2(v5) & r1(v5, v6) &
% 133.80/18.54 | | r1(v4, v5) & ~ p2(v6)) | (p2(v5) & r1(v5, v6) & r1(v3, v5)
% 133.80/18.54 | | & ~ p2(v6)))))
% 133.80/18.54 | |
% 133.80/18.54 | | GROUND_INST: instantiating (10) with all_2_5, simplifying with (4), (18)
% 133.80/18.54 | | gives:
% 133.80/18.54 | | (22) p2(all_2_5) | ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0)
% 133.80/18.54 | | & r1(v0, v1) & r1(all_2_5, v0) & ~ p2(v1))
% 133.80/18.54 | |
% 133.80/18.54 | | BETA: splitting (19) gives:
% 133.80/18.54 | |
% 133.80/18.54 | | Case 1:
% 133.80/18.54 | | |
% 133.80/18.54 | | | (23) r1(all_2_4, all_2_3) & r1(all_2_5, all_2_4) & ~ p2(all_2_3) & !
% 133.80/18.54 | | | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~
% 133.80/18.54 | | | r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1)) & ! [v0: $i] : ( ~
% 133.80/18.54 | | | $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1: $i] : ? [v2: $i]
% 133.80/18.54 | | | : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) & r1(v0, v1) & ~
% 133.80/18.54 | | | p2(v2)))
% 133.80/18.54 | | |
% 133.80/18.54 | | | ALPHA: (23) implies:
% 133.80/18.54 | | | (24) ~ p2(all_2_3)
% 133.80/18.54 | | | (25) r1(all_2_5, all_2_4)
% 133.80/18.55 | | | (26) r1(all_2_4, all_2_3)
% 133.80/18.55 | | | (27) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_5, v0) | p2(v0) | ? [v1:
% 133.80/18.55 | | | $i] : ? [v2: $i] : ($i(v2) & $i(v1) & p2(v1) & r1(v1, v2) &
% 133.80/18.55 | | | r1(v0, v1) & ~ p2(v2)))
% 133.80/18.55 | | | (28) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) |
% 133.80/18.55 | | | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1))
% 133.80/18.55 | | |
% 133.80/18.55 | | | GROUND_INST: instantiating (27) with all_2_4, simplifying with (5), (25)
% 133.80/18.55 | | | gives:
% 133.80/18.55 | | | (29) p2(all_2_4) | ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) &
% 133.80/18.55 | | | p2(v0) & r1(v0, v1) & r1(all_2_4, v0) & ~ p2(v1))
% 133.80/18.55 | | |
% 133.80/18.55 | | | BETA: splitting (29) gives:
% 133.80/18.55 | | |
% 133.80/18.55 | | | Case 1:
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | (30) p2(all_2_4)
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | GROUND_INST: instantiating (20) with all_2_4, all_2_3, all_2_3,
% 133.80/18.55 | | | | simplifying with (5), (6), (24), (25), (26), (30) gives:
% 133.80/18.55 | | | | (31) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0,
% 133.80/18.55 | | | | v1) & r1(all_2_3, v0) & ~ p2(v1))
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | DELTA: instantiating (31) with fresh symbols all_130_0, all_130_1 gives:
% 133.80/18.55 | | | | (32) $i(all_130_0) & $i(all_130_1) & p2(all_130_1) & r1(all_130_1,
% 133.80/18.55 | | | | all_130_0) & r1(all_2_3, all_130_1) & ~ p2(all_130_0)
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | ALPHA: (32) implies:
% 133.80/18.55 | | | | (33) ~ p2(all_130_0)
% 133.80/18.55 | | | | (34) r1(all_2_3, all_130_1)
% 133.80/18.55 | | | | (35) r1(all_130_1, all_130_0)
% 133.80/18.55 | | | | (36) p2(all_130_1)
% 133.80/18.55 | | | | (37) $i(all_130_1)
% 133.80/18.55 | | | | (38) $i(all_130_0)
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | GROUND_INST: instantiating (28) with all_130_1, all_130_0, simplifying
% 133.80/18.55 | | | | with (33), (34), (35), (36), (37), (38) gives:
% 133.80/18.55 | | | | (39) $false
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | CLOSE: (39) is inconsistent.
% 133.80/18.55 | | | |
% 133.80/18.55 | | | Case 2:
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | (40) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0,
% 133.80/18.55 | | | | v1) & r1(all_2_4, v0) & ~ p2(v1))
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | DELTA: instantiating (40) with fresh symbols all_125_0, all_125_1 gives:
% 133.80/18.55 | | | | (41) $i(all_125_0) & $i(all_125_1) & p2(all_125_1) & r1(all_125_1,
% 133.80/18.55 | | | | all_125_0) & r1(all_2_4, all_125_1) & ~ p2(all_125_0)
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | ALPHA: (41) implies:
% 133.80/18.55 | | | | (42) ~ p2(all_125_0)
% 133.80/18.55 | | | | (43) r1(all_2_4, all_125_1)
% 133.80/18.55 | | | | (44) r1(all_125_1, all_125_0)
% 133.80/18.55 | | | | (45) p2(all_125_1)
% 133.80/18.55 | | | | (46) $i(all_125_1)
% 133.80/18.55 | | | | (47) $i(all_125_0)
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | GROUND_INST: instantiating (21) with all_2_4, all_125_1, all_125_0,
% 133.80/18.55 | | | | all_2_3, all_2_3, simplifying with (5), (6), (24), (25),
% 133.80/18.55 | | | | (26), (42), (43), (44), (45), (46), (47) gives:
% 133.80/18.55 | | | | (48) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0,
% 133.80/18.55 | | | | v1) & r1(all_2_3, v0) & ~ p2(v1))
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | DELTA: instantiating (48) with fresh symbols all_132_0, all_132_1 gives:
% 133.80/18.55 | | | | (49) $i(all_132_0) & $i(all_132_1) & p2(all_132_1) & r1(all_132_1,
% 133.80/18.55 | | | | all_132_0) & r1(all_2_3, all_132_1) & ~ p2(all_132_0)
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | ALPHA: (49) implies:
% 133.80/18.55 | | | | (50) ~ p2(all_132_0)
% 133.80/18.55 | | | | (51) r1(all_2_3, all_132_1)
% 133.80/18.55 | | | | (52) r1(all_132_1, all_132_0)
% 133.80/18.55 | | | | (53) p2(all_132_1)
% 133.80/18.55 | | | | (54) $i(all_132_1)
% 133.80/18.55 | | | | (55) $i(all_132_0)
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | GROUND_INST: instantiating (28) with all_132_1, all_132_0, simplifying
% 133.80/18.55 | | | | with (50), (51), (52), (53), (54), (55) gives:
% 133.80/18.55 | | | | (56) $false
% 133.80/18.55 | | | |
% 133.80/18.55 | | | | CLOSE: (56) is inconsistent.
% 133.80/18.55 | | | |
% 133.80/18.55 | | | End of split
% 133.80/18.55 | | |
% 133.80/18.55 | | Case 2:
% 133.80/18.55 | | |
% 133.80/18.55 | | | (57) ~ p2(all_2_5) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 133.80/18.55 | | | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_5, v0) |
% 133.80/18.55 | | | p2(v1))
% 133.80/18.55 | | |
% 133.80/18.55 | | | ALPHA: (57) implies:
% 133.80/18.56 | | | (58) ~ p2(all_2_5)
% 133.80/18.56 | | | (59) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) |
% 133.80/18.56 | | | ~ r1(v0, v1) | ~ r1(all_2_5, v0) | p2(v1))
% 133.80/18.56 | | |
% 133.80/18.56 | | | BETA: splitting (22) gives:
% 133.80/18.56 | | |
% 133.80/18.56 | | | Case 1:
% 133.80/18.56 | | | |
% 133.80/18.56 | | | | (60) p2(all_2_5)
% 133.80/18.56 | | | |
% 133.80/18.56 | | | | PRED_UNIFY: (58), (60) imply:
% 133.80/18.56 | | | | (61) $false
% 133.80/18.56 | | | |
% 133.80/18.56 | | | | CLOSE: (61) is inconsistent.
% 133.80/18.56 | | | |
% 133.80/18.56 | | | Case 2:
% 133.80/18.56 | | | |
% 133.80/18.56 | | | | (62) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0,
% 133.80/18.56 | | | | v1) & r1(all_2_5, v0) & ~ p2(v1))
% 133.80/18.56 | | | |
% 133.80/18.56 | | | | DELTA: instantiating (62) with fresh symbols all_101_0, all_101_1 gives:
% 133.80/18.56 | | | | (63) $i(all_101_0) & $i(all_101_1) & p2(all_101_1) & r1(all_101_1,
% 133.80/18.56 | | | | all_101_0) & r1(all_2_5, all_101_1) & ~ p2(all_101_0)
% 133.80/18.56 | | | |
% 133.80/18.56 | | | | ALPHA: (63) implies:
% 133.80/18.56 | | | | (64) ~ p2(all_101_0)
% 133.80/18.56 | | | | (65) r1(all_2_5, all_101_1)
% 133.80/18.56 | | | | (66) r1(all_101_1, all_101_0)
% 133.80/18.56 | | | | (67) p2(all_101_1)
% 133.80/18.56 | | | | (68) $i(all_101_1)
% 133.80/18.56 | | | | (69) $i(all_101_0)
% 133.80/18.56 | | | |
% 133.80/18.56 | | | | GROUND_INST: instantiating (59) with all_101_1, all_101_0, simplifying
% 133.80/18.56 | | | | with (64), (65), (66), (67), (68), (69) gives:
% 133.80/18.56 | | | | (70) $false
% 133.80/18.56 | | | |
% 133.80/18.56 | | | | CLOSE: (70) is inconsistent.
% 133.80/18.56 | | | |
% 133.80/18.56 | | | End of split
% 133.80/18.56 | | |
% 133.80/18.56 | | End of split
% 133.80/18.56 | |
% 133.80/18.56 | Case 2:
% 133.80/18.56 | |
% 133.80/18.56 | | (71) (p2(all_2_14) | (p2(all_2_5) & r1(all_2_5, all_2_4) & r1(all_2_14,
% 133.80/18.56 | | all_2_5) & ~ p2(all_2_4))) & ( ! [v0: $i] : ! [v1: $i] : ( ~
% 133.80/18.56 | | $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_14, v0) |
% 133.80/18.56 | | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & p2(v2) &
% 133.80/18.56 | | r1(v2, v3) & r1(v1, v2) & ~ p2(v3))) | (r1(all_2_14, all_2_3)
% 133.80/18.56 | | & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 133.80/18.56 | | $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~ r1(all_2_3, v0) |
% 133.80/18.56 | | p2(v1))))
% 133.80/18.56 | |
% 133.80/18.56 | | ALPHA: (71) implies:
% 133.80/18.56 | | (72) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) |
% 133.80/18.56 | | ~ r1(all_2_14, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3)
% 133.80/18.56 | | & $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~ p2(v3))) |
% 133.80/18.56 | | (r1(all_2_14, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i]
% 133.80/18.56 | | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.80/18.56 | | r1(all_2_3, v0) | p2(v1)))
% 133.80/18.56 | |
% 133.80/18.56 | | BETA: splitting (72) gives:
% 133.80/18.56 | |
% 133.80/18.56 | | Case 1:
% 133.80/18.56 | | |
% 133.80/18.56 | | | (73) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1)
% 133.80/18.56 | | | | ~ r1(all_2_14, v0) | p2(v1) | ? [v2: $i] : ? [v3: $i] :
% 133.80/18.56 | | | ($i(v3) & $i(v2) & p2(v2) & r1(v2, v3) & r1(v1, v2) & ~
% 133.80/18.56 | | | p2(v3)))
% 133.80/18.56 | | |
% 133.80/18.56 | | | GROUND_INST: instantiating (73) with all_2_1, all_16_0, simplifying with
% 133.80/18.56 | | | (3), (7), (13), (14), (15) gives:
% 133.80/18.56 | | | (74) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, v1)
% 133.80/18.56 | | | & r1(all_16_0, v0) & ~ p2(v1))
% 133.80/18.56 | | |
% 133.80/18.56 | | | DELTA: instantiating (74) with fresh symbols all_100_0, all_100_1 gives:
% 133.80/18.56 | | | (75) $i(all_100_0) & $i(all_100_1) & p2(all_100_1) & r1(all_100_1,
% 133.80/18.56 | | | all_100_0) & r1(all_16_0, all_100_1) & ~ p2(all_100_0)
% 133.80/18.56 | | |
% 133.80/18.56 | | | ALPHA: (75) implies:
% 133.80/18.56 | | | (76) ~ p2(all_100_0)
% 133.80/18.56 | | | (77) r1(all_16_0, all_100_1)
% 133.80/18.56 | | | (78) r1(all_100_1, all_100_0)
% 133.80/18.56 | | | (79) p2(all_100_1)
% 133.80/18.56 | | | (80) $i(all_100_1)
% 133.80/18.56 | | | (81) $i(all_100_0)
% 133.80/18.56 | | |
% 133.80/18.56 | | | GROUND_INST: instantiating (16) with all_100_1, all_100_0, simplifying
% 133.80/18.56 | | | with (76), (77), (78), (79), (80), (81) gives:
% 133.80/18.56 | | | (82) $false
% 133.80/18.56 | | |
% 133.80/18.56 | | | CLOSE: (82) is inconsistent.
% 133.80/18.56 | | |
% 133.80/18.56 | | Case 2:
% 133.80/18.56 | | |
% 133.80/18.56 | | | (83) r1(all_2_14, all_2_3) & ~ p2(all_2_3) & ! [v0: $i] : ! [v1: $i]
% 133.80/18.56 | | | : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) | ~ r1(v0, v1) | ~
% 133.80/18.56 | | | r1(all_2_3, v0) | p2(v1))
% 133.80/18.56 | | |
% 133.80/18.56 | | | ALPHA: (83) implies:
% 133.80/18.56 | | | (84) ~ p2(all_2_3)
% 133.80/18.56 | | | (85) r1(all_2_14, all_2_3)
% 133.80/18.56 | | | (86) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p2(v0) |
% 133.80/18.56 | | | ~ r1(v0, v1) | ~ r1(all_2_3, v0) | p2(v1))
% 133.80/18.56 | | |
% 133.80/18.56 | | | GROUND_INST: instantiating (10) with all_2_3, simplifying with (6), (84),
% 133.80/18.56 | | | (85) gives:
% 133.80/18.56 | | | (87) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p2(v0) & r1(v0, v1)
% 133.80/18.56 | | | & r1(all_2_3, v0) & ~ p2(v1))
% 133.80/18.56 | | |
% 133.80/18.56 | | | DELTA: instantiating (87) with fresh symbols all_104_0, all_104_1 gives:
% 133.80/18.56 | | | (88) $i(all_104_0) & $i(all_104_1) & p2(all_104_1) & r1(all_104_1,
% 133.80/18.56 | | | all_104_0) & r1(all_2_3, all_104_1) & ~ p2(all_104_0)
% 133.80/18.56 | | |
% 133.80/18.56 | | | ALPHA: (88) implies:
% 133.80/18.56 | | | (89) ~ p2(all_104_0)
% 133.80/18.56 | | | (90) r1(all_2_3, all_104_1)
% 133.80/18.56 | | | (91) r1(all_104_1, all_104_0)
% 133.80/18.56 | | | (92) p2(all_104_1)
% 133.80/18.56 | | | (93) $i(all_104_1)
% 133.80/18.56 | | | (94) $i(all_104_0)
% 133.80/18.56 | | |
% 133.80/18.57 | | | GROUND_INST: instantiating (86) with all_104_1, all_104_0, simplifying
% 133.80/18.57 | | | with (89), (90), (91), (92), (93), (94) gives:
% 133.80/18.57 | | | (95) $false
% 133.80/18.57 | | |
% 133.80/18.57 | | | CLOSE: (95) is inconsistent.
% 133.80/18.57 | | |
% 133.80/18.57 | | End of split
% 133.80/18.57 | |
% 133.80/18.57 | End of split
% 133.80/18.57 |
% 133.80/18.57 End of proof
% 133.80/18.57 % SZS output end Proof for theBenchmark
% 133.80/18.57
% 133.80/18.57 17945ms
%------------------------------------------------------------------------------