TSTP Solution File: LCL658+1.015 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL658+1.015 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n006.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 08:12:10 EDT 2023
% Result : Theorem 137.14s 18.98s
% Output : Proof 137.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL658+1.015 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 18:34:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.63 ________ _____
% 0.22/0.63 ___ __ \_________(_)________________________________
% 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.63
% 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.63 (2023-06-19)
% 0.22/0.63
% 0.22/0.63 (c) Philipp Rümmer, 2009-2023
% 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.63 Amanda Stjerna.
% 0.22/0.63 Free software under BSD-3-Clause.
% 0.22/0.63
% 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.63
% 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.64 Running up to 7 provers in parallel.
% 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.20/1.35 Prover 4: Preprocessing ...
% 4.20/1.35 Prover 1: Preprocessing ...
% 4.56/1.41 Prover 2: Preprocessing ...
% 4.56/1.41 Prover 6: Preprocessing ...
% 4.56/1.41 Prover 3: Preprocessing ...
% 4.56/1.41 Prover 0: Preprocessing ...
% 4.56/1.41 Prover 5: Preprocessing ...
% 8.03/1.85 Prover 2: Proving ...
% 8.71/1.94 Prover 5: Proving ...
% 12.35/2.48 Prover 6: Proving ...
% 13.79/2.63 Prover 1: Constructing countermodel ...
% 13.79/2.64 Prover 3: Constructing countermodel ...
% 15.86/2.92 Prover 0: Proving ...
% 15.86/2.95 Prover 4: Constructing countermodel ...
% 72.71/10.42 Prover 2: stopped
% 73.80/10.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.67/10.63 Prover 7: Preprocessing ...
% 75.54/10.70 Prover 7: Warning: ignoring some quantifiers
% 75.54/10.72 Prover 7: Constructing countermodel ...
% 100.67/13.99 Prover 5: stopped
% 100.67/14.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 101.93/14.20 Prover 8: Preprocessing ...
% 104.14/14.45 Prover 8: Warning: ignoring some quantifiers
% 104.14/14.46 Prover 8: Constructing countermodel ...
% 115.92/16.01 Prover 1: stopped
% 115.92/16.01 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 116.53/16.16 Prover 9: Preprocessing ...
% 118.82/16.44 Prover 9: Constructing countermodel ...
% 129.28/17.91 Prover 6: stopped
% 129.28/17.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 131.03/18.07 Prover 10: Preprocessing ...
% 131.03/18.11 Prover 10: Warning: ignoring some quantifiers
% 131.03/18.11 Prover 10: Constructing countermodel ...
% 136.75/18.81 Prover 10: Found proof (size 50)
% 136.75/18.81 Prover 10: proved (885ms)
% 136.75/18.81 Prover 9: stopped
% 136.75/18.81 Prover 8: stopped
% 136.75/18.81 Prover 4: stopped
% 136.75/18.81 Prover 3: stopped
% 136.75/18.82 Prover 7: stopped
% 137.14/18.98 Prover 0: stopped
% 137.14/18.98
% 137.14/18.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 137.14/18.98
% 137.14/18.98 % SZS output start Proof for theBenchmark
% 137.14/18.98 Assumptions after simplification:
% 137.14/18.98 ---------------------------------
% 137.14/18.98
% 137.14/18.98 (main)
% 137.31/19.02 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 137.31/19.02 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 137.31/19.02 ($i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 137.33/19.02 $i(v2) & $i(v1) & $i(v0) & r1(v8, v10) & r1(v8, v9) & r1(v7, v8) & r1(v6,
% 137.33/19.02 v7) & r1(v5, v6) & r1(v4, v5) & r1(v3, v4) & r1(v2, v3) & r1(v1, v2) &
% 137.33/19.02 r1(v0, v1) & ~ p1(v10) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : !
% 137.33/19.02 [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : !
% 137.33/19.02 [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : !
% 137.33/19.02 [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ $i(v26) | ~ $i(v25) | ~
% 137.33/19.02 $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) |
% 137.33/19.02 ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~
% 137.33/19.02 $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ r1(v25, v26) | ~ r1(v24, v25) | ~
% 137.33/19.02 r1(v23, v24) | ~ r1(v22, v23) | ~ r1(v21, v22) | ~ r1(v20, v21) | ~
% 137.33/19.02 r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~
% 137.33/19.02 r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~
% 137.33/19.02 r1(v11, v12) | ~ r1(v0, v11) | p1(v26) | ? [v27: $i] : ($i(v27) &
% 137.33/19.03 r1(v24, v27) & ~ p1(v27))) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i]
% 137.33/19.03 : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] :
% 137.33/19.03 ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] :
% 137.33/19.03 ! [v24: $i] : ! [v25: $i] : ( ~ $i(v25) | ~ $i(v24) | ~ $i(v23) | ~
% 137.33/19.03 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) |
% 137.33/19.03 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~
% 137.33/19.03 $i(v11) | ~ r1(v24, v25) | ~ r1(v23, v24) | ~ r1(v22, v23) | ~ r1(v21,
% 137.33/19.03 v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17,
% 137.33/19.03 v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13,
% 137.33/19.03 v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v25) | ?
% 137.33/19.03 [v26: $i] : ($i(v26) & r1(v23, v26) & ~ p1(v26))) & ! [v11: $i] : !
% 137.33/19.03 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : !
% 137.33/19.03 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : !
% 137.33/19.03 [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ $i(v24) | ~ $i(v23) | ~
% 137.33/19.03 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) |
% 137.33/19.03 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~
% 137.33/19.03 $i(v11) | ~ r1(v23, v24) | ~ r1(v22, v23) | ~ r1(v21, v22) | ~ r1(v20,
% 137.33/19.03 v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16,
% 137.33/19.03 v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12,
% 137.33/19.03 v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v24) | ? [v25: $i] :
% 137.33/19.03 ($i(v25) & r1(v22, v25) & ~ p1(v25))) & ! [v11: $i] : ! [v12: $i] : !
% 137.33/19.03 [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : !
% 137.33/19.03 [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 137.33/19.03 [v23: $i] : ( ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19)
% 137.33/19.03 | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~
% 137.33/19.03 $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ r1(v22, v23) | ~ r1(v21, v22) | ~
% 137.33/19.03 r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~
% 137.33/19.03 r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~
% 137.33/19.03 r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v23) | ? [v24: $i] :
% 137.33/19.03 ($i(v24) & r1(v21, v24) & ~ p1(v24))) & ! [v11: $i] : ! [v12: $i] : !
% 137.33/19.03 [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : !
% 137.33/19.03 [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~
% 137.33/19.03 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) |
% 137.33/19.03 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~
% 137.33/19.03 $i(v11) | ~ r1(v21, v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18,
% 137.33/19.03 v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14,
% 137.33/19.03 v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0,
% 137.33/19.03 v11) | p1(v22) | ? [v23: $i] : ($i(v23) & r1(v20, v23) & ~ p1(v23))) &
% 137.33/19.03 ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] :
% 137.33/19.03 ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : !
% 137.33/19.03 [v21: $i] : ( ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17)
% 137.33/19.03 | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~
% 137.33/19.03 $i(v11) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17,
% 137.33/19.03 v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13,
% 137.33/19.03 v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v21) | ?
% 137.33/19.03 [v22: $i] : ($i(v22) & r1(v19, v22) & ~ p1(v22))) & ! [v11: $i] : !
% 137.33/19.03 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : !
% 137.33/19.03 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( ~ $i(v20) | ~
% 137.33/19.03 $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) |
% 137.33/19.03 ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ p1(v18) | ~ r1(v18, v20) | ~
% 137.33/19.03 r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~
% 137.33/19.03 r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~
% 137.33/19.03 r1(v0, v11) | p1(v20) | ? [v21: $i] : ? [v22: $i] : ($i(v22) & $i(v21) &
% 137.33/19.03 ((p1(v21) & r1(v21, v22) & r1(v19, v21) & ~ p1(v22)) | (p1(v21) &
% 137.33/19.03 r1(v21, v22) & r1(v18, v21) & ~ p1(v22) & ! [v23: $i] : ! [v24:
% 137.33/19.03 $i] : ! [v25: $i] : ( ~ $i(v25) | ~ $i(v24) | ~ $i(v23) | ~
% 137.33/19.03 p1(v24) | ~ r1(v24, v25) | ~ r1(v23, v24) | ~ r1(v21, v23) |
% 137.33/19.03 p1(v25) | p1(v23)) & ! [v23: $i] : ! [v24: $i] : ! [v25: $i] :
% 137.33/19.03 ( ~ $i(v25) | ~ $i(v24) | ~ $i(v23) | ~ p1(v24) | ~ r1(v24, v25)
% 137.33/19.03 | ~ r1(v23, v24) | ~ r1(v21, v23) | p1(v25) | ? [v26: $i] :
% 137.33/19.03 ($i(v26) & r1(v23, v26) & ~ p1(v26))))))) & ! [v11: $i] : !
% 137.33/19.03 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : !
% 137.33/19.03 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( ~ $i(v20) | ~
% 137.33/19.03 $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) |
% 137.33/19.03 ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ r1(v19, v20) | ~ r1(v18, v19) |
% 137.33/19.03 ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~
% 137.33/19.03 r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) |
% 137.33/19.03 p1(v20) | ? [v21: $i] : ? [v22: $i] : ($i(v22) & $i(v21) & ((p1(v21) &
% 137.33/19.03 r1(v21, v22) & r1(v20, v21) & ~ p1(v22)) | (r1(v18, v21) & ~
% 137.33/19.03 p1(v21) & ! [v23: $i] : ! [v24: $i] : ( ~ $i(v24) | ~ $i(v23) |
% 137.33/19.03 ~ p1(v23) | ~ r1(v23, v24) | ~ r1(v21, v23) | p1(v24)))))) & !
% 137.33/19.03 [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : !
% 137.33/19.03 [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ( ~ $i(v19) | ~
% 137.33/19.03 $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) |
% 137.33/19.03 ~ $i(v12) | ~ $i(v11) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16,
% 137.33/19.03 v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12,
% 137.33/19.03 v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v19) | ? [v20: $i] :
% 137.33/19.04 ($i(v20) & r1(v17, v20) & ~ p1(v20))) & ! [v11: $i] : ! [v12: $i] : !
% 137.33/19.04 [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : !
% 137.33/19.04 [v18: $i] : ! [v19: $i] : ( ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~
% 137.33/19.04 $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) |
% 137.33/19.04 ~ r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~
% 137.33/19.04 r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~
% 137.33/19.04 r1(v0, v11) | p1(v18) | ? [v20: $i] : ($i(v20) & ((r1(v19, v20) & ~
% 137.33/19.04 p1(v20)) | (r1(v18, v20) & ~ p1(v20) & ! [v21: $i] : ! [v22: $i]
% 137.33/19.04 : ( ~ $i(v22) | ~ $i(v21) | ~ p1(v21) | ~ r1(v21, v22) | ~
% 137.33/19.04 r1(v20, v21) | p1(v22)))))) & ! [v11: $i] : ! [v12: $i] : !
% 137.33/19.04 [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : !
% 137.33/19.04 [v18: $i] : ( ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14)
% 137.33/19.04 | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ r1(v17, v18) | ~ r1(v16, v17)
% 137.33/19.04 | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) |
% 137.33/19.04 ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v18) | ? [v19: $i] : ($i(v19) &
% 137.33/19.04 r1(v16, v19) & ~ p1(v19))) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i]
% 137.33/19.04 : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) |
% 137.33/19.04 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11)
% 137.33/19.04 | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) |
% 137.33/19.04 ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v17) | ? [v18: $i]
% 137.33/19.04 : ($i(v18) & r1(v15, v18) & ~ p1(v18))) & ! [v11: $i] : ! [v12: $i] :
% 137.33/19.04 ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ( ~ $i(v16) | ~
% 137.33/19.04 $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ r1(v15,
% 137.33/19.04 v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11,
% 137.33/19.04 v12) | ~ r1(v0, v11) | p1(v16) | ? [v17: $i] : ($i(v17) & r1(v14, v17)
% 137.33/19.04 & ~ p1(v17))) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14:
% 137.33/19.04 $i] : ! [v15: $i] : ( ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) |
% 137.33/19.04 ~ $i(v11) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~
% 137.33/19.04 r1(v11, v12) | ~ r1(v0, v11) | p1(v15) | ? [v16: $i] : ($i(v16) &
% 137.33/19.04 r1(v13, v16) & ~ p1(v16))) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i]
% 137.33/19.04 : ! [v14: $i] : ( ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~
% 137.33/19.04 r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) |
% 137.33/19.04 p1(v14) | ? [v15: $i] : ($i(v15) & r1(v12, v15) & ~ p1(v15))) & ! [v11:
% 137.33/19.04 $i] : ! [v12: $i] : ! [v13: $i] : ( ~ $i(v13) | ~ $i(v12) | ~ $i(v11)
% 137.33/19.04 | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v0, v11) | p1(v13) | ? [v14:
% 137.33/19.04 $i] : ($i(v14) & r1(v11, v14) & ~ p1(v14))) & ! [v11: $i] : ( ~
% 137.33/19.04 $i(v11) | ~ r1(v9, v11) | p1(v11)) & ! [v11: $i] : ( ~ $i(v11) | ~
% 137.33/19.04 r1(v8, v11) | p1(v11) | ? [v12: $i] : ? [v13: $i] : ($i(v13) & $i(v12) &
% 137.33/19.04 p1(v12) & r1(v12, v13) & r1(v11, v12) & ~ p1(v13))))
% 137.33/19.04
% 137.33/19.04 Further assumptions not needed in the proof:
% 137.33/19.04 --------------------------------------------
% 137.33/19.04 reflexivity
% 137.33/19.04
% 137.33/19.04 Those formulas are unsatisfiable:
% 137.33/19.04 ---------------------------------
% 137.33/19.04
% 137.33/19.04 Begin of proof
% 137.33/19.04 |
% 137.33/19.04 | DELTA: instantiating (main) with fresh symbols all_3_0, all_3_1, all_3_2,
% 137.33/19.04 | all_3_3, all_3_4, all_3_5, all_3_6, all_3_7, all_3_8, all_3_9, all_3_10
% 137.33/19.04 | gives:
% 137.33/19.08 | (1) $i(all_3_0) & $i(all_3_1) & $i(all_3_2) & $i(all_3_3) & $i(all_3_4) &
% 137.33/19.08 | $i(all_3_5) & $i(all_3_6) & $i(all_3_7) & $i(all_3_8) & $i(all_3_9) &
% 137.33/19.08 | $i(all_3_10) & r1(all_3_2, all_3_0) & r1(all_3_2, all_3_1) &
% 137.33/19.08 | r1(all_3_3, all_3_2) & r1(all_3_4, all_3_3) & r1(all_3_5, all_3_4) &
% 137.33/19.08 | r1(all_3_6, all_3_5) & r1(all_3_7, all_3_6) & r1(all_3_8, all_3_7) &
% 137.33/19.08 | r1(all_3_9, all_3_8) & r1(all_3_10, all_3_9) & ~ p1(all_3_0) & ! [v0:
% 137.33/19.08 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 137.33/19.08 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 137.33/19.08 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] :
% 137.33/19.08 | ! [v15: $i] : ( ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~
% 137.33/19.08 | $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6)
% 137.33/19.08 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 137.33/19.08 | $i(v0) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~
% 137.33/19.08 | r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~
% 137.33/19.08 | r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 137.33/19.08 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 137.33/19.08 | r1(all_3_10, v0) | p1(v15) | ? [v16: $i] : ($i(v16) & r1(v13, v16) &
% 137.33/19.08 | ~ p1(v16))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 137.33/19.08 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 137.33/19.08 | $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : !
% 137.33/19.08 | [v13: $i] : ! [v14: $i] : ( ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~
% 137.33/19.08 | $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6)
% 137.33/19.08 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 137.33/19.08 | $i(v0) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~
% 137.33/19.08 | r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~
% 137.33/19.08 | r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 137.33/19.08 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) |
% 137.33/19.08 | p1(v14) | ? [v15: $i] : ($i(v15) & r1(v12, v15) & ~ p1(v15))) & !
% 137.33/19.08 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 137.33/19.08 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 137.33/19.08 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ $i(v13) |
% 137.33/19.08 | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~
% 137.33/19.08 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 137.33/19.08 | ~ $i(v1) | ~ $i(v0) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10,
% 137.33/19.08 | v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6,
% 137.33/19.08 | v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3)
% 137.33/19.08 | | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v13) | ?
% 137.33/19.08 | [v14: $i] : ($i(v14) & r1(v11, v14) & ~ p1(v14))) & ! [v0: $i] : !
% 137.33/19.08 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 137.33/19.08 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 137.33/19.08 | [v11: $i] : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~
% 137.33/19.08 | $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 137.33/19.08 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v11, v12) | ~
% 137.33/19.08 | r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~
% 137.33/19.08 | r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 137.33/19.08 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) |
% 137.33/19.08 | p1(v12) | ? [v13: $i] : ($i(v13) & r1(v10, v13) & ~ p1(v13))) & !
% 137.33/19.08 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 137.33/19.08 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 137.33/19.08 | [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~
% 137.33/19.08 | $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 137.33/19.08 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v10, v11) | ~ r1(v9, v10) |
% 137.33/19.08 | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~
% 137.33/19.08 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 137.33/19.08 | r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v11) | ? [v12: $i] : ($i(v12)
% 137.33/19.09 | & r1(v9, v12) & ~ p1(v12))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 137.33/19.09 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 137.33/19.09 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~
% 137.33/19.09 | $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 137.33/19.09 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v9, v10) | ~
% 137.33/19.09 | r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~
% 137.33/19.09 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 137.33/19.09 | r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v10) | ? [v11: $i] : ($i(v11)
% 137.33/19.09 | & r1(v8, v11) & ~ p1(v11))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 137.33/19.09 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 137.33/19.09 | $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ $i(v7)
% 137.33/19.09 | | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 137.33/19.09 | $i(v1) | ~ $i(v0) | ~ p1(v7) | ~ r1(v7, v9) | ~ r1(v7, v8) | ~
% 137.33/19.09 | r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 137.33/19.09 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) |
% 137.33/19.09 | p1(v9) | ? [v10: $i] : ? [v11: $i] : ($i(v11) & $i(v10) & ((p1(v10)
% 137.33/19.09 | & r1(v10, v11) & r1(v8, v10) & ~ p1(v11)) | (p1(v10) & r1(v10,
% 137.33/19.09 | v11) & r1(v7, v10) & ~ p1(v11) & ! [v12: $i] : ! [v13: $i]
% 137.33/19.09 | : ! [v14: $i] : ( ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~
% 137.33/19.09 | p1(v13) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v10, v12)
% 137.33/19.09 | | p1(v14) | p1(v12)) & ! [v12: $i] : ! [v13: $i] : ! [v14:
% 137.33/19.09 | $i] : ( ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ p1(v13) | ~
% 137.33/19.09 | r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v10, v12) | p1(v14) |
% 137.33/19.09 | ? [v15: $i] : ($i(v15) & r1(v12, v15) & ~ p1(v15))))))) & !
% 137.33/19.09 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 137.33/19.09 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 137.33/19.09 | $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 137.33/19.09 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v8, v9) | ~
% 137.33/19.09 | r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 137.33/19.09 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 137.33/19.09 | r1(all_3_10, v0) | p1(v9) | ? [v10: $i] : ? [v11: $i] : ($i(v11) &
% 137.33/19.09 | $i(v10) & ((p1(v10) & r1(v10, v11) & r1(v9, v10) & ~ p1(v11)) |
% 137.33/19.09 | (r1(v7, v10) & ~ p1(v10) & ! [v12: $i] : ! [v13: $i] : ( ~
% 137.33/19.09 | $i(v13) | ~ $i(v12) | ~ p1(v12) | ~ r1(v12, v13) | ~
% 137.33/19.09 | r1(v10, v12) | p1(v13)))))) & ! [v0: $i] : ! [v1: $i] : !
% 137.33/19.09 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 137.33/19.09 | [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5)
% 137.33/19.09 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 137.33/19.09 | r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 137.33/19.09 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 137.33/19.09 | r1(all_3_10, v0) | p1(v8) | ? [v9: $i] : ($i(v9) & r1(v6, v9) & ~
% 137.33/19.09 | p1(v9))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 137.33/19.09 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (
% 137.33/19.09 | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3)
% 137.33/19.09 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v7, v8) | ~ r1(v6, v7) |
% 137.33/19.09 | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~
% 137.33/19.09 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v7) | ? [v9:
% 137.33/19.09 | $i] : ($i(v9) & ((r1(v8, v9) & ~ p1(v9)) | (r1(v7, v9) & ~ p1(v9)
% 137.33/19.09 | & ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~
% 137.33/19.09 | p1(v10) | ~ r1(v10, v11) | ~ r1(v9, v10) | p1(v11)))))) &
% 137.33/19.09 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 137.33/19.09 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~
% 137.33/19.09 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 137.33/19.09 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 137.33/19.09 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) |
% 137.33/19.09 | p1(v7) | ? [v8: $i] : ($i(v8) & r1(v5, v8) & ~ p1(v8))) & ! [v0:
% 137.33/19.09 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 137.33/19.09 | $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 137.33/19.09 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 137.33/19.09 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 137.33/19.09 | r1(all_3_10, v0) | p1(v6) | ? [v7: $i] : ($i(v7) & r1(v4, v7) & ~
% 137.33/19.09 | p1(v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 137.33/19.09 | ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 137.33/19.09 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 137.33/19.09 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) |
% 137.33/19.09 | p1(v5) | ? [v6: $i] : ($i(v6) & r1(v3, v6) & ~ p1(v6))) & ! [v0:
% 137.33/19.09 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 137.33/19.09 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v3,
% 137.33/19.09 | v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 137.33/19.09 | r1(all_3_10, v0) | p1(v4) | ? [v5: $i] : ($i(v5) & r1(v2, v5) & ~
% 137.33/19.09 | p1(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 137.33/19.09 | ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~
% 137.33/19.09 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v3) | ? [v4:
% 137.33/19.09 | $i] : ($i(v4) & r1(v1, v4) & ~ p1(v4))) & ! [v0: $i] : ! [v1:
% 137.33/19.09 | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1,
% 137.33/19.09 | v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v2) | ? [v3: $i] :
% 137.33/19.09 | ($i(v3) & r1(v0, v3) & ~ p1(v3))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 137.33/19.09 | r1(all_3_1, v0) | p1(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2,
% 137.33/19.09 | v0) | p1(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) &
% 137.33/19.09 | p1(v1) & r1(v1, v2) & r1(v0, v1) & ~ p1(v2)))
% 137.33/19.09 |
% 137.33/19.09 | ALPHA: (1) implies:
% 137.33/19.09 | (2) ~ p1(all_3_0)
% 137.33/19.09 | (3) r1(all_3_10, all_3_9)
% 137.33/19.09 | (4) r1(all_3_9, all_3_8)
% 137.33/19.09 | (5) r1(all_3_8, all_3_7)
% 137.33/19.09 | (6) r1(all_3_7, all_3_6)
% 137.33/19.09 | (7) r1(all_3_6, all_3_5)
% 137.33/19.09 | (8) r1(all_3_5, all_3_4)
% 137.33/19.09 | (9) r1(all_3_4, all_3_3)
% 137.33/19.09 | (10) r1(all_3_3, all_3_2)
% 137.33/19.09 | (11) r1(all_3_2, all_3_1)
% 137.33/19.09 | (12) r1(all_3_2, all_3_0)
% 137.33/19.09 | (13) $i(all_3_9)
% 137.33/19.09 | (14) $i(all_3_8)
% 137.33/19.09 | (15) $i(all_3_7)
% 137.33/19.09 | (16) $i(all_3_6)
% 137.33/19.09 | (17) $i(all_3_5)
% 137.33/19.09 | (18) $i(all_3_4)
% 137.33/19.09 | (19) $i(all_3_3)
% 137.33/19.09 | (20) $i(all_3_2)
% 137.33/19.09 | (21) $i(all_3_1)
% 137.33/19.09 | (22) $i(all_3_0)
% 137.33/19.09 | (23) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2, v0) | p1(v0) | ? [v1: $i] :
% 137.33/19.09 | ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) & r1(v0, v1) &
% 137.33/19.09 | ~ p1(v2)))
% 137.33/19.10 | (24) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_1, v0) | p1(v0))
% 137.33/19.10 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 137.33/19.10 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~
% 137.33/19.10 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 137.33/19.10 | ~ $i(v1) | ~ $i(v0) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5,
% 137.33/19.10 | v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1,
% 137.33/19.10 | v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v7) | ? [v9: $i] :
% 137.33/19.10 | ($i(v9) & ((r1(v8, v9) & ~ p1(v9)) | (r1(v7, v9) & ~ p1(v9) & !
% 137.33/19.10 | [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~
% 137.33/19.10 | p1(v10) | ~ r1(v10, v11) | ~ r1(v9, v10) | p1(v11))))))
% 137.33/19.10 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 137.33/19.10 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (
% 137.33/19.10 | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4)
% 137.33/19.10 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v8, v9) | ~
% 137.33/19.10 | r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 137.33/19.10 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 137.33/19.10 | r1(all_3_10, v0) | p1(v9) | ? [v10: $i] : ? [v11: $i] : ($i(v11) &
% 137.33/19.10 | $i(v10) & ((p1(v10) & r1(v10, v11) & r1(v9, v10) & ~ p1(v11)) |
% 137.33/19.10 | (r1(v7, v10) & ~ p1(v10) & ! [v12: $i] : ! [v13: $i] : ( ~
% 137.33/19.10 | $i(v13) | ~ $i(v12) | ~ p1(v12) | ~ r1(v12, v13) | ~
% 137.33/19.10 | r1(v10, v12) | p1(v13))))))
% 137.33/19.11 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 137.33/19.11 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (
% 137.33/19.11 | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4)
% 137.33/19.11 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v7) | ~
% 137.33/19.11 | r1(v7, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~
% 137.33/19.11 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 137.33/19.11 | r1(v0, v1) | ~ r1(all_3_10, v0) | p1(v9) | ? [v10: $i] : ? [v11:
% 137.33/19.11 | $i] : ($i(v11) & $i(v10) & ((p1(v10) & r1(v10, v11) & r1(v8, v10)
% 137.33/19.11 | & ~ p1(v11)) | (p1(v10) & r1(v10, v11) & r1(v7, v10) & ~
% 137.33/19.11 | p1(v11) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 137.33/19.11 | $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ p1(v13) | ~ r1(v13,
% 137.33/19.11 | v14) | ~ r1(v12, v13) | ~ r1(v10, v12) | p1(v14) |
% 137.33/19.11 | p1(v12)) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 137.33/19.11 | $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ p1(v13) | ~ r1(v13,
% 137.33/19.11 | v14) | ~ r1(v12, v13) | ~ r1(v10, v12) | p1(v14) | ?
% 137.33/19.11 | [v15: $i] : ($i(v15) & r1(v12, v15) & ~ p1(v15)))))))
% 137.33/19.11 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 137.33/19.11 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 137.33/19.11 | ! [v10: $i] : ( ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~
% 137.33/19.11 | $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 137.33/19.11 | ~ $i(v0) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~
% 137.33/19.11 | r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 137.33/19.11 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_10, v0) |
% 137.33/19.11 | p1(v10) | ? [v11: $i] : ($i(v11) & r1(v8, v11) & ~ p1(v11)))
% 137.33/19.11 |
% 137.33/19.11 | GROUND_INST: instantiating (25) with all_3_9, all_3_8, all_3_7, all_3_6,
% 137.33/19.11 | all_3_5, all_3_4, all_3_3, all_3_2, all_3_1, simplifying with
% 137.33/19.11 | (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), (15),
% 137.33/19.11 | (16), (17), (18), (19), (20), (21) gives:
% 137.33/19.11 | (29) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) |
% 137.33/19.11 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 137.33/19.11 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1)
% 137.33/19.11 | | p1(v2)))))
% 137.33/19.11 |
% 137.33/19.12 | GROUND_INST: instantiating (25) with all_3_9, all_3_8, all_3_7, all_3_6,
% 137.33/19.12 | all_3_5, all_3_4, all_3_3, all_3_2, all_3_0, simplifying with
% 137.33/19.12 | (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14), (15),
% 137.33/19.12 | (16), (17), (18), (19), (20), (22) gives:
% 137.33/19.12 | (30) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_0, v0) & ~ p1(v0)) |
% 137.33/19.12 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 137.33/19.12 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1)
% 137.33/19.12 | | p1(v2)))))
% 137.33/19.12 |
% 137.33/19.12 | BETA: splitting (30) gives:
% 137.33/19.12 |
% 137.33/19.12 | Case 1:
% 137.33/19.12 | |
% 137.33/19.12 | | (31) p1(all_3_2)
% 137.33/19.12 | |
% 137.33/19.12 | | GROUND_INST: instantiating (27) with all_3_9, all_3_8, all_3_7, all_3_6,
% 137.33/19.12 | | all_3_5, all_3_4, all_3_3, all_3_2, all_3_1, all_3_0,
% 137.33/19.12 | | simplifying with (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 137.33/19.12 | | (11), (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 137.33/19.12 | | (21), (22), (31) gives:
% 137.33/19.12 | | (32) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0, v1)
% 137.33/19.12 | | & r1(all_3_1, v0) & ~ p1(v1)) | (p1(v0) & r1(v0, v1) &
% 137.33/19.12 | | r1(all_3_2, v0) & ~ p1(v1) & ! [v2: $i] : ! [v3: $i] : !
% 137.33/19.12 | | [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~
% 137.33/19.12 | | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) |
% 137.33/19.12 | | p1(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 137.33/19.12 | | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~ r1(v3, v4) |
% 137.33/19.12 | | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | ? [v5: $i] :
% 137.33/19.12 | | ($i(v5) & r1(v2, v5) & ~ p1(v5))))))
% 137.33/19.12 | |
% 137.33/19.12 | | DELTA: instantiating (32) with fresh symbols all_101_0, all_101_1 gives:
% 137.33/19.13 | | (33) $i(all_101_0) & $i(all_101_1) & ((p1(all_101_1) & r1(all_101_1,
% 137.33/19.13 | | all_101_0) & r1(all_3_1, all_101_1) & ~ p1(all_101_0)) |
% 137.33/19.13 | | (p1(all_101_1) & r1(all_101_1, all_101_0) & r1(all_3_2, all_101_1)
% 137.33/19.13 | | & ~ p1(all_101_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 137.33/19.13 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) |
% 137.33/19.13 | | ~ r1(v0, v1) | ~ r1(all_101_1, v0) | p1(v2) | p1(v0)) & !
% 137.33/19.13 | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) |
% 137.33/19.13 | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 137.33/19.13 | | r1(all_101_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0,
% 137.33/19.13 | | v3) & ~ p1(v3)))))
% 137.33/19.13 | |
% 137.33/19.13 | | ALPHA: (33) implies:
% 137.33/19.13 | | (34) $i(all_101_1)
% 137.33/19.13 | | (35) $i(all_101_0)
% 137.33/19.13 | | (36) (p1(all_101_1) & r1(all_101_1, all_101_0) & r1(all_3_1, all_101_1) &
% 137.33/19.13 | | ~ p1(all_101_0)) | (p1(all_101_1) & r1(all_101_1, all_101_0) &
% 137.33/19.13 | | r1(all_3_2, all_101_1) & ~ p1(all_101_0) & ! [v0: $i] : ! [v1:
% 137.33/19.13 | | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 137.33/19.13 | | p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_101_1, v0) |
% 137.33/19.13 | | p1(v2) | p1(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 137.33/19.13 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~
% 137.33/19.13 | | r1(v0, v1) | ~ r1(all_101_1, v0) | p1(v2) | ? [v3: $i] :
% 137.33/19.13 | | ($i(v3) & r1(v0, v3) & ~ p1(v3))))
% 137.33/19.13 | |
% 137.33/19.13 | | BETA: splitting (36) gives:
% 137.33/19.13 | |
% 137.33/19.13 | | Case 1:
% 137.33/19.13 | | |
% 137.33/19.13 | | | (37) p1(all_101_1) & r1(all_101_1, all_101_0) & r1(all_3_1, all_101_1)
% 137.33/19.13 | | | & ~ p1(all_101_0)
% 137.33/19.13 | | |
% 137.33/19.13 | | | ALPHA: (37) implies:
% 137.33/19.13 | | | (38) ~ p1(all_101_0)
% 137.33/19.13 | | | (39) r1(all_3_1, all_101_1)
% 137.33/19.13 | | | (40) r1(all_101_1, all_101_0)
% 137.33/19.13 | | |
% 137.33/19.13 | | | GROUND_INST: instantiating (28) with all_3_9, all_3_8, all_3_7, all_3_6,
% 137.33/19.13 | | | all_3_5, all_3_4, all_3_3, all_3_2, all_3_1, all_101_1,
% 137.33/19.13 | | | all_101_0, simplifying with (3), (4), (5), (6), (7), (8),
% 137.33/19.13 | | | (9), (10), (11), (13), (14), (15), (16), (17), (18), (19),
% 137.33/19.13 | | | (20), (21), (34), (35), (38), (39), (40) gives:
% 137.33/19.13 | | | (41) ? [v0: $i] : ($i(v0) & r1(all_3_1, v0) & ~ p1(v0))
% 137.33/19.13 | | |
% 137.33/19.13 | | | DELTA: instantiating (41) with fresh symbol all_164_0 gives:
% 137.33/19.13 | | | (42) $i(all_164_0) & r1(all_3_1, all_164_0) & ~ p1(all_164_0)
% 137.33/19.13 | | |
% 137.33/19.13 | | | ALPHA: (42) implies:
% 137.33/19.13 | | | (43) ~ p1(all_164_0)
% 137.33/19.13 | | | (44) r1(all_3_1, all_164_0)
% 137.33/19.13 | | | (45) $i(all_164_0)
% 137.33/19.13 | | |
% 137.33/19.13 | | | GROUND_INST: instantiating (24) with all_164_0, simplifying with (43),
% 137.33/19.13 | | | (44), (45) gives:
% 137.33/19.13 | | | (46) $false
% 137.33/19.14 | | |
% 137.33/19.14 | | | CLOSE: (46) is inconsistent.
% 137.33/19.14 | | |
% 137.33/19.14 | | Case 2:
% 137.33/19.14 | | |
% 137.33/19.14 | | | (47) p1(all_101_1) & r1(all_101_1, all_101_0) & r1(all_3_2, all_101_1)
% 137.33/19.14 | | | & ~ p1(all_101_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 137.33/19.14 | | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~
% 137.33/19.14 | | | r1(v0, v1) | ~ r1(all_101_1, v0) | p1(v2) | p1(v0)) & ! [v0:
% 137.33/19.14 | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 137.33/19.14 | | | $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 137.33/19.14 | | | r1(all_101_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, v3)
% 137.33/19.14 | | | & ~ p1(v3)))
% 137.33/19.14 | | |
% 137.33/19.14 | | | ALPHA: (47) implies:
% 137.33/19.14 | | | (48) ~ p1(all_101_0)
% 137.33/19.14 | | | (49) r1(all_3_2, all_101_1)
% 137.33/19.14 | | | (50) r1(all_101_1, all_101_0)
% 137.33/19.14 | | | (51) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) |
% 137.33/19.14 | | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 137.33/19.14 | | | r1(all_101_1, v0) | p1(v2) | p1(v0))
% 137.33/19.14 | | |
% 137.33/19.14 | | | GROUND_INST: instantiating (26) with all_3_9, all_3_8, all_3_7, all_3_6,
% 137.33/19.14 | | | all_3_5, all_3_4, all_3_3, all_3_2, all_101_1, all_101_0,
% 137.33/19.14 | | | simplifying with (3), (4), (5), (6), (7), (8), (9), (10),
% 137.33/19.14 | | | (13), (14), (15), (16), (17), (18), (19), (20), (34), (35),
% 137.33/19.14 | | | (48), (49), (50) gives:
% 137.33/19.14 | | | (52) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0,
% 137.33/19.14 | | | v1) & r1(all_101_0, v0) & ~ p1(v1)) | (r1(all_3_2, v0) &
% 137.33/19.15 | | | ~ p1(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 137.33/19.15 | | | $i(v2) | ~ p1(v2) | ~ r1(v2, v3) | ~ r1(v0, v2) |
% 137.33/19.15 | | | p1(v3)))))
% 137.33/19.15 | | |
% 137.33/19.15 | | | DELTA: instantiating (52) with fresh symbols all_165_0, all_165_1 gives:
% 137.33/19.15 | | | (53) $i(all_165_0) & $i(all_165_1) & ((p1(all_165_1) & r1(all_165_1,
% 137.33/19.15 | | | all_165_0) & r1(all_101_0, all_165_1) & ~ p1(all_165_0)) |
% 137.33/19.15 | | | (r1(all_3_2, all_165_1) & ~ p1(all_165_1) & ! [v0: $i] : !
% 137.33/19.15 | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1)
% 137.33/19.15 | | | | ~ r1(all_165_1, v0) | p1(v1))))
% 137.33/19.15 | | |
% 137.33/19.15 | | | ALPHA: (53) implies:
% 137.33/19.15 | | | (54) $i(all_165_1)
% 137.33/19.15 | | | (55) $i(all_165_0)
% 137.33/19.15 | | | (56) (p1(all_165_1) & r1(all_165_1, all_165_0) & r1(all_101_0,
% 137.33/19.15 | | | all_165_1) & ~ p1(all_165_0)) | (r1(all_3_2, all_165_1) & ~
% 137.33/19.15 | | | p1(all_165_1) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 137.33/19.15 | | | $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_165_1, v0) |
% 137.33/19.15 | | | p1(v1)))
% 137.33/19.15 | | |
% 137.33/19.15 | | | BETA: splitting (56) gives:
% 137.33/19.15 | | |
% 137.33/19.15 | | | Case 1:
% 137.33/19.15 | | | |
% 137.33/19.15 | | | | (57) p1(all_165_1) & r1(all_165_1, all_165_0) & r1(all_101_0,
% 137.33/19.15 | | | | all_165_1) & ~ p1(all_165_0)
% 137.33/19.15 | | | |
% 137.33/19.15 | | | | ALPHA: (57) implies:
% 137.33/19.15 | | | | (58) ~ p1(all_165_0)
% 137.33/19.15 | | | | (59) r1(all_101_0, all_165_1)
% 137.33/19.15 | | | | (60) r1(all_165_1, all_165_0)
% 137.33/19.15 | | | | (61) p1(all_165_1)
% 137.33/19.15 | | | |
% 137.33/19.15 | | | | GROUND_INST: instantiating (51) with all_101_0, all_165_1, all_165_0,
% 137.33/19.15 | | | | simplifying with (35), (48), (50), (54), (55), (58), (59),
% 137.33/19.15 | | | | (60), (61) gives:
% 137.33/19.15 | | | | (62) $false
% 137.33/19.15 | | | |
% 137.33/19.15 | | | | CLOSE: (62) is inconsistent.
% 137.33/19.15 | | | |
% 137.33/19.15 | | | Case 2:
% 137.33/19.15 | | | |
% 137.33/19.15 | | | | (63) r1(all_3_2, all_165_1) & ~ p1(all_165_1) & ! [v0: $i] : !
% 137.33/19.15 | | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) |
% 137.33/19.15 | | | | ~ r1(all_165_1, v0) | p1(v1))
% 137.33/19.15 | | | |
% 137.33/19.15 | | | | ALPHA: (63) implies:
% 137.33/19.15 | | | | (64) ~ p1(all_165_1)
% 137.33/19.15 | | | | (65) r1(all_3_2, all_165_1)
% 137.33/19.15 | | | | (66) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) |
% 137.33/19.15 | | | | ~ r1(v0, v1) | ~ r1(all_165_1, v0) | p1(v1))
% 137.33/19.15 | | | |
% 137.33/19.15 | | | | GROUND_INST: instantiating (23) with all_165_1, simplifying with (54),
% 137.33/19.15 | | | | (64), (65) gives:
% 137.33/19.15 | | | | (67) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0,
% 137.33/19.15 | | | | v1) & r1(all_165_1, v0) & ~ p1(v1))
% 137.33/19.15 | | | |
% 137.33/19.15 | | | | DELTA: instantiating (67) with fresh symbols all_229_0, all_229_1 gives:
% 137.33/19.15 | | | | (68) $i(all_229_0) & $i(all_229_1) & p1(all_229_1) & r1(all_229_1,
% 137.33/19.15 | | | | all_229_0) & r1(all_165_1, all_229_1) & ~ p1(all_229_0)
% 137.33/19.15 | | | |
% 137.33/19.15 | | | | ALPHA: (68) implies:
% 137.33/19.15 | | | | (69) ~ p1(all_229_0)
% 137.33/19.15 | | | | (70) r1(all_165_1, all_229_1)
% 137.33/19.15 | | | | (71) r1(all_229_1, all_229_0)
% 137.33/19.15 | | | | (72) p1(all_229_1)
% 137.33/19.15 | | | | (73) $i(all_229_1)
% 137.33/19.15 | | | | (74) $i(all_229_0)
% 137.33/19.15 | | | |
% 137.33/19.15 | | | | GROUND_INST: instantiating (66) with all_229_1, all_229_0, simplifying
% 137.33/19.15 | | | | with (69), (70), (71), (72), (73), (74) gives:
% 137.33/19.15 | | | | (75) $false
% 137.33/19.15 | | | |
% 137.33/19.15 | | | | CLOSE: (75) is inconsistent.
% 137.33/19.15 | | | |
% 137.33/19.15 | | | End of split
% 137.33/19.15 | | |
% 137.33/19.15 | | End of split
% 137.33/19.15 | |
% 137.33/19.15 | Case 2:
% 137.33/19.15 | |
% 137.33/19.15 | | (76) ~ p1(all_3_2)
% 137.33/19.15 | |
% 137.33/19.15 | | BETA: splitting (29) gives:
% 137.33/19.15 | |
% 137.33/19.15 | | Case 1:
% 137.33/19.15 | | |
% 137.33/19.16 | | | (77) p1(all_3_2)
% 137.33/19.16 | | |
% 137.33/19.16 | | | PRED_UNIFY: (76), (77) imply:
% 137.33/19.16 | | | (78) $false
% 137.33/19.16 | | |
% 137.33/19.16 | | | CLOSE: (78) is inconsistent.
% 137.33/19.16 | | |
% 137.33/19.16 | | Case 2:
% 137.33/19.16 | | |
% 137.33/19.16 | | | (79) ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) |
% 137.33/19.16 | | | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 137.33/19.16 | | | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0,
% 137.33/19.16 | | | v1) | p1(v2)))))
% 137.33/19.16 | | |
% 137.33/19.16 | | | DELTA: instantiating (79) with fresh symbol all_107_0 gives:
% 137.33/19.16 | | | (80) $i(all_107_0) & ((r1(all_3_1, all_107_0) & ~ p1(all_107_0)) |
% 137.33/19.16 | | | (r1(all_3_2, all_107_0) & ~ p1(all_107_0) & ! [v0: $i] : !
% 137.33/19.16 | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1)
% 137.33/19.16 | | | | ~ r1(all_107_0, v0) | p1(v1))))
% 137.33/19.16 | | |
% 137.33/19.16 | | | ALPHA: (80) implies:
% 137.33/19.16 | | | (81) $i(all_107_0)
% 137.33/19.16 | | | (82) (r1(all_3_1, all_107_0) & ~ p1(all_107_0)) | (r1(all_3_2,
% 137.33/19.16 | | | all_107_0) & ~ p1(all_107_0) & ! [v0: $i] : ! [v1: $i] : (
% 137.33/19.16 | | | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~
% 137.33/19.16 | | | r1(all_107_0, v0) | p1(v1)))
% 137.33/19.16 | | |
% 137.33/19.16 | | | BETA: splitting (82) gives:
% 137.33/19.16 | | |
% 137.33/19.16 | | | Case 1:
% 137.33/19.16 | | | |
% 137.33/19.16 | | | | (83) r1(all_3_1, all_107_0) & ~ p1(all_107_0)
% 137.33/19.16 | | | |
% 137.33/19.16 | | | | ALPHA: (83) implies:
% 137.33/19.16 | | | | (84) ~ p1(all_107_0)
% 137.33/19.16 | | | | (85) r1(all_3_1, all_107_0)
% 137.33/19.16 | | | |
% 137.33/19.16 | | | | GROUND_INST: instantiating (24) with all_107_0, simplifying with (81),
% 137.33/19.16 | | | | (84), (85) gives:
% 137.33/19.16 | | | | (86) $false
% 137.33/19.16 | | | |
% 137.33/19.16 | | | | CLOSE: (86) is inconsistent.
% 137.33/19.16 | | | |
% 137.33/19.16 | | | Case 2:
% 137.33/19.16 | | | |
% 137.33/19.16 | | | | (87) r1(all_3_2, all_107_0) & ~ p1(all_107_0) & ! [v0: $i] : !
% 137.33/19.16 | | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) |
% 137.33/19.16 | | | | ~ r1(all_107_0, v0) | p1(v1))
% 137.33/19.16 | | | |
% 137.33/19.16 | | | | ALPHA: (87) implies:
% 137.33/19.16 | | | | (88) ~ p1(all_107_0)
% 137.33/19.16 | | | | (89) r1(all_3_2, all_107_0)
% 137.33/19.16 | | | | (90) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) |
% 137.33/19.16 | | | | ~ r1(v0, v1) | ~ r1(all_107_0, v0) | p1(v1))
% 137.33/19.16 | | | |
% 137.33/19.16 | | | | GROUND_INST: instantiating (23) with all_107_0, simplifying with (81),
% 137.33/19.16 | | | | (88), (89) gives:
% 137.33/19.16 | | | | (91) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0,
% 137.33/19.16 | | | | v1) & r1(all_107_0, v0) & ~ p1(v1))
% 137.33/19.16 | | | |
% 137.33/19.16 | | | | DELTA: instantiating (91) with fresh symbols all_213_0, all_213_1 gives:
% 137.33/19.16 | | | | (92) $i(all_213_0) & $i(all_213_1) & p1(all_213_1) & r1(all_213_1,
% 137.33/19.16 | | | | all_213_0) & r1(all_107_0, all_213_1) & ~ p1(all_213_0)
% 137.33/19.16 | | | |
% 137.33/19.16 | | | | ALPHA: (92) implies:
% 137.33/19.17 | | | | (93) ~ p1(all_213_0)
% 137.33/19.17 | | | | (94) r1(all_107_0, all_213_1)
% 137.33/19.17 | | | | (95) r1(all_213_1, all_213_0)
% 137.33/19.17 | | | | (96) p1(all_213_1)
% 137.33/19.17 | | | | (97) $i(all_213_1)
% 137.33/19.17 | | | | (98) $i(all_213_0)
% 137.33/19.17 | | | |
% 137.33/19.17 | | | | GROUND_INST: instantiating (90) with all_213_1, all_213_0, simplifying
% 137.33/19.17 | | | | with (93), (94), (95), (96), (97), (98) gives:
% 137.33/19.17 | | | | (99) $false
% 137.33/19.17 | | | |
% 137.33/19.17 | | | | CLOSE: (99) is inconsistent.
% 137.33/19.17 | | | |
% 137.33/19.17 | | | End of split
% 137.33/19.17 | | |
% 137.33/19.17 | | End of split
% 137.33/19.17 | |
% 137.33/19.17 | End of split
% 137.33/19.17 |
% 137.33/19.17 End of proof
% 137.33/19.17 % SZS output end Proof for theBenchmark
% 137.33/19.17
% 137.33/19.17 18539ms
%------------------------------------------------------------------------------