TSTP Solution File: LCL658+1.020 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL658+1.020 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:12:10 EDT 2023
% Result : Theorem 155.17s 21.11s
% Output : Proof 156.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL658+1.020 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 20:29:56 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.09/1.46 Prover 1: Preprocessing ...
% 4.09/1.47 Prover 4: Preprocessing ...
% 4.78/1.51 Prover 5: Preprocessing ...
% 4.78/1.51 Prover 3: Preprocessing ...
% 4.78/1.51 Prover 0: Preprocessing ...
% 4.78/1.51 Prover 2: Preprocessing ...
% 4.78/1.51 Prover 6: Preprocessing ...
% 8.71/1.98 Prover 2: Proving ...
% 9.37/2.15 Prover 5: Proving ...
% 14.75/2.84 Prover 6: Proving ...
% 14.75/2.86 Prover 0: Proving ...
% 14.75/2.91 Prover 1: Constructing countermodel ...
% 14.75/2.91 Prover 3: Constructing countermodel ...
% 16.05/2.96 Prover 4: Constructing countermodel ...
% 75.67/10.67 Prover 2: stopped
% 75.67/10.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 77.01/10.82 Prover 7: Preprocessing ...
% 77.60/10.90 Prover 7: Warning: ignoring some quantifiers
% 77.81/10.92 Prover 7: Constructing countermodel ...
% 100.94/13.98 Prover 5: stopped
% 100.94/13.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 102.76/14.12 Prover 8: Preprocessing ...
% 105.22/14.49 Prover 8: Warning: ignoring some quantifiers
% 105.22/14.51 Prover 8: Constructing countermodel ...
% 116.91/15.98 Prover 1: stopped
% 116.91/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 118.88/16.29 Prover 9: Preprocessing ...
% 125.43/17.11 Prover 9: Constructing countermodel ...
% 130.82/17.89 Prover 6: stopped
% 130.82/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 133.62/18.18 Prover 10: Preprocessing ...
% 133.94/18.25 Prover 10: Warning: ignoring some quantifiers
% 133.94/18.26 Prover 10: Constructing countermodel ...
% 154.73/21.04 Prover 10: Found proof (size 50)
% 154.73/21.04 Prover 10: proved (3148ms)
% 154.73/21.04 Prover 3: stopped
% 154.73/21.05 Prover 8: stopped
% 154.73/21.06 Prover 0: stopped
% 154.73/21.07 Prover 7: stopped
% 155.17/21.11 Prover 4: stopped
% 155.17/21.11 Prover 9: stopped
% 155.17/21.11
% 155.17/21.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 155.17/21.11
% 155.17/21.11 % SZS output start Proof for theBenchmark
% 155.17/21.12 Assumptions after simplification:
% 155.17/21.12 ---------------------------------
% 155.17/21.12
% 155.17/21.12 (main)
% 155.65/21.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 155.65/21.19 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 155.65/21.19 ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ($i(v13) & $i(v12) & $i(v11) &
% 155.65/21.19 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 155.65/21.19 $i(v2) & $i(v1) & $i(v0) & r1(v11, v13) & r1(v11, v12) & r1(v10, v11) &
% 155.65/21.19 r1(v9, v10) & r1(v8, v9) & r1(v7, v8) & r1(v6, v7) & r1(v5, v6) & r1(v4, v5)
% 155.65/21.19 & r1(v3, v4) & r1(v2, v3) & r1(v1, v2) & r1(v0, v1) & ~ p1(v13) & ! [v14:
% 155.65/21.19 $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19:
% 155.65/21.19 $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24:
% 155.65/21.19 $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ! [v28: $i] : ! [v29:
% 155.65/21.19 $i] : ! [v30: $i] : ! [v31: $i] : ! [v32: $i] : ! [v33: $i] : ! [v34:
% 155.65/21.19 $i] : ( ~ $i(v34) | ~ $i(v33) | ~ $i(v32) | ~ $i(v31) | ~ $i(v30) | ~
% 155.65/21.19 $i(v29) | ~ $i(v28) | ~ $i(v27) | ~ $i(v26) | ~ $i(v25) | ~ $i(v24) |
% 155.65/21.19 ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~
% 155.65/21.19 $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v33,
% 155.65/21.19 v34) | ~ r1(v32, v33) | ~ r1(v31, v32) | ~ r1(v30, v31) | ~ r1(v29,
% 155.65/21.19 v30) | ~ r1(v28, v29) | ~ r1(v27, v28) | ~ r1(v26, v27) | ~ r1(v25,
% 155.65/21.19 v26) | ~ r1(v24, v25) | ~ r1(v23, v24) | ~ r1(v22, v23) | ~ r1(v21,
% 155.65/21.20 v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17,
% 155.65/21.20 v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v0,
% 155.65/21.20 v14) | p1(v34) | ? [v35: $i] : ($i(v35) & r1(v32, v35) & ~ p1(v35))) &
% 155.65/21.20 ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] :
% 155.65/21.20 ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : !
% 155.65/21.20 [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ! [v28: $i] : !
% 155.65/21.20 [v29: $i] : ! [v30: $i] : ! [v31: $i] : ! [v32: $i] : ! [v33: $i] : ( ~
% 155.65/21.20 $i(v33) | ~ $i(v32) | ~ $i(v31) | ~ $i(v30) | ~ $i(v29) | ~ $i(v28) |
% 155.65/21.20 ~ $i(v27) | ~ $i(v26) | ~ $i(v25) | ~ $i(v24) | ~ $i(v23) | ~
% 155.65/21.20 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) |
% 155.65/21.20 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v32, v33) | ~ r1(v31, v32) |
% 155.65/21.20 ~ r1(v30, v31) | ~ r1(v29, v30) | ~ r1(v28, v29) | ~ r1(v27, v28) | ~
% 155.65/21.20 r1(v26, v27) | ~ r1(v25, v26) | ~ r1(v24, v25) | ~ r1(v23, v24) | ~
% 155.65/21.20 r1(v22, v23) | ~ r1(v21, v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~
% 155.65/21.20 r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~
% 155.65/21.20 r1(v14, v15) | ~ r1(v0, v14) | p1(v33) | ? [v34: $i] : ($i(v34) &
% 155.65/21.20 r1(v31, v34) & ~ p1(v34))) & ! [v14: $i] : ! [v15: $i] : ! [v16: $i]
% 155.65/21.20 : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] :
% 155.65/21.20 ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] :
% 155.65/21.20 ! [v27: $i] : ! [v28: $i] : ! [v29: $i] : ! [v30: $i] : ! [v31: $i] : !
% 155.65/21.20 [v32: $i] : ( ~ $i(v32) | ~ $i(v31) | ~ $i(v30) | ~ $i(v29) | ~ $i(v28)
% 155.65/21.20 | ~ $i(v27) | ~ $i(v26) | ~ $i(v25) | ~ $i(v24) | ~ $i(v23) | ~
% 155.65/21.20 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) |
% 155.65/21.20 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v31, v32) | ~ r1(v30, v31) |
% 155.65/21.20 ~ r1(v29, v30) | ~ r1(v28, v29) | ~ r1(v27, v28) | ~ r1(v26, v27) | ~
% 155.65/21.20 r1(v25, v26) | ~ r1(v24, v25) | ~ r1(v23, v24) | ~ r1(v22, v23) | ~
% 155.65/21.20 r1(v21, v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~
% 155.65/21.20 r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~
% 155.65/21.20 r1(v0, v14) | p1(v32) | ? [v33: $i] : ($i(v33) & r1(v30, v33) & ~
% 155.65/21.20 p1(v33))) & ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] :
% 155.65/21.20 ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 155.65/21.20 [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : !
% 155.65/21.20 [v28: $i] : ! [v29: $i] : ! [v30: $i] : ! [v31: $i] : ( ~ $i(v31) | ~
% 155.65/21.20 $i(v30) | ~ $i(v29) | ~ $i(v28) | ~ $i(v27) | ~ $i(v26) | ~ $i(v25) |
% 155.65/21.20 ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~
% 155.65/21.20 $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) |
% 155.65/21.20 ~ r1(v30, v31) | ~ r1(v29, v30) | ~ r1(v28, v29) | ~ r1(v27, v28) | ~
% 155.65/21.20 r1(v26, v27) | ~ r1(v25, v26) | ~ r1(v24, v25) | ~ r1(v23, v24) | ~
% 155.65/21.20 r1(v22, v23) | ~ r1(v21, v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~
% 155.65/21.20 r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~
% 155.65/21.20 r1(v14, v15) | ~ r1(v0, v14) | p1(v31) | ? [v32: $i] : ($i(v32) &
% 155.65/21.20 r1(v29, v32) & ~ p1(v32))) & ! [v14: $i] : ! [v15: $i] : ! [v16: $i]
% 155.65/21.20 : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] :
% 155.65/21.20 ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] :
% 155.65/21.20 ! [v27: $i] : ! [v28: $i] : ! [v29: $i] : ! [v30: $i] : ( ~ $i(v30) | ~
% 155.65/21.20 $i(v29) | ~ $i(v28) | ~ $i(v27) | ~ $i(v26) | ~ $i(v25) | ~ $i(v24) |
% 155.65/21.20 ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~
% 155.65/21.20 $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v29,
% 155.65/21.20 v30) | ~ r1(v28, v29) | ~ r1(v27, v28) | ~ r1(v26, v27) | ~ r1(v25,
% 155.65/21.20 v26) | ~ r1(v24, v25) | ~ r1(v23, v24) | ~ r1(v22, v23) | ~ r1(v21,
% 155.65/21.20 v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17,
% 155.65/21.20 v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v0,
% 155.65/21.20 v14) | p1(v30) | ? [v31: $i] : ($i(v31) & r1(v28, v31) & ~ p1(v31))) &
% 155.65/21.20 ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] :
% 155.65/21.20 ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : !
% 155.65/21.20 [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ! [v28: $i] : !
% 155.65/21.20 [v29: $i] : ( ~ $i(v29) | ~ $i(v28) | ~ $i(v27) | ~ $i(v26) | ~ $i(v25)
% 155.65/21.20 | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~
% 155.65/21.20 $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) |
% 155.65/21.20 ~ r1(v28, v29) | ~ r1(v27, v28) | ~ r1(v26, v27) | ~ r1(v25, v26) | ~
% 155.65/21.20 r1(v24, v25) | ~ r1(v23, v24) | ~ r1(v22, v23) | ~ r1(v21, v22) | ~
% 155.65/21.21 r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~
% 155.65/21.21 r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v0, v14) |
% 155.65/21.21 p1(v29) | ? [v30: $i] : ($i(v30) & r1(v27, v30) & ~ p1(v30))) & ! [v14:
% 155.65/21.21 $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19:
% 155.65/21.21 $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24:
% 155.65/21.21 $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ! [v28: $i] : ( ~
% 155.65/21.21 $i(v28) | ~ $i(v27) | ~ $i(v26) | ~ $i(v25) | ~ $i(v24) | ~ $i(v23) |
% 155.65/21.21 ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~
% 155.65/21.21 $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v27, v28) | ~
% 155.65/21.21 r1(v26, v27) | ~ r1(v25, v26) | ~ r1(v24, v25) | ~ r1(v23, v24) | ~
% 155.65/21.21 r1(v22, v23) | ~ r1(v21, v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~
% 155.65/21.21 r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~
% 155.65/21.21 r1(v14, v15) | ~ r1(v0, v14) | p1(v28) | ? [v29: $i] : ($i(v29) &
% 155.65/21.21 r1(v26, v29) & ~ p1(v29))) & ! [v14: $i] : ! [v15: $i] : ! [v16: $i]
% 155.65/21.21 : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] :
% 155.65/21.21 ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] :
% 155.65/21.21 ! [v27: $i] : ( ~ $i(v27) | ~ $i(v26) | ~ $i(v25) | ~ $i(v24) | ~
% 155.65/21.21 $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) |
% 155.65/21.21 ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v26, v27) | ~
% 155.65/21.21 r1(v25, v26) | ~ r1(v24, v25) | ~ r1(v23, v24) | ~ r1(v22, v23) | ~
% 155.65/21.21 r1(v21, v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~
% 155.65/21.21 r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~
% 155.65/21.21 r1(v0, v14) | p1(v27) | ? [v28: $i] : ($i(v28) & r1(v25, v28) & ~
% 155.65/21.21 p1(v28))) & ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] :
% 155.65/21.21 ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 155.65/21.21 [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ $i(v26) | ~
% 155.65/21.21 $i(v25) | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) |
% 155.65/21.21 ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~
% 155.65/21.21 $i(v14) | ~ p1(v24) | ~ r1(v24, v26) | ~ r1(v24, v25) | ~ r1(v23, v24)
% 155.65/21.21 | ~ r1(v22, v23) | ~ r1(v21, v22) | ~ r1(v20, v21) | ~ r1(v19, v20) |
% 155.65/21.21 ~ r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~
% 155.65/21.21 r1(v14, v15) | ~ r1(v0, v14) | p1(v26) | ? [v27: $i] : ? [v28: $i] :
% 155.65/21.21 ($i(v28) & $i(v27) & ((p1(v27) & r1(v27, v28) & r1(v25, v27) & ~ p1(v28))
% 155.65/21.21 | (p1(v27) & r1(v27, v28) & r1(v24, v27) & ~ p1(v28) & ! [v29: $i] :
% 155.65/21.21 ! [v30: $i] : ! [v31: $i] : ( ~ $i(v31) | ~ $i(v30) | ~ $i(v29)
% 155.65/21.21 | ~ p1(v30) | ~ r1(v30, v31) | ~ r1(v29, v30) | ~ r1(v27, v29)
% 155.65/21.21 | p1(v31) | p1(v29)) & ! [v29: $i] : ! [v30: $i] : ! [v31: $i]
% 155.65/21.21 : ( ~ $i(v31) | ~ $i(v30) | ~ $i(v29) | ~ p1(v30) | ~ r1(v30,
% 155.65/21.21 v31) | ~ r1(v29, v30) | ~ r1(v27, v29) | p1(v31) | ? [v32:
% 155.65/21.21 $i] : ($i(v32) & r1(v29, v32) & ~ p1(v32))))))) & ! [v14: $i]
% 155.65/21.21 : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] :
% 155.65/21.21 ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] :
% 155.65/21.21 ! [v25: $i] : ! [v26: $i] : ( ~ $i(v26) | ~ $i(v25) | ~ $i(v24) | ~
% 155.65/21.21 $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) |
% 155.65/21.21 ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v25, v26) | ~
% 155.65/21.21 r1(v24, v25) | ~ r1(v23, v24) | ~ r1(v22, v23) | ~ r1(v21, v22) | ~
% 155.65/21.21 r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~
% 155.65/21.21 r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v0, v14) |
% 155.79/21.21 p1(v26) | ? [v27: $i] : ? [v28: $i] : ($i(v28) & $i(v27) & ((p1(v27) &
% 155.79/21.21 r1(v27, v28) & r1(v26, v27) & ~ p1(v28)) | (r1(v24, v27) & ~
% 155.79/21.21 p1(v27) & ! [v29: $i] : ! [v30: $i] : ( ~ $i(v30) | ~ $i(v29) |
% 155.79/21.21 ~ p1(v29) | ~ r1(v29, v30) | ~ r1(v27, v29) | p1(v30)))))) & !
% 155.79/21.21 [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : !
% 155.79/21.21 [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : !
% 155.79/21.21 [v24: $i] : ! [v25: $i] : ( ~ $i(v25) | ~ $i(v24) | ~ $i(v23) | ~
% 155.79/21.21 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) |
% 155.79/21.21 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v24, v25) | ~ r1(v23, v24) |
% 155.79/21.22 ~ r1(v22, v23) | ~ r1(v21, v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~
% 155.79/21.22 r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~
% 155.79/21.22 r1(v14, v15) | ~ r1(v0, v14) | p1(v25) | ? [v26: $i] : ($i(v26) &
% 155.79/21.22 r1(v23, v26) & ~ p1(v26))) & ! [v14: $i] : ! [v15: $i] : ! [v16: $i]
% 155.79/21.22 : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] :
% 155.79/21.22 ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~ $i(v25) | ~
% 155.79/21.22 $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) |
% 155.79/21.22 ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~
% 155.79/21.22 r1(v24, v25) | ~ r1(v23, v24) | ~ r1(v22, v23) | ~ r1(v21, v22) | ~
% 155.79/21.22 r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~
% 155.79/21.22 r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v0, v14) |
% 155.79/21.22 p1(v24) | ? [v26: $i] : ($i(v26) & ((r1(v25, v26) & ~ p1(v26)) |
% 155.79/21.22 (r1(v24, v26) & ~ p1(v26) & ! [v27: $i] : ! [v28: $i] : ( ~ $i(v28)
% 155.79/21.22 | ~ $i(v27) | ~ p1(v27) | ~ r1(v27, v28) | ~ r1(v26, v27) |
% 155.79/21.22 p1(v28)))))) & ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : !
% 155.79/21.22 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : !
% 155.79/21.22 [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ $i(v24) | ~ $i(v23) | ~
% 155.79/21.22 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) |
% 155.79/21.22 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v23, v24) | ~ r1(v22, v23) |
% 155.79/21.22 ~ r1(v21, v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~
% 155.79/21.22 r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~
% 155.79/21.22 r1(v0, v14) | p1(v24) | ? [v25: $i] : ($i(v25) & r1(v22, v25) & ~
% 155.79/21.22 p1(v25))) & ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] :
% 155.79/21.22 ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 155.79/21.22 [v23: $i] : ( ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19)
% 155.79/21.22 | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~
% 155.79/21.22 r1(v22, v23) | ~ r1(v21, v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~
% 155.79/21.22 r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~
% 155.79/21.22 r1(v14, v15) | ~ r1(v0, v14) | p1(v23) | ? [v24: $i] : ($i(v24) &
% 155.79/21.22 r1(v21, v24) & ~ p1(v24))) & ! [v14: $i] : ! [v15: $i] : ! [v16: $i]
% 155.79/21.22 : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] :
% 155.79/21.22 ! [v22: $i] : ( ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ $i(v19) | ~
% 155.79/21.22 $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v21,
% 155.79/21.22 v22) | ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17,
% 155.79/21.22 v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v0,
% 155.79/21.22 v14) | p1(v22) | ? [v23: $i] : ($i(v23) & r1(v20, v23) & ~ p1(v23))) &
% 155.79/21.22 ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] :
% 155.79/21.22 ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~ $i(v21) | ~ $i(v20) | ~
% 155.79/21.22 $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) |
% 155.79/21.22 ~ r1(v20, v21) | ~ r1(v19, v20) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~
% 155.79/21.22 r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v0, v14) |
% 155.79/21.22 p1(v21) | ? [v22: $i] : ($i(v22) & r1(v19, v22) & ~ p1(v22))) & ! [v14:
% 155.79/21.22 $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19:
% 155.79/21.22 $i] : ! [v20: $i] : ( ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) |
% 155.79/21.22 ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v19, v20) | ~ r1(v18, v19) |
% 155.79/21.22 ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~
% 155.79/21.22 r1(v0, v14) | p1(v20) | ? [v21: $i] : ($i(v21) & r1(v18, v21) & ~
% 155.79/21.22 p1(v21))) & ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] :
% 155.79/21.22 ! [v18: $i] : ! [v19: $i] : ( ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~
% 155.79/21.22 $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v18, v19) | ~ r1(v17, v18) | ~
% 155.79/21.22 r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v0, v14) |
% 155.79/21.22 p1(v19) | ? [v20: $i] : ($i(v20) & r1(v17, v20) & ~ p1(v20))) & ! [v14:
% 155.79/21.22 $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ( ~
% 155.79/21.22 $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v17,
% 155.79/21.22 v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v0,
% 155.79/21.22 v14) | p1(v18) | ? [v19: $i] : ($i(v19) & r1(v16, v19) & ~ p1(v19))) &
% 155.79/21.22 ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~
% 155.85/21.23 $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~
% 155.85/21.23 r1(v14, v15) | ~ r1(v0, v14) | p1(v17) | ? [v18: $i] : ($i(v18) &
% 155.85/21.23 r1(v15, v18) & ~ p1(v18))) & ! [v14: $i] : ! [v15: $i] : ! [v16: $i]
% 155.85/21.23 : ( ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ r1(v15, v16) | ~ r1(v14, v15)
% 155.85/21.23 | ~ r1(v0, v14) | p1(v16) | ? [v17: $i] : ($i(v17) & r1(v14, v17) & ~
% 155.85/21.23 p1(v17))) & ! [v14: $i] : ( ~ $i(v14) | ~ r1(v12, v14) | p1(v14)) & !
% 155.85/21.23 [v14: $i] : ( ~ $i(v14) | ~ r1(v11, v14) | p1(v14) | ? [v15: $i] : ?
% 155.85/21.23 [v16: $i] : ($i(v16) & $i(v15) & p1(v15) & r1(v15, v16) & r1(v14, v15) &
% 155.85/21.23 ~ p1(v16))))
% 155.85/21.23
% 155.85/21.23 Further assumptions not needed in the proof:
% 155.85/21.23 --------------------------------------------
% 155.85/21.23 reflexivity
% 155.85/21.23
% 155.85/21.23 Those formulas are unsatisfiable:
% 155.85/21.23 ---------------------------------
% 155.85/21.23
% 155.85/21.23 Begin of proof
% 155.85/21.23 |
% 155.85/21.23 | DELTA: instantiating (main) with fresh symbols all_3_0, all_3_1, all_3_2,
% 155.85/21.23 | all_3_3, all_3_4, all_3_5, all_3_6, all_3_7, all_3_8, all_3_9,
% 155.85/21.23 | all_3_10, all_3_11, all_3_12, all_3_13 gives:
% 155.85/21.29 | (1) $i(all_3_0) & $i(all_3_1) & $i(all_3_2) & $i(all_3_3) & $i(all_3_4) &
% 155.85/21.29 | $i(all_3_5) & $i(all_3_6) & $i(all_3_7) & $i(all_3_8) & $i(all_3_9) &
% 155.85/21.29 | $i(all_3_10) & $i(all_3_11) & $i(all_3_12) & $i(all_3_13) & r1(all_3_2,
% 155.85/21.29 | all_3_0) & r1(all_3_2, all_3_1) & r1(all_3_3, all_3_2) & r1(all_3_4,
% 155.85/21.29 | all_3_3) & r1(all_3_5, all_3_4) & r1(all_3_6, all_3_5) & r1(all_3_7,
% 155.85/21.29 | all_3_6) & r1(all_3_8, all_3_7) & r1(all_3_9, all_3_8) & r1(all_3_10,
% 155.85/21.29 | all_3_9) & r1(all_3_11, all_3_10) & r1(all_3_12, all_3_11) &
% 155.85/21.29 | r1(all_3_13, all_3_12) & ~ p1(all_3_0) & ! [v0: $i] : ! [v1: $i] :
% 155.85/21.29 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 155.85/21.29 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 155.85/21.29 | [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] :
% 155.85/21.29 | ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( ~ $i(v20)
% 155.85/21.29 | | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~
% 155.85/21.29 | $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~
% 155.85/21.29 | $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 155.85/21.29 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v19, v20) | ~
% 155.85/21.29 | r1(v18, v19) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) |
% 155.85/21.29 | ~ r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12)
% 155.85/21.29 | | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) |
% 155.85/21.29 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 155.85/21.29 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0) |
% 155.85/21.29 | p1(v20) | ? [v21: $i] : ($i(v21) & r1(v18, v21) & ~ p1(v21))) & !
% 155.85/21.29 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 155.85/21.29 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 155.85/21.29 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] :
% 155.85/21.29 | ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19:
% 155.85/21.29 | $i] : ( ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ $i(v16) | ~ $i(v15)
% 155.85/21.29 | | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~
% 155.85/21.29 | $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 155.85/21.29 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v18, v19) | ~
% 155.85/21.29 | r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) |
% 155.85/21.29 | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11)
% 155.85/21.29 | | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~
% 155.85/21.29 | r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~
% 155.85/21.29 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0) | p1(v19) | ? [v20:
% 155.85/21.29 | $i] : ($i(v20) & r1(v17, v20) & ~ p1(v20))) & ! [v0: $i] : !
% 155.85/21.29 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 155.85/21.29 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 155.85/21.29 | [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] :
% 155.85/21.29 | ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ( ~ $i(v18) | ~ $i(v17) |
% 155.85/21.29 | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~
% 155.85/21.29 | $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6)
% 155.85/21.29 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 155.85/21.29 | $i(v0) | ~ r1(v17, v18) | ~ r1(v16, v17) | ~ r1(v15, v16) | ~
% 155.85/21.29 | r1(v14, v15) | ~ r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) |
% 155.85/21.29 | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~
% 155.85/21.29 | r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 155.85/21.30 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0) |
% 155.85/21.30 | p1(v18) | ? [v19: $i] : ($i(v19) & r1(v16, v19) & ~ p1(v19))) & !
% 155.85/21.30 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 155.85/21.30 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 155.85/21.30 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] :
% 155.85/21.30 | ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ $i(v17) | ~ $i(v16) |
% 155.85/21.30 | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~
% 155.85/21.30 | $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) |
% 155.85/21.30 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 155.85/21.30 | r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) |
% 155.85/21.30 | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) |
% 155.85/21.30 | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~
% 155.85/21.30 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 155.85/21.30 | r1(v0, v1) | ~ r1(all_3_13, v0) | p1(v17) | ? [v18: $i] : ($i(v18)
% 155.85/21.30 | & r1(v15, v18) & ~ p1(v18))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 155.85/21.30 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 155.85/21.30 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 155.85/21.30 | [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] :
% 155.85/21.30 | ( ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~
% 155.85/21.30 | $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6)
% 155.85/21.30 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 155.85/21.30 | $i(v0) | ~ r1(v15, v16) | ~ r1(v14, v15) | ~ r1(v13, v14) | ~
% 155.85/21.30 | r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) |
% 155.85/21.30 | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~
% 155.85/21.30 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 155.85/21.30 | r1(v0, v1) | ~ r1(all_3_13, v0) | p1(v16) | ? [v17: $i] : ($i(v17)
% 155.85/21.30 | & r1(v14, v17) & ~ p1(v17))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 155.85/21.30 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 155.85/21.30 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 155.85/21.30 | [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ( ~ $i(v15) |
% 155.85/21.30 | ~ $i(v14) | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~
% 155.85/21.30 | $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 155.85/21.30 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v14, v15) | ~
% 155.85/21.30 | r1(v13, v14) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~ r1(v10, v11) |
% 155.85/21.30 | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~
% 155.85/21.30 | r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~
% 155.85/21.30 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0) | p1(v15) | ? [v16:
% 155.85/21.30 | $i] : ($i(v16) & r1(v13, v16) & ~ p1(v16))) & ! [v0: $i] : !
% 155.85/21.30 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 155.85/21.30 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 155.85/21.30 | [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~ $i(v14) |
% 155.85/21.30 | ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~
% 155.85/21.30 | $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 155.85/21.30 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v13, v14) | ~ r1(v12, v13)
% 155.85/21.30 | | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9)
% 155.85/21.30 | | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 155.85/21.30 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 155.85/21.30 | r1(all_3_13, v0) | p1(v14) | ? [v15: $i] : ($i(v15) & r1(v12, v15) &
% 155.85/21.30 | ~ p1(v15))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 155.85/21.30 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 155.85/21.30 | $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : !
% 155.85/21.30 | [v13: $i] : ( ~ $i(v13) | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~
% 155.85/21.30 | $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 155.85/21.30 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v12, v13) | ~
% 155.85/21.30 | r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~
% 155.85/21.30 | r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 155.85/21.30 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 155.85/21.30 | r1(all_3_13, v0) | p1(v13) | ? [v14: $i] : ($i(v14) & r1(v11, v14) &
% 155.85/21.30 | ~ p1(v14))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 155.85/21.30 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 155.85/21.30 | $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 155.85/21.30 | $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7)
% 155.85/21.30 | | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 155.85/21.30 | $i(v1) | ~ $i(v0) | ~ p1(v10) | ~ r1(v10, v12) | ~ r1(v10, v11) |
% 155.85/21.30 | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~
% 155.85/21.30 | r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~
% 155.85/21.30 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0) | p1(v12) | ? [v13:
% 155.85/21.30 | $i] : ? [v14: $i] : ($i(v14) & $i(v13) & ((p1(v13) & r1(v13, v14)
% 155.85/21.30 | & r1(v11, v13) & ~ p1(v14)) | (p1(v13) & r1(v13, v14) &
% 155.85/21.30 | r1(v10, v13) & ~ p1(v14) & ! [v15: $i] : ! [v16: $i] : !
% 155.85/21.30 | [v17: $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p1(v16)
% 155.85/21.30 | | ~ r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v13, v15) |
% 155.85/21.30 | p1(v17) | p1(v15)) & ! [v15: $i] : ! [v16: $i] : ! [v17:
% 155.85/21.30 | $i] : ( ~ $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p1(v16) | ~
% 155.85/21.30 | r1(v16, v17) | ~ r1(v15, v16) | ~ r1(v13, v15) | p1(v17) |
% 155.85/21.30 | ? [v18: $i] : ($i(v18) & r1(v15, v18) & ~ p1(v18))))))) & !
% 155.85/21.30 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 155.85/21.30 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 155.85/21.30 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) | ~
% 155.85/21.30 | $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) |
% 155.85/21.30 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 155.85/21.30 | r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~
% 155.85/21.30 | r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 155.85/21.30 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 155.85/21.30 | r1(all_3_13, v0) | p1(v12) | ? [v13: $i] : ? [v14: $i] : ($i(v14) &
% 155.85/21.30 | $i(v13) & ((p1(v13) & r1(v13, v14) & r1(v12, v13) & ~ p1(v14)) |
% 155.85/21.30 | (r1(v10, v13) & ~ p1(v13) & ! [v15: $i] : ! [v16: $i] : ( ~
% 155.85/21.30 | $i(v16) | ~ $i(v15) | ~ p1(v15) | ~ r1(v15, v16) | ~
% 155.85/21.30 | r1(v13, v15) | p1(v16)))))) & ! [v0: $i] : ! [v1: $i] : !
% 155.85/21.30 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 155.85/21.30 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : (
% 155.85/21.30 | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~
% 155.85/21.30 | $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 155.85/21.30 | ~ $i(v0) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~
% 155.85/21.30 | r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 155.85/21.30 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 155.85/21.30 | r1(all_3_13, v0) | p1(v11) | ? [v12: $i] : ($i(v12) & r1(v9, v12) &
% 155.85/21.30 | ~ p1(v12))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 155.85/21.30 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] :
% 155.85/21.30 | ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) |
% 155.85/21.30 | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4)
% 155.85/21.30 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v10, v11) |
% 155.85/21.30 | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~
% 155.85/21.30 | r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~
% 155.85/21.30 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0) | p1(v10) | ? [v12:
% 155.85/21.30 | $i] : ($i(v12) & ((r1(v11, v12) & ~ p1(v12)) | (r1(v10, v12) & ~
% 155.85/21.30 | p1(v12) & ! [v13: $i] : ! [v14: $i] : ( ~ $i(v14) | ~
% 155.85/21.30 | $i(v13) | ~ p1(v13) | ~ r1(v13, v14) | ~ r1(v12, v13) |
% 155.85/21.30 | p1(v14)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 155.85/21.30 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 155.85/21.30 | [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~ $i(v10) | ~ $i(v9) | ~
% 155.85/21.30 | $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 155.85/21.30 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v9, v10) | ~ r1(v8, v9) |
% 155.85/21.30 | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 155.85/21.30 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 155.85/21.30 | r1(all_3_13, v0) | p1(v10) | ? [v11: $i] : ($i(v11) & r1(v8, v11) &
% 155.85/21.30 | ~ p1(v11))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 155.85/21.30 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] :
% 155.85/21.30 | ! [v9: $i] : ( ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~
% 155.85/21.30 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 155.85/21.30 | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~
% 155.85/21.30 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 155.85/21.30 | r1(v0, v1) | ~ r1(all_3_13, v0) | p1(v9) | ? [v10: $i] : ($i(v10) &
% 155.85/21.30 | r1(v7, v10) & ~ p1(v10))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 155.85/21.30 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 155.85/21.30 | $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) |
% 155.85/21.30 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v7,
% 155.85/21.30 | v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4)
% 155.85/21.30 | | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0)
% 155.85/21.30 | | p1(v8) | ? [v9: $i] : ($i(v9) & r1(v6, v9) & ~ p1(v9))) & ! [v0:
% 155.85/21.30 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 155.85/21.30 | $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5)
% 155.85/21.30 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 155.85/21.30 | r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 155.85/21.30 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0) |
% 155.85/21.30 | p1(v7) | ? [v8: $i] : ($i(v8) & r1(v5, v8) & ~ p1(v8))) & ! [v0:
% 155.85/21.30 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 155.85/21.30 | $i] : ! [v6: $i] : ( ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 155.85/21.30 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 155.85/21.30 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 155.85/21.30 | r1(all_3_13, v0) | p1(v6) | ? [v7: $i] : ($i(v7) & r1(v4, v7) & ~
% 155.85/21.30 | p1(v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 155.85/21.30 | ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 155.85/21.30 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 155.85/21.30 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0) |
% 155.85/21.30 | p1(v5) | ? [v6: $i] : ($i(v6) & r1(v3, v6) & ~ p1(v6))) & ! [v0:
% 155.85/21.30 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 155.85/21.30 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v3,
% 155.85/21.30 | v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 155.85/21.30 | r1(all_3_13, v0) | p1(v4) | ? [v5: $i] : ($i(v5) & r1(v2, v5) & ~
% 155.85/21.30 | p1(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 155.85/21.30 | ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~
% 155.85/21.30 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0) | p1(v3) | ? [v4:
% 155.85/21.30 | $i] : ($i(v4) & r1(v1, v4) & ~ p1(v4))) & ! [v0: $i] : ! [v1:
% 155.85/21.30 | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1,
% 155.85/21.30 | v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0) | p1(v2) | ? [v3: $i] :
% 155.85/21.30 | ($i(v3) & r1(v0, v3) & ~ p1(v3))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 155.85/21.30 | r1(all_3_1, v0) | p1(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2,
% 155.85/21.30 | v0) | p1(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) &
% 155.85/21.30 | p1(v1) & r1(v1, v2) & r1(v0, v1) & ~ p1(v2)))
% 155.85/21.31 |
% 155.85/21.31 | ALPHA: (1) implies:
% 155.85/21.31 | (2) ~ p1(all_3_0)
% 156.25/21.31 | (3) r1(all_3_13, all_3_12)
% 156.25/21.31 | (4) r1(all_3_12, all_3_11)
% 156.25/21.31 | (5) r1(all_3_11, all_3_10)
% 156.25/21.31 | (6) r1(all_3_10, all_3_9)
% 156.25/21.31 | (7) r1(all_3_9, all_3_8)
% 156.25/21.31 | (8) r1(all_3_8, all_3_7)
% 156.25/21.31 | (9) r1(all_3_7, all_3_6)
% 156.25/21.31 | (10) r1(all_3_6, all_3_5)
% 156.25/21.31 | (11) r1(all_3_5, all_3_4)
% 156.25/21.31 | (12) r1(all_3_4, all_3_3)
% 156.25/21.31 | (13) r1(all_3_3, all_3_2)
% 156.25/21.31 | (14) r1(all_3_2, all_3_1)
% 156.25/21.31 | (15) r1(all_3_2, all_3_0)
% 156.25/21.31 | (16) $i(all_3_12)
% 156.25/21.31 | (17) $i(all_3_11)
% 156.25/21.31 | (18) $i(all_3_10)
% 156.25/21.31 | (19) $i(all_3_9)
% 156.25/21.31 | (20) $i(all_3_8)
% 156.25/21.31 | (21) $i(all_3_7)
% 156.25/21.31 | (22) $i(all_3_6)
% 156.25/21.31 | (23) $i(all_3_5)
% 156.25/21.31 | (24) $i(all_3_4)
% 156.25/21.31 | (25) $i(all_3_3)
% 156.25/21.31 | (26) $i(all_3_2)
% 156.25/21.31 | (27) $i(all_3_1)
% 156.25/21.32 | (28) $i(all_3_0)
% 156.25/21.32 | (29) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_2, v0) | p1(v0) | ? [v1: $i] :
% 156.25/21.32 | ? [v2: $i] : ($i(v2) & $i(v1) & p1(v1) & r1(v1, v2) & r1(v0, v1) &
% 156.25/21.32 | ~ p1(v2)))
% 156.25/21.32 | (30) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_1, v0) | p1(v0))
% 156.25/21.32 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 156.25/21.32 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 156.25/21.32 | ! [v10: $i] : ! [v11: $i] : ( ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~
% 156.25/21.32 | $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 156.25/21.32 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v10, v11) | ~ r1(v9, v10)
% 156.25/21.32 | | ~ r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~
% 156.25/21.32 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 156.25/21.32 | r1(v0, v1) | ~ r1(all_3_13, v0) | p1(v10) | ? [v12: $i] : ($i(v12)
% 156.25/21.32 | & ((r1(v11, v12) & ~ p1(v12)) | (r1(v10, v12) & ~ p1(v12) & !
% 156.25/21.32 | [v13: $i] : ! [v14: $i] : ( ~ $i(v14) | ~ $i(v13) | ~
% 156.25/21.32 | p1(v13) | ~ r1(v13, v14) | ~ r1(v12, v13) | p1(v14))))))
% 156.25/21.32 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 156.25/21.32 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 156.25/21.32 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) |
% 156.25/21.32 | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~
% 156.25/21.32 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 156.25/21.32 | ~ r1(v11, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) |
% 156.25/21.32 | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~
% 156.25/21.32 | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 156.25/21.32 | r1(all_3_13, v0) | p1(v12) | ? [v13: $i] : ? [v14: $i] : ($i(v14)
% 156.25/21.32 | & $i(v13) & ((p1(v13) & r1(v13, v14) & r1(v12, v13) & ~ p1(v14))
% 156.25/21.32 | | (r1(v10, v13) & ~ p1(v13) & ! [v15: $i] : ! [v16: $i] : ( ~
% 156.25/21.32 | $i(v16) | ~ $i(v15) | ~ p1(v15) | ~ r1(v15, v16) | ~
% 156.25/21.32 | r1(v13, v15) | p1(v16))))))
% 156.25/21.33 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 156.25/21.33 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 156.25/21.33 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~ $i(v12) | ~ $i(v11) |
% 156.25/21.33 | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~
% 156.25/21.33 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 156.25/21.33 | ~ p1(v10) | ~ r1(v10, v12) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~
% 156.25/21.33 | r1(v8, v9) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~
% 156.25/21.33 | r1(v4, v5) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 156.25/21.33 | r1(v0, v1) | ~ r1(all_3_13, v0) | p1(v12) | ? [v13: $i] : ? [v14:
% 156.25/21.33 | $i] : ($i(v14) & $i(v13) & ((p1(v13) & r1(v13, v14) & r1(v11, v13)
% 156.25/21.33 | & ~ p1(v14)) | (p1(v13) & r1(v13, v14) & r1(v10, v13) & ~
% 156.25/21.33 | p1(v14) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~
% 156.25/21.33 | $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p1(v16) | ~ r1(v16,
% 156.25/21.33 | v17) | ~ r1(v15, v16) | ~ r1(v13, v15) | p1(v17) |
% 156.25/21.33 | p1(v15)) & ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~
% 156.25/21.33 | $i(v17) | ~ $i(v16) | ~ $i(v15) | ~ p1(v16) | ~ r1(v16,
% 156.25/21.33 | v17) | ~ r1(v15, v16) | ~ r1(v13, v15) | p1(v17) | ?
% 156.25/21.33 | [v18: $i] : ($i(v18) & r1(v15, v18) & ~ p1(v18)))))))
% 156.25/21.33 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 156.25/21.33 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 156.25/21.33 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ $i(v13)
% 156.25/21.33 | | ~ $i(v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ~ $i(v8) | ~
% 156.25/21.33 | $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 156.25/21.33 | ~ $i(v1) | ~ $i(v0) | ~ r1(v12, v13) | ~ r1(v11, v12) | ~
% 156.25/21.33 | r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v8, v9) | ~ r1(v7, v8) | ~
% 156.25/21.33 | r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v3, v4) | ~
% 156.25/21.33 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_13, v0) |
% 156.25/21.33 | p1(v13) | ? [v14: $i] : ($i(v14) & r1(v11, v14) & ~ p1(v14)))
% 156.25/21.33 |
% 156.25/21.34 | GROUND_INST: instantiating (31) with all_3_12, all_3_11, all_3_10, all_3_9,
% 156.25/21.34 | all_3_8, all_3_7, all_3_6, all_3_5, all_3_4, all_3_3, all_3_2,
% 156.25/21.34 | all_3_1, simplifying with (3), (4), (5), (6), (7), (8), (9),
% 156.25/21.34 | (10), (11), (12), (13), (14), (16), (17), (18), (19), (20), (21),
% 156.25/21.34 | (22), (23), (24), (25), (26), (27) gives:
% 156.25/21.34 | (35) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) |
% 156.25/21.34 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 156.25/21.34 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1)
% 156.25/21.34 | | p1(v2)))))
% 156.25/21.34 |
% 156.25/21.34 | GROUND_INST: instantiating (31) with all_3_12, all_3_11, all_3_10, all_3_9,
% 156.25/21.34 | all_3_8, all_3_7, all_3_6, all_3_5, all_3_4, all_3_3, all_3_2,
% 156.25/21.34 | all_3_0, simplifying with (3), (4), (5), (6), (7), (8), (9),
% 156.25/21.34 | (10), (11), (12), (13), (15), (16), (17), (18), (19), (20), (21),
% 156.25/21.34 | (22), (23), (24), (25), (26), (28) gives:
% 156.25/21.34 | (36) p1(all_3_2) | ? [v0: $i] : ($i(v0) & ((r1(all_3_0, v0) & ~ p1(v0)) |
% 156.25/21.34 | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 156.25/21.34 | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1)
% 156.25/21.34 | | p1(v2)))))
% 156.25/21.34 |
% 156.25/21.34 | BETA: splitting (36) gives:
% 156.25/21.34 |
% 156.25/21.34 | Case 1:
% 156.25/21.34 | |
% 156.25/21.34 | | (37) p1(all_3_2)
% 156.25/21.34 | |
% 156.25/21.34 | | GROUND_INST: instantiating (33) with all_3_12, all_3_11, all_3_10, all_3_9,
% 156.25/21.34 | | all_3_8, all_3_7, all_3_6, all_3_5, all_3_4, all_3_3, all_3_2,
% 156.25/21.34 | | all_3_1, all_3_0, simplifying with (2), (3), (4), (5), (6),
% 156.25/21.34 | | (7), (8), (9), (10), (11), (12), (13), (14), (15), (16), (17),
% 156.25/21.34 | | (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 156.25/21.34 | | (28), (37) gives:
% 156.25/21.35 | | (38) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0, v1)
% 156.25/21.35 | | & r1(all_3_1, v0) & ~ p1(v1)) | (p1(v0) & r1(v0, v1) &
% 156.25/21.35 | | r1(all_3_2, v0) & ~ p1(v1) & ! [v2: $i] : ! [v3: $i] : !
% 156.25/21.35 | | [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~
% 156.25/21.35 | | r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) |
% 156.25/21.35 | | p1(v2)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 156.25/21.35 | | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ p1(v3) | ~ r1(v3, v4) |
% 156.25/21.35 | | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | ? [v5: $i] :
% 156.25/21.35 | | ($i(v5) & r1(v2, v5) & ~ p1(v5))))))
% 156.25/21.35 | |
% 156.25/21.35 | | DELTA: instantiating (38) with fresh symbols all_173_0, all_173_1 gives:
% 156.25/21.35 | | (39) $i(all_173_0) & $i(all_173_1) & ((p1(all_173_1) & r1(all_173_1,
% 156.25/21.35 | | all_173_0) & r1(all_3_1, all_173_1) & ~ p1(all_173_0)) |
% 156.25/21.35 | | (p1(all_173_1) & r1(all_173_1, all_173_0) & r1(all_3_2, all_173_1)
% 156.25/21.35 | | & ~ p1(all_173_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 156.25/21.35 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) |
% 156.25/21.35 | | ~ r1(v0, v1) | ~ r1(all_173_1, v0) | p1(v2) | p1(v0)) & !
% 156.25/21.35 | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) |
% 156.25/21.35 | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 156.25/21.35 | | r1(all_173_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0,
% 156.25/21.35 | | v3) & ~ p1(v3)))))
% 156.25/21.35 | |
% 156.25/21.35 | | ALPHA: (39) implies:
% 156.25/21.35 | | (40) $i(all_173_1)
% 156.25/21.35 | | (41) $i(all_173_0)
% 156.25/21.35 | | (42) (p1(all_173_1) & r1(all_173_1, all_173_0) & r1(all_3_1, all_173_1) &
% 156.25/21.35 | | ~ p1(all_173_0)) | (p1(all_173_1) & r1(all_173_1, all_173_0) &
% 156.25/21.35 | | r1(all_3_2, all_173_1) & ~ p1(all_173_0) & ! [v0: $i] : ! [v1:
% 156.25/21.35 | | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 156.25/21.35 | | p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_173_1, v0) |
% 156.25/21.35 | | p1(v2) | p1(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 156.25/21.35 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~
% 156.25/21.35 | | r1(v0, v1) | ~ r1(all_173_1, v0) | p1(v2) | ? [v3: $i] :
% 156.25/21.35 | | ($i(v3) & r1(v0, v3) & ~ p1(v3))))
% 156.25/21.35 | |
% 156.25/21.35 | | BETA: splitting (42) gives:
% 156.25/21.35 | |
% 156.25/21.35 | | Case 1:
% 156.25/21.35 | | |
% 156.25/21.35 | | | (43) p1(all_173_1) & r1(all_173_1, all_173_0) & r1(all_3_1, all_173_1)
% 156.25/21.35 | | | & ~ p1(all_173_0)
% 156.25/21.35 | | |
% 156.25/21.35 | | | ALPHA: (43) implies:
% 156.25/21.35 | | | (44) ~ p1(all_173_0)
% 156.25/21.35 | | | (45) r1(all_3_1, all_173_1)
% 156.25/21.35 | | | (46) r1(all_173_1, all_173_0)
% 156.25/21.35 | | |
% 156.25/21.36 | | | GROUND_INST: instantiating (34) with all_3_12, all_3_11, all_3_10,
% 156.25/21.36 | | | all_3_9, all_3_8, all_3_7, all_3_6, all_3_5, all_3_4,
% 156.25/21.36 | | | all_3_3, all_3_2, all_3_1, all_173_1, all_173_0, simplifying
% 156.25/21.36 | | | with (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 156.25/21.36 | | | (13), (14), (16), (17), (18), (19), (20), (21), (22), (23),
% 156.25/21.36 | | | (24), (25), (26), (27), (40), (41), (44), (45), (46) gives:
% 156.25/21.36 | | | (47) ? [v0: $i] : ($i(v0) & r1(all_3_1, v0) & ~ p1(v0))
% 156.25/21.36 | | |
% 156.25/21.36 | | | DELTA: instantiating (47) with fresh symbol all_253_0 gives:
% 156.25/21.36 | | | (48) $i(all_253_0) & r1(all_3_1, all_253_0) & ~ p1(all_253_0)
% 156.25/21.36 | | |
% 156.25/21.36 | | | ALPHA: (48) implies:
% 156.25/21.36 | | | (49) ~ p1(all_253_0)
% 156.25/21.36 | | | (50) r1(all_3_1, all_253_0)
% 156.25/21.36 | | | (51) $i(all_253_0)
% 156.25/21.36 | | |
% 156.25/21.36 | | | GROUND_INST: instantiating (30) with all_253_0, simplifying with (49),
% 156.25/21.36 | | | (50), (51) gives:
% 156.25/21.36 | | | (52) $false
% 156.25/21.36 | | |
% 156.25/21.36 | | | CLOSE: (52) is inconsistent.
% 156.25/21.36 | | |
% 156.25/21.36 | | Case 2:
% 156.25/21.36 | | |
% 156.25/21.36 | | | (53) p1(all_173_1) & r1(all_173_1, all_173_0) & r1(all_3_2, all_173_1)
% 156.25/21.36 | | | & ~ p1(all_173_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 156.25/21.36 | | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~
% 156.25/21.36 | | | r1(v0, v1) | ~ r1(all_173_1, v0) | p1(v2) | p1(v0)) & ! [v0:
% 156.25/21.36 | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 156.25/21.36 | | | $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 156.25/21.36 | | | r1(all_173_1, v0) | p1(v2) | ? [v3: $i] : ($i(v3) & r1(v0, v3)
% 156.25/21.36 | | | & ~ p1(v3)))
% 156.25/21.36 | | |
% 156.25/21.36 | | | ALPHA: (53) implies:
% 156.25/21.36 | | | (54) ~ p1(all_173_0)
% 156.25/21.36 | | | (55) r1(all_3_2, all_173_1)
% 156.25/21.36 | | | (56) r1(all_173_1, all_173_0)
% 156.25/21.37 | | | (57) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) |
% 156.25/21.37 | | | ~ $i(v0) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 156.25/21.37 | | | r1(all_173_1, v0) | p1(v2) | p1(v0))
% 156.25/21.37 | | |
% 156.25/21.37 | | | GROUND_INST: instantiating (32) with all_3_12, all_3_11, all_3_10,
% 156.25/21.37 | | | all_3_9, all_3_8, all_3_7, all_3_6, all_3_5, all_3_4,
% 156.25/21.37 | | | all_3_3, all_3_2, all_173_1, all_173_0, simplifying with (3),
% 156.25/21.37 | | | (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (16),
% 156.25/21.37 | | | (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 156.25/21.37 | | | (40), (41), (54), (55), (56) gives:
% 156.25/21.37 | | | (58) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((p1(v0) & r1(v0,
% 156.25/21.37 | | | v1) & r1(all_173_0, v0) & ~ p1(v1)) | (r1(all_3_2, v0) &
% 156.25/21.37 | | | ~ p1(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 156.25/21.37 | | | $i(v2) | ~ p1(v2) | ~ r1(v2, v3) | ~ r1(v0, v2) |
% 156.25/21.37 | | | p1(v3)))))
% 156.25/21.37 | | |
% 156.25/21.37 | | | DELTA: instantiating (58) with fresh symbols all_254_0, all_254_1 gives:
% 156.25/21.37 | | | (59) $i(all_254_0) & $i(all_254_1) & ((p1(all_254_1) & r1(all_254_1,
% 156.25/21.37 | | | all_254_0) & r1(all_173_0, all_254_1) & ~ p1(all_254_0)) |
% 156.25/21.37 | | | (r1(all_3_2, all_254_1) & ~ p1(all_254_1) & ! [v0: $i] : !
% 156.25/21.37 | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1)
% 156.25/21.37 | | | | ~ r1(all_254_1, v0) | p1(v1))))
% 156.25/21.37 | | |
% 156.25/21.37 | | | ALPHA: (59) implies:
% 156.25/21.37 | | | (60) $i(all_254_1)
% 156.25/21.37 | | | (61) $i(all_254_0)
% 156.25/21.37 | | | (62) (p1(all_254_1) & r1(all_254_1, all_254_0) & r1(all_173_0,
% 156.25/21.37 | | | all_254_1) & ~ p1(all_254_0)) | (r1(all_3_2, all_254_1) & ~
% 156.25/21.37 | | | p1(all_254_1) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 156.25/21.37 | | | $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_254_1, v0) |
% 156.25/21.37 | | | p1(v1)))
% 156.25/21.37 | | |
% 156.25/21.37 | | | BETA: splitting (62) gives:
% 156.25/21.37 | | |
% 156.25/21.37 | | | Case 1:
% 156.25/21.37 | | | |
% 156.25/21.37 | | | | (63) p1(all_254_1) & r1(all_254_1, all_254_0) & r1(all_173_0,
% 156.25/21.37 | | | | all_254_1) & ~ p1(all_254_0)
% 156.25/21.37 | | | |
% 156.25/21.37 | | | | ALPHA: (63) implies:
% 156.25/21.37 | | | | (64) ~ p1(all_254_0)
% 156.25/21.37 | | | | (65) r1(all_173_0, all_254_1)
% 156.25/21.37 | | | | (66) r1(all_254_1, all_254_0)
% 156.25/21.37 | | | | (67) p1(all_254_1)
% 156.25/21.37 | | | |
% 156.25/21.37 | | | | GROUND_INST: instantiating (57) with all_173_0, all_254_1, all_254_0,
% 156.25/21.37 | | | | simplifying with (41), (54), (56), (60), (61), (64), (65),
% 156.25/21.37 | | | | (66), (67) gives:
% 156.25/21.37 | | | | (68) $false
% 156.25/21.37 | | | |
% 156.25/21.37 | | | | CLOSE: (68) is inconsistent.
% 156.25/21.37 | | | |
% 156.25/21.37 | | | Case 2:
% 156.25/21.37 | | | |
% 156.25/21.37 | | | | (69) r1(all_3_2, all_254_1) & ~ p1(all_254_1) & ! [v0: $i] : !
% 156.25/21.37 | | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) |
% 156.25/21.37 | | | | ~ r1(all_254_1, v0) | p1(v1))
% 156.25/21.37 | | | |
% 156.25/21.37 | | | | ALPHA: (69) implies:
% 156.25/21.37 | | | | (70) ~ p1(all_254_1)
% 156.25/21.37 | | | | (71) r1(all_3_2, all_254_1)
% 156.25/21.37 | | | | (72) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) |
% 156.25/21.37 | | | | ~ r1(v0, v1) | ~ r1(all_254_1, v0) | p1(v1))
% 156.25/21.37 | | | |
% 156.25/21.38 | | | | GROUND_INST: instantiating (29) with all_254_1, simplifying with (60),
% 156.25/21.38 | | | | (70), (71) gives:
% 156.25/21.38 | | | | (73) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0,
% 156.25/21.38 | | | | v1) & r1(all_254_1, v0) & ~ p1(v1))
% 156.25/21.38 | | | |
% 156.25/21.38 | | | | DELTA: instantiating (73) with fresh symbols all_322_0, all_322_1 gives:
% 156.25/21.38 | | | | (74) $i(all_322_0) & $i(all_322_1) & p1(all_322_1) & r1(all_322_1,
% 156.25/21.38 | | | | all_322_0) & r1(all_254_1, all_322_1) & ~ p1(all_322_0)
% 156.25/21.38 | | | |
% 156.25/21.38 | | | | ALPHA: (74) implies:
% 156.25/21.38 | | | | (75) ~ p1(all_322_0)
% 156.25/21.38 | | | | (76) r1(all_254_1, all_322_1)
% 156.25/21.38 | | | | (77) r1(all_322_1, all_322_0)
% 156.25/21.38 | | | | (78) p1(all_322_1)
% 156.25/21.38 | | | | (79) $i(all_322_1)
% 156.25/21.38 | | | | (80) $i(all_322_0)
% 156.25/21.38 | | | |
% 156.25/21.38 | | | | GROUND_INST: instantiating (72) with all_322_1, all_322_0, simplifying
% 156.25/21.38 | | | | with (75), (76), (77), (78), (79), (80) gives:
% 156.25/21.38 | | | | (81) $false
% 156.25/21.38 | | | |
% 156.25/21.38 | | | | CLOSE: (81) is inconsistent.
% 156.25/21.38 | | | |
% 156.25/21.38 | | | End of split
% 156.25/21.38 | | |
% 156.25/21.38 | | End of split
% 156.25/21.38 | |
% 156.25/21.38 | Case 2:
% 156.25/21.38 | |
% 156.25/21.38 | | (82) ~ p1(all_3_2)
% 156.25/21.38 | |
% 156.25/21.38 | | BETA: splitting (35) gives:
% 156.25/21.38 | |
% 156.25/21.38 | | Case 1:
% 156.25/21.38 | | |
% 156.25/21.38 | | | (83) p1(all_3_2)
% 156.25/21.38 | | |
% 156.25/21.38 | | | PRED_UNIFY: (82), (83) imply:
% 156.25/21.38 | | | (84) $false
% 156.25/21.38 | | |
% 156.25/21.38 | | | CLOSE: (84) is inconsistent.
% 156.25/21.38 | | |
% 156.25/21.38 | | Case 2:
% 156.25/21.38 | | |
% 156.56/21.38 | | | (85) ? [v0: $i] : ($i(v0) & ((r1(all_3_1, v0) & ~ p1(v0)) |
% 156.56/21.38 | | | (r1(all_3_2, v0) & ~ p1(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 156.56/21.38 | | | $i(v2) | ~ $i(v1) | ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0,
% 156.56/21.38 | | | v1) | p1(v2)))))
% 156.56/21.38 | | |
% 156.56/21.38 | | | DELTA: instantiating (85) with fresh symbol all_141_0 gives:
% 156.56/21.38 | | | (86) $i(all_141_0) & ((r1(all_3_1, all_141_0) & ~ p1(all_141_0)) |
% 156.56/21.38 | | | (r1(all_3_2, all_141_0) & ~ p1(all_141_0) & ! [v0: $i] : !
% 156.56/21.38 | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1)
% 156.56/21.38 | | | | ~ r1(all_141_0, v0) | p1(v1))))
% 156.56/21.38 | | |
% 156.56/21.38 | | | ALPHA: (86) implies:
% 156.56/21.38 | | | (87) $i(all_141_0)
% 156.56/21.38 | | | (88) (r1(all_3_1, all_141_0) & ~ p1(all_141_0)) | (r1(all_3_2,
% 156.56/21.38 | | | all_141_0) & ~ p1(all_141_0) & ! [v0: $i] : ! [v1: $i] : (
% 156.56/21.38 | | | ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) | ~
% 156.56/21.38 | | | r1(all_141_0, v0) | p1(v1)))
% 156.56/21.38 | | |
% 156.56/21.38 | | | BETA: splitting (88) gives:
% 156.56/21.38 | | |
% 156.56/21.38 | | | Case 1:
% 156.56/21.38 | | | |
% 156.56/21.38 | | | | (89) r1(all_3_1, all_141_0) & ~ p1(all_141_0)
% 156.56/21.38 | | | |
% 156.56/21.38 | | | | ALPHA: (89) implies:
% 156.56/21.38 | | | | (90) ~ p1(all_141_0)
% 156.56/21.38 | | | | (91) r1(all_3_1, all_141_0)
% 156.56/21.38 | | | |
% 156.56/21.38 | | | | GROUND_INST: instantiating (30) with all_141_0, simplifying with (87),
% 156.56/21.38 | | | | (90), (91) gives:
% 156.56/21.38 | | | | (92) $false
% 156.56/21.38 | | | |
% 156.56/21.38 | | | | CLOSE: (92) is inconsistent.
% 156.56/21.38 | | | |
% 156.56/21.38 | | | Case 2:
% 156.56/21.38 | | | |
% 156.56/21.38 | | | | (93) r1(all_3_2, all_141_0) & ~ p1(all_141_0) & ! [v0: $i] : !
% 156.56/21.38 | | | | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ r1(v0, v1) |
% 156.56/21.38 | | | | ~ r1(all_141_0, v0) | p1(v1))
% 156.56/21.38 | | | |
% 156.56/21.38 | | | | ALPHA: (93) implies:
% 156.56/21.38 | | | | (94) ~ p1(all_141_0)
% 156.56/21.38 | | | | (95) r1(all_3_2, all_141_0)
% 156.56/21.39 | | | | (96) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) |
% 156.56/21.39 | | | | ~ r1(v0, v1) | ~ r1(all_141_0, v0) | p1(v1))
% 156.56/21.39 | | | |
% 156.56/21.39 | | | | GROUND_INST: instantiating (29) with all_141_0, simplifying with (87),
% 156.56/21.39 | | | | (94), (95) gives:
% 156.56/21.39 | | | | (97) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & p1(v0) & r1(v0,
% 156.56/21.39 | | | | v1) & r1(all_141_0, v0) & ~ p1(v1))
% 156.56/21.39 | | | |
% 156.56/21.39 | | | | DELTA: instantiating (97) with fresh symbols all_271_0, all_271_1 gives:
% 156.56/21.39 | | | | (98) $i(all_271_0) & $i(all_271_1) & p1(all_271_1) & r1(all_271_1,
% 156.56/21.39 | | | | all_271_0) & r1(all_141_0, all_271_1) & ~ p1(all_271_0)
% 156.56/21.39 | | | |
% 156.56/21.39 | | | | ALPHA: (98) implies:
% 156.56/21.39 | | | | (99) ~ p1(all_271_0)
% 156.56/21.39 | | | | (100) r1(all_141_0, all_271_1)
% 156.56/21.39 | | | | (101) r1(all_271_1, all_271_0)
% 156.56/21.39 | | | | (102) p1(all_271_1)
% 156.56/21.39 | | | | (103) $i(all_271_1)
% 156.56/21.39 | | | | (104) $i(all_271_0)
% 156.56/21.39 | | | |
% 156.56/21.39 | | | | GROUND_INST: instantiating (96) with all_271_1, all_271_0, simplifying
% 156.56/21.39 | | | | with (99), (100), (101), (102), (103), (104) gives:
% 156.56/21.39 | | | | (105) $false
% 156.56/21.39 | | | |
% 156.56/21.39 | | | | CLOSE: (105) is inconsistent.
% 156.56/21.39 | | | |
% 156.56/21.39 | | | End of split
% 156.56/21.39 | | |
% 156.56/21.39 | | End of split
% 156.56/21.39 | |
% 156.56/21.39 | End of split
% 156.56/21.39 |
% 156.56/21.39 End of proof
% 156.56/21.39 % SZS output end Proof for theBenchmark
% 156.56/21.39
% 156.56/21.39 20771ms
%------------------------------------------------------------------------------