TSTP Solution File: LCL646+1.005 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LCL646+1.005 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:11:58 EDT 2023
% Result : Theorem 184.73s 25.78s
% Output : Proof 185.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL646+1.005 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Aug 24 19:59:53 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.59 ________ _____
% 0.16/0.59 ___ __ \_________(_)________________________________
% 0.16/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.59
% 0.16/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.59 (2023-06-19)
% 0.16/0.59
% 0.16/0.59 (c) Philipp Rümmer, 2009-2023
% 0.16/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.59 Amanda Stjerna.
% 0.16/0.59 Free software under BSD-3-Clause.
% 0.16/0.59
% 0.16/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.59
% 0.16/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.61 Running up to 7 provers in parallel.
% 0.16/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.29/1.61 Prover 4: Preprocessing ...
% 4.29/1.62 Prover 1: Preprocessing ...
% 4.29/1.64 Prover 6: Preprocessing ...
% 4.29/1.64 Prover 5: Preprocessing ...
% 4.29/1.64 Prover 3: Preprocessing ...
% 4.29/1.64 Prover 2: Preprocessing ...
% 4.29/1.64 Prover 0: Preprocessing ...
% 12.64/2.59 Prover 2: Constructing countermodel ...
% 14.13/2.79 Prover 5: Constructing countermodel ...
% 17.77/3.30 Prover 6: Proving ...
% 17.77/3.32 Prover 3: Constructing countermodel ...
% 18.21/3.33 Prover 1: Constructing countermodel ...
% 20.00/3.59 Prover 0: Proving ...
% 21.07/3.77 Prover 4: Constructing countermodel ...
% 71.56/10.42 Prover 2: stopped
% 71.56/10.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 72.03/10.54 Prover 7: Preprocessing ...
% 72.93/10.62 Prover 7: Constructing countermodel ...
% 98.52/13.95 Prover 5: stopped
% 98.52/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 99.66/14.14 Prover 8: Preprocessing ...
% 101.68/14.42 Prover 8: Warning: ignoring some quantifiers
% 101.68/14.45 Prover 8: Constructing countermodel ...
% 113.91/15.99 Prover 1: stopped
% 113.91/16.00 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 115.28/16.16 Prover 9: Preprocessing ...
% 117.89/16.52 Prover 9: Constructing countermodel ...
% 128.23/17.88 Prover 6: stopped
% 128.23/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 130.45/18.16 Prover 10: Preprocessing ...
% 130.94/18.24 Prover 10: Constructing countermodel ...
% 184.73/25.71 Prover 10: Found proof (size 17)
% 184.73/25.71 Prover 10: proved (7821ms)
% 184.73/25.72 Prover 7: stopped
% 184.73/25.72 Prover 8: stopped
% 184.73/25.73 Prover 4: stopped
% 184.73/25.74 Prover 3: stopped
% 184.73/25.78 Prover 0: stopped
% 184.73/25.78 Prover 9: stopped
% 184.73/25.78
% 184.73/25.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 184.73/25.78
% 184.73/25.78 % SZS output start Proof for theBenchmark
% 184.73/25.79 Assumptions after simplification:
% 184.73/25.79 ---------------------------------
% 184.73/25.79
% 184.73/25.79 (main)
% 185.06/25.83 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v4)
% 185.06/25.83 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & r1(v0, v4) & r1(v0, v3) & r1(v0, v2) &
% 185.06/25.83 r1(v0, v1) & ~ p1(v1) & ~ p3(v3) & ~ p5(v4) & ~ p2(v2) & ! [v5: $i] :
% 185.06/25.83 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~
% 185.06/25.83 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v8, v9) | ~ r1(v7, v8)
% 185.06/25.83 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p2(v9)) & ! [v5: $i] :
% 185.06/25.83 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~
% 185.06/25.83 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v8, v9) | ~ r1(v7, v8)
% 185.06/25.83 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p4(v9)) & ! [v5: $i] :
% 185.06/25.83 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~
% 185.06/25.83 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v8, v9) | ~ r1(v7, v8)
% 185.06/25.83 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p6(v9)) & ! [v5: $i] :
% 185.06/25.83 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6)
% 185.06/25.83 | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0,
% 185.06/25.83 v5) | p1(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p1(v9))) & !
% 185.06/25.83 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7)
% 185.06/25.83 | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) |
% 185.06/25.83 ~ r1(v0, v5) | p1(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p3(v9))) &
% 185.06/25.83 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~
% 185.06/25.83 $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5,
% 185.06/25.83 v6) | ~ r1(v0, v5) | p1(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~
% 185.06/25.83 p5(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 185.06/25.83 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7)
% 185.06/25.83 | ~ r1(v5, v6) | ~ r1(v0, v5) | p1(v8) | ? [v9: $i] : ($i(v9) & r1(v8,
% 185.06/25.83 v9) & ~ p4(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 185.06/25.83 $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~
% 185.06/25.83 r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p3(v8) | ? [v9: $i] :
% 185.06/25.83 ($i(v9) & r1(v8, v9) & ~ p1(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7:
% 185.06/25.83 $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~
% 185.06/25.83 r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p3(v8) | ?
% 185.06/25.83 [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p3(v9))) & ! [v5: $i] : ! [v6: $i]
% 185.06/25.83 : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5)
% 185.06/25.83 | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p3(v8) |
% 185.06/25.83 ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p5(v9))) & ! [v5: $i] : ! [v6:
% 185.06/25.83 $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~
% 185.06/25.83 $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) |
% 185.06/25.83 p5(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p1(v9))) & ! [v5: $i] :
% 185.06/25.83 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6)
% 185.06/25.83 | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0,
% 185.06/25.84 v5) | p5(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p3(v9))) & !
% 185.06/25.84 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7)
% 185.06/25.84 | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) |
% 185.06/25.84 ~ r1(v0, v5) | p5(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p5(v9))) &
% 185.06/25.84 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~
% 185.06/25.84 $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5,
% 185.06/25.84 v6) | ~ r1(v0, v5) | p2(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~
% 185.06/25.84 p2(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 185.06/25.84 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7)
% 185.06/25.84 | ~ r1(v5, v6) | ~ r1(v0, v5) | p2(v8) | ? [v9: $i] : ($i(v9) & r1(v8,
% 185.06/25.84 v9) & ~ p4(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 185.06/25.84 $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~
% 185.06/25.84 r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p2(v8) | ? [v9: $i] :
% 185.06/25.84 ($i(v9) & r1(v8, v9) & ~ p6(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7:
% 185.06/25.84 $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~
% 185.06/25.84 r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p4(v8) | ?
% 185.06/25.84 [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p2(v9))) & ! [v5: $i] : ! [v6: $i]
% 185.06/25.84 : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5)
% 185.06/25.84 | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p4(v8) |
% 185.06/25.84 ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p4(v9))) & ! [v5: $i] : ! [v6:
% 185.06/25.84 $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~
% 185.06/25.84 $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) |
% 185.06/25.84 p4(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p6(v9))) & ! [v5: $i] :
% 185.06/25.84 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6)
% 185.06/25.84 | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0,
% 185.06/25.84 v5) | p6(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p2(v9))) & !
% 185.06/25.84 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7)
% 185.06/25.84 | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) |
% 185.06/25.84 ~ r1(v0, v5) | p6(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p4(v9))) &
% 185.06/25.84 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~
% 185.06/25.84 $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5,
% 185.06/25.84 v6) | ~ r1(v0, v5) | p6(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~
% 185.06/25.84 p6(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~
% 185.06/25.84 $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) |
% 185.06/25.84 p1(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p3(v8))) & ! [v5: $i] :
% 185.06/25.84 ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6,
% 185.06/25.84 v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p1(v7) | ? [v8: $i] : ($i(v8) &
% 185.06/25.84 r1(v7, v8) & ~ p5(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 185.06/25.84 $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0,
% 185.06/25.84 v5) | p3(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p3(v8))) & !
% 185.06/25.84 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) |
% 185.06/25.84 ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p3(v7) | ? [v8: $i] :
% 185.06/25.84 ($i(v8) & r1(v7, v8) & ~ p5(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7:
% 185.06/25.84 $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) |
% 185.06/25.84 ~ r1(v0, v5) | p5(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p3(v8)))
% 185.06/25.84 & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~
% 185.06/25.84 $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p5(v7) | ? [v8:
% 185.06/25.84 $i] : ($i(v8) & r1(v7, v8) & ~ p5(v8))) & ! [v5: $i] : ! [v6: $i] :
% 185.06/25.84 ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5,
% 185.06/25.84 v6) | ~ r1(v0, v5) | p2(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~
% 185.06/25.84 p2(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~
% 185.06/25.84 $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) |
% 185.06/25.84 p2(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p4(v8))) & ! [v5: $i] :
% 185.06/25.84 ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6,
% 185.06/25.84 v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p2(v7) | ? [v8: $i] : ($i(v8) &
% 185.06/25.84 r1(v7, v8) & ~ p6(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 185.06/25.84 $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0,
% 185.06/25.84 v5) | p4(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p1(v8))) & !
% 185.06/25.84 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) |
% 185.06/25.84 ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p6(v7) | ? [v8: $i] :
% 185.06/25.84 ($i(v8) & r1(v7, v8) & ~ p2(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7:
% 185.06/25.84 $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) |
% 185.06/25.84 ~ r1(v0, v5) | p6(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p4(v8)))
% 185.06/25.84 & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~
% 185.06/25.84 $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p6(v7) | ? [v8:
% 185.06/25.84 $i] : ($i(v8) & r1(v7, v8) & ~ p6(v8))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p1(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p1(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p1(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p3(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p1(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p5(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p1(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p4(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p3(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p1(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p3(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p3(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p3(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p5(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p5(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p1(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p5(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p3(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p5(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p5(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p2(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p2(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p2(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p4(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p2(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p6(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p4(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p2(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p4(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p4(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p4(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p6(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p6(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p2(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p6(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p4(v7))) & ! [v5: $i] : ! [v6: $i] : (
% 185.06/25.84 ~ $i(v6) | ~ $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p6(v6) | ? [v7:
% 185.06/25.84 $i] : ($i(v7) & r1(v6, v7) & ~ p6(v7))) & ! [v5: $i] : ( ~ $i(v5) | ~
% 185.06/25.84 r1(v0, v5) | p1(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ p3(v6))) &
% 185.06/25.84 ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | p1(v5) | ? [v6: $i] : ($i(v6) &
% 185.06/25.84 r1(v5, v6) & ~ p5(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) |
% 185.06/25.84 p3(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ p3(v6))) & ! [v5: $i] :
% 185.06/25.84 ( ~ $i(v5) | ~ r1(v0, v5) | p3(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) &
% 185.06/25.84 ~ p5(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | p5(v5) | ? [v6:
% 185.06/25.85 $i] : ($i(v6) & r1(v5, v6) & ~ p3(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~
% 185.06/25.85 r1(v0, v5) | p5(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ p5(v6))) &
% 185.06/25.85 ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | p2(v5) | ? [v6: $i] : ($i(v6) &
% 185.06/25.85 r1(v5, v6) & ~ p1(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) |
% 185.06/25.85 p4(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ p2(v6))) & ! [v5: $i] :
% 185.06/25.85 ( ~ $i(v5) | ~ r1(v0, v5) | p4(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) &
% 185.06/25.85 ~ p4(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | p4(v5) | ? [v6:
% 185.06/25.85 $i] : ($i(v6) & r1(v5, v6) & ~ p6(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~
% 185.06/25.85 r1(v0, v5) | p6(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ p2(v6))) &
% 185.06/25.85 ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | p6(v5) | ? [v6: $i] : ($i(v6) &
% 185.06/25.85 r1(v5, v6) & ~ p4(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) |
% 185.06/25.85 p6(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ p6(v6))))
% 185.06/25.85
% 185.06/25.85 Those formulas are unsatisfiable:
% 185.06/25.85 ---------------------------------
% 185.06/25.85
% 185.06/25.85 Begin of proof
% 185.06/25.85 |
% 185.06/25.85 | DELTA: instantiating (main) with fresh symbols all_2_0, all_2_1, all_2_2,
% 185.06/25.85 | all_2_3, all_2_4 gives:
% 185.06/25.87 | (1) $i(all_2_0) & $i(all_2_1) & $i(all_2_2) & $i(all_2_3) & $i(all_2_4) &
% 185.06/25.87 | r1(all_2_4, all_2_0) & r1(all_2_4, all_2_1) & r1(all_2_4, all_2_2) &
% 185.06/25.87 | r1(all_2_4, all_2_3) & ~ p1(all_2_3) & ~ p3(all_2_1) & ~ p5(all_2_0)
% 185.06/25.87 | & ~ p2(all_2_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 185.06/25.87 | $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 185.06/25.87 | ~ $i(v0) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0,
% 185.06/25.87 | v1) | ~ r1(all_2_4, v0) | p2(v4)) & ! [v0: $i] : ! [v1: $i] : !
% 185.06/25.87 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~
% 185.06/25.87 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~
% 185.06/25.87 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p4(v4)) & ! [v0:
% 185.06/25.87 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 185.06/25.87 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v3,
% 185.06/25.87 | v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 185.06/25.87 | r1(all_2_4, v0) | p6(v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 185.06/25.87 | ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.87 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) |
% 185.06/25.87 | p1(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p1(v4))) & ! [v0:
% 185.06/25.87 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 185.06/25.87 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 185.06/25.87 | r1(v0, v1) | ~ r1(all_2_4, v0) | p1(v3) | ? [v4: $i] : ($i(v4) &
% 185.06/25.87 | r1(v3, v4) & ~ p3(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 185.06/25.87 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.87 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) |
% 185.06/25.87 | p1(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p5(v4))) & ! [v0:
% 185.06/25.87 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 185.06/25.87 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 185.06/25.87 | r1(v0, v1) | ~ r1(all_2_4, v0) | p1(v3) | ? [v4: $i] : ($i(v4) &
% 185.06/25.87 | r1(v3, v4) & ~ p4(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 185.06/25.87 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.87 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) |
% 185.06/25.87 | p3(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p1(v4))) & ! [v0:
% 185.06/25.87 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 185.06/25.87 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 185.06/25.87 | r1(v0, v1) | ~ r1(all_2_4, v0) | p3(v3) | ? [v4: $i] : ($i(v4) &
% 185.06/25.87 | r1(v3, v4) & ~ p3(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 185.06/25.87 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.87 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) |
% 185.06/25.87 | p3(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p5(v4))) & ! [v0:
% 185.06/25.87 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 185.06/25.87 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 185.06/25.87 | r1(v0, v1) | ~ r1(all_2_4, v0) | p5(v3) | ? [v4: $i] : ($i(v4) &
% 185.06/25.87 | r1(v3, v4) & ~ p1(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 185.06/25.87 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.87 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) |
% 185.06/25.87 | p5(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p3(v4))) & ! [v0:
% 185.06/25.87 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 185.06/25.87 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 185.06/25.87 | r1(v0, v1) | ~ r1(all_2_4, v0) | p5(v3) | ? [v4: $i] : ($i(v4) &
% 185.06/25.87 | r1(v3, v4) & ~ p5(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 185.06/25.87 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.87 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) |
% 185.06/25.87 | p2(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p2(v4))) & ! [v0:
% 185.06/25.87 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 185.06/25.87 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 185.06/25.87 | r1(v0, v1) | ~ r1(all_2_4, v0) | p2(v3) | ? [v4: $i] : ($i(v4) &
% 185.06/25.87 | r1(v3, v4) & ~ p4(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 185.06/25.87 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.87 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) |
% 185.06/25.87 | p2(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p6(v4))) & ! [v0:
% 185.06/25.87 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 185.06/25.87 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 185.06/25.87 | r1(v0, v1) | ~ r1(all_2_4, v0) | p4(v3) | ? [v4: $i] : ($i(v4) &
% 185.06/25.88 | r1(v3, v4) & ~ p2(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 185.06/25.88 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.88 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) |
% 185.06/25.88 | p4(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p4(v4))) & ! [v0:
% 185.06/25.88 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 185.06/25.88 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 185.06/25.88 | r1(v0, v1) | ~ r1(all_2_4, v0) | p4(v3) | ? [v4: $i] : ($i(v4) &
% 185.06/25.88 | r1(v3, v4) & ~ p6(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 185.06/25.88 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.88 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) |
% 185.06/25.88 | p6(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p2(v4))) & ! [v0:
% 185.06/25.88 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 185.06/25.88 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 185.06/25.88 | r1(v0, v1) | ~ r1(all_2_4, v0) | p6(v3) | ? [v4: $i] : ($i(v4) &
% 185.06/25.88 | r1(v3, v4) & ~ p4(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 185.06/25.88 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.88 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) |
% 185.06/25.88 | p6(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p6(v4))) & ! [v0:
% 185.06/25.88 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 185.06/25.88 | | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p1(v2) | ?
% 185.06/25.88 | [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p3(v3))) & ! [v0: $i] : ! [v1:
% 185.06/25.88 | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1,
% 185.06/25.88 | v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p1(v2) | ? [v3: $i] :
% 185.06/25.88 | ($i(v3) & r1(v2, v3) & ~ p5(v3))) & ! [v0: $i] : ! [v1: $i] : !
% 185.06/25.88 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~
% 185.06/25.88 | r1(v0, v1) | ~ r1(all_2_4, v0) | p3(v2) | ? [v3: $i] : ($i(v3) &
% 185.06/25.88 | r1(v2, v3) & ~ p3(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 185.06/25.88 | : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) |
% 185.06/25.88 | ~ r1(all_2_4, v0) | p3(v2) | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~
% 185.06/25.88 | p5(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) |
% 185.06/25.88 | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4,
% 185.06/25.88 | v0) | p5(v2) | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p3(v3))) &
% 185.06/25.88 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 185.06/25.88 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p5(v2)
% 185.06/25.88 | | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p5(v3))) & ! [v0: $i] : !
% 185.06/25.88 | [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1,
% 185.06/25.88 | v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p2(v2) | ? [v3: $i] :
% 185.06/25.88 | ($i(v3) & r1(v2, v3) & ~ p2(v3))) & ! [v0: $i] : ! [v1: $i] : !
% 185.06/25.88 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~
% 185.06/25.88 | r1(v0, v1) | ~ r1(all_2_4, v0) | p2(v2) | ? [v3: $i] : ($i(v3) &
% 185.06/25.88 | r1(v2, v3) & ~ p4(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 185.06/25.88 | : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) |
% 185.06/25.88 | ~ r1(all_2_4, v0) | p2(v2) | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~
% 185.06/25.88 | p6(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) |
% 185.06/25.88 | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4,
% 185.06/25.88 | v0) | p4(v2) | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p1(v3))) &
% 185.06/25.88 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 185.06/25.88 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p6(v2)
% 185.06/25.88 | | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p2(v3))) & ! [v0: $i] : !
% 185.06/25.88 | [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1,
% 185.06/25.88 | v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p6(v2) | ? [v3: $i] :
% 185.06/25.88 | ($i(v3) & r1(v2, v3) & ~ p4(v3))) & ! [v0: $i] : ! [v1: $i] : !
% 185.06/25.88 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~
% 185.06/25.88 | r1(v0, v1) | ~ r1(all_2_4, v0) | p6(v2) | ? [v3: $i] : ($i(v3) &
% 185.06/25.88 | r1(v2, v3) & ~ p6(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) |
% 185.06/25.88 | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p1(v1) | ? [v2: $i]
% 185.06/25.88 | : ($i(v2) & r1(v1, v2) & ~ p1(v2))) & ! [v0: $i] : ! [v1: $i] : (
% 185.06/25.88 | ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p1(v1) |
% 185.06/25.88 | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p3(v2))) & ! [v0: $i] : !
% 185.06/25.88 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0)
% 185.06/25.88 | | p1(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p5(v2))) & ! [v0:
% 185.06/25.88 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~
% 185.06/25.88 | r1(all_2_4, v0) | p1(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~
% 185.06/25.88 | p4(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.88 | r1(v0, v1) | ~ r1(all_2_4, v0) | p3(v1) | ? [v2: $i] : ($i(v2) &
% 185.06/25.88 | r1(v1, v2) & ~ p1(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) |
% 185.06/25.88 | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p3(v1) | ? [v2: $i]
% 185.06/25.88 | : ($i(v2) & r1(v1, v2) & ~ p3(v2))) & ! [v0: $i] : ! [v1: $i] : (
% 185.06/25.88 | ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p3(v1) |
% 185.06/25.88 | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p5(v2))) & ! [v0: $i] : !
% 185.06/25.88 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0)
% 185.06/25.88 | | p5(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p1(v2))) & ! [v0:
% 185.06/25.88 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~
% 185.06/25.88 | r1(all_2_4, v0) | p5(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~
% 185.06/25.88 | p3(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.88 | r1(v0, v1) | ~ r1(all_2_4, v0) | p5(v1) | ? [v2: $i] : ($i(v2) &
% 185.06/25.88 | r1(v1, v2) & ~ p5(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) |
% 185.06/25.88 | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p2(v1) | ? [v2: $i]
% 185.06/25.88 | : ($i(v2) & r1(v1, v2) & ~ p2(v2))) & ! [v0: $i] : ! [v1: $i] : (
% 185.06/25.88 | ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p2(v1) |
% 185.06/25.88 | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p4(v2))) & ! [v0: $i] : !
% 185.06/25.88 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0)
% 185.06/25.88 | | p2(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p6(v2))) & ! [v0:
% 185.06/25.88 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~
% 185.06/25.89 | r1(all_2_4, v0) | p4(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~
% 185.06/25.89 | p2(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 185.06/25.89 | r1(v0, v1) | ~ r1(all_2_4, v0) | p4(v1) | ? [v2: $i] : ($i(v2) &
% 185.06/25.89 | r1(v1, v2) & ~ p4(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) |
% 185.06/25.89 | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p4(v1) | ? [v2: $i]
% 185.06/25.89 | : ($i(v2) & r1(v1, v2) & ~ p6(v2))) & ! [v0: $i] : ! [v1: $i] : (
% 185.06/25.89 | ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p6(v1) |
% 185.06/25.89 | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p2(v2))) & ! [v0: $i] : !
% 185.06/25.89 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_2_4, v0)
% 185.06/25.89 | | p6(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p4(v2))) & ! [v0:
% 185.06/25.89 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~
% 185.06/25.89 | r1(all_2_4, v0) | p6(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~
% 185.06/25.89 | p6(v2))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_4, v0) | p1(v0) |
% 185.06/25.89 | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ p3(v1))) & ! [v0: $i] : ( ~
% 185.06/25.89 | $i(v0) | ~ r1(all_2_4, v0) | p1(v0) | ? [v1: $i] : ($i(v1) & r1(v0,
% 185.06/25.89 | v1) & ~ p5(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_4, v0)
% 185.06/25.89 | | p3(v0) | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ p3(v1))) & ! [v0:
% 185.06/25.89 | $i] : ( ~ $i(v0) | ~ r1(all_2_4, v0) | p3(v0) | ? [v1: $i] :
% 185.06/25.89 | ($i(v1) & r1(v0, v1) & ~ p5(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 185.06/25.89 | r1(all_2_4, v0) | p5(v0) | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~
% 185.06/25.89 | p3(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_4, v0) | p5(v0) |
% 185.06/25.89 | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ p5(v1))) & ! [v0: $i] : ( ~
% 185.06/25.89 | $i(v0) | ~ r1(all_2_4, v0) | p2(v0) | ? [v1: $i] : ($i(v1) & r1(v0,
% 185.06/25.89 | v1) & ~ p1(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_4, v0)
% 185.06/25.89 | | p4(v0) | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ p2(v1))) & ! [v0:
% 185.06/25.89 | $i] : ( ~ $i(v0) | ~ r1(all_2_4, v0) | p4(v0) | ? [v1: $i] :
% 185.06/25.89 | ($i(v1) & r1(v0, v1) & ~ p4(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 185.06/25.89 | r1(all_2_4, v0) | p4(v0) | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~
% 185.06/25.89 | p6(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_4, v0) | p6(v0) |
% 185.06/25.89 | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ p2(v1))) & ! [v0: $i] : ( ~
% 185.06/25.89 | $i(v0) | ~ r1(all_2_4, v0) | p6(v0) | ? [v1: $i] : ($i(v1) & r1(v0,
% 185.06/25.89 | v1) & ~ p4(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_4, v0)
% 185.06/25.89 | | p6(v0) | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ p6(v1)))
% 185.06/25.89 |
% 185.06/25.89 | ALPHA: (1) implies:
% 185.06/25.89 | (2) ~ p2(all_2_2)
% 185.06/25.89 | (3) r1(all_2_4, all_2_2)
% 185.06/25.89 | (4) $i(all_2_2)
% 185.06/25.89 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_4, v0) | p2(v0) | ? [v1: $i] :
% 185.06/25.89 | ($i(v1) & r1(v0, v1) & ~ p1(v1)))
% 185.50/25.89 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~
% 185.50/25.89 | r1(all_2_4, v0) | p1(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~
% 185.50/25.89 | p4(v2)))
% 185.50/25.89 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 185.50/25.89 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_2_4, v0) | p4(v2)
% 185.50/25.89 | | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p1(v3)))
% 185.50/25.89 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 185.50/25.89 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~
% 185.50/25.89 | r1(v0, v1) | ~ r1(all_2_4, v0) | p1(v3) | ? [v4: $i] : ($i(v4) &
% 185.50/25.89 | r1(v3, v4) & ~ p4(v4)))
% 185.50/25.89 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 185.50/25.89 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v3,
% 185.50/25.89 | v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~
% 185.50/25.89 | r1(all_2_4, v0) | p4(v4))
% 185.50/25.89 |
% 185.50/25.89 | GROUND_INST: instantiating (5) with all_2_2, simplifying with (2), (3), (4)
% 185.50/25.89 | gives:
% 185.50/25.90 | (10) ? [v0: $i] : ($i(v0) & r1(all_2_2, v0) & ~ p1(v0))
% 185.50/25.90 |
% 185.50/25.90 | DELTA: instantiating (10) with fresh symbol all_22_0 gives:
% 185.50/25.90 | (11) $i(all_22_0) & r1(all_2_2, all_22_0) & ~ p1(all_22_0)
% 185.50/25.90 |
% 185.50/25.90 | ALPHA: (11) implies:
% 185.50/25.90 | (12) ~ p1(all_22_0)
% 185.50/25.90 | (13) r1(all_2_2, all_22_0)
% 185.50/25.90 | (14) $i(all_22_0)
% 185.50/25.90 |
% 185.50/25.90 | GROUND_INST: instantiating (6) with all_2_2, all_22_0, simplifying with (3),
% 185.50/25.90 | (4), (12), (13), (14) gives:
% 185.50/25.90 | (15) ? [v0: $i] : ($i(v0) & r1(all_22_0, v0) & ~ p4(v0))
% 185.50/25.90 |
% 185.50/25.90 | DELTA: instantiating (15) with fresh symbol all_41_0 gives:
% 185.50/25.90 | (16) $i(all_41_0) & r1(all_22_0, all_41_0) & ~ p4(all_41_0)
% 185.50/25.90 |
% 185.50/25.90 | ALPHA: (16) implies:
% 185.50/25.90 | (17) ~ p4(all_41_0)
% 185.50/25.90 | (18) r1(all_22_0, all_41_0)
% 185.50/25.90 | (19) $i(all_41_0)
% 185.50/25.90 |
% 185.50/25.90 | GROUND_INST: instantiating (7) with all_2_2, all_22_0, all_41_0, simplifying
% 185.50/25.90 | with (3), (4), (13), (14), (17), (18), (19) gives:
% 185.50/25.90 | (20) ? [v0: $i] : ($i(v0) & r1(all_41_0, v0) & ~ p1(v0))
% 185.50/25.90 |
% 185.50/25.90 | DELTA: instantiating (20) with fresh symbol all_96_0 gives:
% 185.50/25.90 | (21) $i(all_96_0) & r1(all_41_0, all_96_0) & ~ p1(all_96_0)
% 185.50/25.90 |
% 185.50/25.90 | ALPHA: (21) implies:
% 185.50/25.90 | (22) ~ p1(all_96_0)
% 185.50/25.90 | (23) r1(all_41_0, all_96_0)
% 185.50/25.90 | (24) $i(all_96_0)
% 185.50/25.90 |
% 185.50/25.90 | GROUND_INST: instantiating (8) with all_2_2, all_22_0, all_41_0, all_96_0,
% 185.50/25.90 | simplifying with (3), (4), (13), (14), (18), (19), (22), (23),
% 185.50/25.90 | (24) gives:
% 185.50/25.90 | (25) ? [v0: $i] : ($i(v0) & r1(all_96_0, v0) & ~ p4(v0))
% 185.50/25.90 |
% 185.50/25.90 | DELTA: instantiating (25) with fresh symbol all_195_0 gives:
% 185.50/25.90 | (26) $i(all_195_0) & r1(all_96_0, all_195_0) & ~ p4(all_195_0)
% 185.50/25.90 |
% 185.50/25.90 | ALPHA: (26) implies:
% 185.50/25.90 | (27) ~ p4(all_195_0)
% 185.50/25.90 | (28) r1(all_96_0, all_195_0)
% 185.50/25.90 | (29) $i(all_195_0)
% 185.50/25.90 |
% 185.50/25.90 | GROUND_INST: instantiating (9) with all_2_2, all_22_0, all_41_0, all_96_0,
% 185.50/25.90 | all_195_0, simplifying with (3), (4), (13), (14), (18), (19),
% 185.50/25.90 | (23), (24), (27), (28), (29) gives:
% 185.50/25.90 | (30) $false
% 185.50/25.90 |
% 185.50/25.90 | CLOSE: (30) is inconsistent.
% 185.50/25.90 |
% 185.50/25.90 End of proof
% 185.50/25.90 % SZS output end Proof for theBenchmark
% 185.50/25.90
% 185.50/25.90 25307ms
%------------------------------------------------------------------------------