TSTP Solution File: NUM853+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM853+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:50:25 EDT 2023
% Result : Theorem 12.47s 2.52s
% Output : Proof 18.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM853+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 16:19:02 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.63 ________ _____
% 0.22/0.63 ___ __ \_________(_)________________________________
% 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.63
% 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.63 (2023-06-19)
% 0.22/0.63
% 0.22/0.63 (c) Philipp Rümmer, 2009-2023
% 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.63 Amanda Stjerna.
% 0.22/0.63 Free software under BSD-3-Clause.
% 0.22/0.63
% 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.63
% 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.64 Running up to 7 provers in parallel.
% 0.22/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.15/1.19 Prover 4: Preprocessing ...
% 3.15/1.19 Prover 1: Preprocessing ...
% 3.66/1.23 Prover 5: Preprocessing ...
% 3.66/1.23 Prover 2: Preprocessing ...
% 3.66/1.23 Prover 0: Preprocessing ...
% 3.66/1.23 Prover 6: Preprocessing ...
% 3.66/1.23 Prover 3: Preprocessing ...
% 7.38/1.77 Prover 1: Warning: ignoring some quantifiers
% 8.25/1.87 Prover 1: Constructing countermodel ...
% 8.25/1.87 Prover 3: Warning: ignoring some quantifiers
% 8.25/1.88 Prover 5: Proving ...
% 8.25/1.90 Prover 4: Warning: ignoring some quantifiers
% 8.25/1.91 Prover 3: Constructing countermodel ...
% 8.25/1.92 Prover 6: Proving ...
% 8.99/2.00 Prover 4: Constructing countermodel ...
% 8.99/2.03 Prover 2: Proving ...
% 8.99/2.04 Prover 0: Proving ...
% 10.68/2.21 Prover 3: gave up
% 10.68/2.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.68/2.24 Prover 7: Preprocessing ...
% 11.14/2.31 Prover 1: gave up
% 11.14/2.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.90/2.38 Prover 8: Preprocessing ...
% 12.18/2.42 Prover 7: Warning: ignoring some quantifiers
% 12.47/2.45 Prover 7: Constructing countermodel ...
% 12.47/2.51 Prover 0: proved (1860ms)
% 12.47/2.51
% 12.47/2.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.47/2.52
% 12.47/2.52 Prover 2: stopped
% 12.47/2.52 Prover 6: stopped
% 12.47/2.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.47/2.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.47/2.52 Prover 5: stopped
% 12.47/2.52 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.47/2.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.22/2.54 Prover 8: Warning: ignoring some quantifiers
% 13.22/2.57 Prover 10: Preprocessing ...
% 13.22/2.57 Prover 8: Constructing countermodel ...
% 13.22/2.58 Prover 16: Preprocessing ...
% 13.72/2.60 Prover 13: Preprocessing ...
% 13.72/2.60 Prover 11: Preprocessing ...
% 14.18/2.72 Prover 10: Warning: ignoring some quantifiers
% 14.18/2.73 Prover 10: Constructing countermodel ...
% 14.18/2.75 Prover 16: Warning: ignoring some quantifiers
% 14.91/2.76 Prover 8: gave up
% 14.91/2.78 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 14.91/2.79 Prover 16: Constructing countermodel ...
% 15.17/2.84 Prover 13: Warning: ignoring some quantifiers
% 15.17/2.85 Prover 19: Preprocessing ...
% 15.17/2.86 Prover 13: Constructing countermodel ...
% 15.17/2.92 Prover 11: Warning: ignoring some quantifiers
% 15.17/2.93 Prover 11: Constructing countermodel ...
% 16.57/3.01 Prover 10: gave up
% 17.03/3.08 Prover 19: Warning: ignoring some quantifiers
% 17.03/3.10 Prover 19: Constructing countermodel ...
% 17.03/3.15 Prover 4: Found proof (size 64)
% 17.03/3.15 Prover 4: proved (2485ms)
% 17.03/3.15 Prover 11: stopped
% 17.03/3.15 Prover 7: stopped
% 17.03/3.15 Prover 13: stopped
% 17.03/3.15 Prover 16: stopped
% 17.03/3.15 Prover 19: stopped
% 17.03/3.15
% 17.03/3.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.03/3.15
% 17.70/3.16 % SZS output start Proof for theBenchmark
% 17.70/3.17 Assumptions after simplification:
% 17.70/3.17 ---------------------------------
% 17.70/3.17
% 17.70/3.17 (ass(cond(140, 0), 0))
% 17.70/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less(v1, v0) = v2) |
% 17.70/3.19 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & greater(v0, v1) = v3))
% 17.70/3.19 & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 17.70/3.19 $i(v0) | less(v1, v0) = 0)
% 17.70/3.19
% 17.70/3.19 (ass(cond(270, 0), 0))
% 17.70/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v1, v0) = v2) | ~ $i(v1)
% 17.70/3.19 | ~ $i(v0) | (vmul(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : !
% 17.70/3.19 [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (vmul(v1, v0) =
% 17.70/3.19 v2 & $i(v2)))
% 17.70/3.19
% 17.70/3.19 (ass(cond(299, 0), 0))
% 17.70/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.70/3.20 int] : (v5 = 0 | ~ (less(v3, v4) = v5) | ~ (vmul(v2, v0) = v4) | ~
% 17.70/3.20 (vmul(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~
% 17.70/3.20 (v6 = 0) & less(v1, v2) = v6))
% 17.70/3.20
% 17.70/3.20 (ass(cond(goal(130), 0), 0))
% 17.87/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (less(v0,
% 17.87/3.20 v1) = v2) | ~ $i(v1) | ~ $i(v0) | greater(v0, v1) = 0) & ! [v0: $i] :
% 17.87/3.20 ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (greater(v0, v1) = v2) |
% 17.87/3.20 ~ $i(v1) | ~ $i(v0) | less(v0, v1) = 0)
% 17.87/3.20
% 17.87/3.20 (ass(cond(goal(130), 0), 2))
% 17.87/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 17.87/3.20 ? [v2: int] : ( ~ (v2 = 0) & greater(v0, v1) = v2)) & ! [v0: $i] : ! [v1:
% 17.87/3.20 $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~
% 17.87/3.20 (v2 = 0) & less(v0, v1) = v2))
% 17.87/3.20
% 17.87/3.20 (ass(cond(goal(177), 0), 0))
% 17.87/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: int] : (v4 =
% 17.87/3.22 0 | ~ (leq(v1, v2) = v3) | ~ (less(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) |
% 17.87/3.22 ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : (leq(v0, v1) = v6 &
% 17.87/3.22 less(v1, v2) = v5 & less(v0, v1) = v7 & ( ~ (v7 = 0) | ~ (v3 = 0)) & ( ~
% 17.87/3.22 (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.87/3.22 [v3: any] : ! [v4: int] : (v4 = 0 | ~ (leq(v0, v1) = v3) | ~ (less(v0, v2)
% 17.87/3.22 = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 17.87/3.22 ? [v7: any] : (leq(v1, v2) = v6 & less(v1, v2) = v5 & less(v0, v1) = v7 & (
% 17.87/3.22 ~ (v7 = 0) | ~ (v6 = 0)) & ( ~ (v5 = 0) | ~ (v3 = 0)))) & ! [v0: $i]
% 17.87/3.22 : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: int] : (v4 = 0 | ~
% 17.87/3.22 (less(v1, v2) = v3) | ~ (less(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 17.87/3.22 $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : (leq(v1, v2) = v6 &
% 17.87/3.22 leq(v0, v1) = v5 & less(v0, v1) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)) & ( ~
% 17.87/3.22 (v5 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.87/3.22 [v3: any] : ! [v4: int] : (v4 = 0 | ~ (less(v0, v2) = v4) | ~ (less(v0, v1)
% 17.87/3.22 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 17.87/3.22 ? [v7: any] : (leq(v1, v2) = v7 & leq(v0, v1) = v6 & less(v1, v2) = v5 & ( ~
% 17.87/3.22 (v7 = 0) | ~ (v3 = 0)) & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] :
% 17.87/3.22 ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ (leq(v1, v2) =
% 17.87/3.22 v4) | ~ (leq(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 17.87/3.22 any] : ? [v6: any] : ? [v7: any] : (less(v1, v2) = v5 & less(v0, v2) =
% 17.87/3.22 v7 & less(v0, v1) = v6 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v4 = 0)) & ( ~ (v5
% 17.87/3.22 = 0) | ~ (v3 = 0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.87/3.22 : ! [v3: any] : ! [v4: any] : ( ~ (leq(v1, v2) = v3) | ~ (less(v0, v1) =
% 17.87/3.22 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ?
% 17.87/3.22 [v7: any] : (leq(v0, v1) = v6 & less(v1, v2) = v5 & less(v0, v2) = v7 & (v7
% 17.87/3.22 = 0 | (( ~ (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = 0) | ~ (v3 = 0)))))) &
% 17.87/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 17.87/3.22 (leq(v0, v1) = v4) | ~ (less(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 17.87/3.22 $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : (leq(v1, v2) = v5 &
% 17.87/3.22 less(v0, v2) = v7 & less(v0, v1) = v6 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v5 =
% 17.87/3.22 0)) & ( ~ (v4 = 0) | ~ (v3 = 0)))))) & ! [v0: $i] : ! [v1: $i]
% 17.87/3.22 : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ (less(v1, v2) = v3) | ~
% 17.87/3.22 (less(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ?
% 17.87/3.22 [v6: any] : ? [v7: any] : (leq(v1, v2) = v6 & leq(v0, v1) = v5 & less(v0,
% 17.87/3.22 v2) = v7 & (v7 = 0 | (( ~ (v6 = 0) | ~ (v4 = 0)) & ( ~ (v5 = 0) | ~
% 17.87/3.22 (v3 = 0))))))
% 17.87/3.22
% 17.87/3.22 (holds(antec(307), 489, 0))
% 17.87/3.22 $i(vd487) & $i(vd488) & $i(vd486) & ? [v0: $i] : ? [v1: $i] : (vmul(vd488,
% 17.87/3.22 vd487) = v1 & vmul(vd486, vd487) = v0 & greater(v0, v1) = 0 & $i(v1) &
% 17.87/3.22 $i(v0))
% 17.87/3.22
% 17.87/3.22 (holds(conseq(307), 490, 0))
% 17.87/3.22 $i(vd488) & $i(vd486) & ? [v0: int] : ( ~ (v0 = 0) & greater(vd486, vd488) =
% 17.87/3.22 v0)
% 17.87/3.22
% 17.87/3.22 (function-axioms)
% 17.87/3.22 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 17.87/3.22 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 17.87/3.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.87/3.22 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 17.87/3.22 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~
% 17.87/3.22 (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.87/3.22 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2)
% 17.87/3.22 = v1) | ~ (less(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.87/3.22 : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) &
% 17.87/3.22 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.87/3.22 $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & !
% 17.87/3.22 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~
% 17.87/3.22 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 17.87/3.22 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 17.87/3.22
% 17.87/3.22 Further assumptions not needed in the proof:
% 17.87/3.22 --------------------------------------------
% 17.87/3.22 ass(cond(12, 0), 0), ass(cond(147, 0), 0), ass(cond(158, 0), 0), ass(cond(163,
% 17.87/3.22 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), ass(cond(189, 0), 0),
% 17.87/3.22 ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223, 0), 0), ass(cond(228,
% 17.87/3.22 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), ass(cond(253, 0), 0),
% 17.87/3.22 ass(cond(261, 0), 0), ass(cond(281, 0), 0), ass(cond(290, 0), 0), ass(cond(299,
% 17.87/3.22 0), 1), ass(cond(299, 0), 2), ass(cond(33, 0), 0), ass(cond(43, 0), 0),
% 17.87/3.22 ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0), 0), ass(cond(73, 0),
% 17.87/3.22 0), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0),
% 17.87/3.22 3), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1),
% 17.87/3.22 ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0),
% 17.87/3.22 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88),
% 17.87/3.22 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2),
% 17.87/3.22 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1),
% 17.87/3.22 def(cond(conseq(axiom(3)), 12), 1), def(cond(conseq(axiom(3)), 16), 1),
% 17.87/3.22 def(cond(conseq(axiom(3)), 17), 1), qu(antec(axiom(3)), imp(antec(axiom(3)))),
% 17.87/3.22 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 17.87/3.22 holds(definiens(29), 44, 0))), qu(cond(conseq(axiom(3)), 32),
% 17.87/3.22 and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))),
% 17.87/3.22 qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))
% 17.87/3.22
% 17.87/3.22 Those formulas are unsatisfiable:
% 17.87/3.22 ---------------------------------
% 17.87/3.22
% 17.87/3.22 Begin of proof
% 17.87/3.22 |
% 17.87/3.22 | ALPHA: (holds(antec(307), 489, 0)) implies:
% 17.87/3.23 | (1) $i(vd487)
% 17.87/3.23 | (2) ? [v0: $i] : ? [v1: $i] : (vmul(vd488, vd487) = v1 & vmul(vd486,
% 17.87/3.23 | vd487) = v0 & greater(v0, v1) = 0 & $i(v1) & $i(v0))
% 17.87/3.23 |
% 17.87/3.23 | ALPHA: (ass(cond(270, 0), 0)) implies:
% 17.87/3.23 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v1, v0) = v2) | ~
% 17.87/3.23 | $i(v1) | ~ $i(v0) | (vmul(v0, v1) = v2 & $i(v2)))
% 17.87/3.23 |
% 17.87/3.23 | ALPHA: (ass(cond(goal(177), 0), 0)) implies:
% 17.87/3.23 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] :
% 17.87/3.23 | ( ~ (less(v1, v2) = v3) | ~ (less(v0, v1) = v4) | ~ $i(v2) | ~
% 17.87/3.23 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 17.87/3.23 | (leq(v1, v2) = v6 & leq(v0, v1) = v5 & less(v0, v2) = v7 & (v7 = 0 |
% 17.87/3.23 | (( ~ (v6 = 0) | ~ (v4 = 0)) & ( ~ (v5 = 0) | ~ (v3 = 0))))))
% 17.87/3.23 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: int] :
% 17.87/3.23 | (v4 = 0 | ~ (less(v1, v2) = v3) | ~ (less(v0, v2) = v4) | ~ $i(v2) |
% 17.87/3.23 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 17.87/3.23 | (leq(v1, v2) = v6 & leq(v0, v1) = v5 & less(v0, v1) = v7 & ( ~ (v7 =
% 17.87/3.23 | 0) | ~ (v6 = 0)) & ( ~ (v5 = 0) | ~ (v3 = 0))))
% 17.87/3.23 |
% 17.87/3.23 | ALPHA: (ass(cond(140, 0), 0)) implies:
% 17.87/3.23 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 17.87/3.23 | $i(v0) | less(v1, v0) = 0)
% 17.87/3.23 |
% 17.87/3.23 | ALPHA: (ass(cond(goal(130), 0), 0)) implies:
% 17.87/3.23 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 17.87/3.23 | (greater(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | less(v0, v1) = 0)
% 17.87/3.23 |
% 17.87/3.23 | ALPHA: (ass(cond(goal(130), 0), 2)) implies:
% 17.87/3.23 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 17.87/3.23 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & less(v0, v1) = v2))
% 17.87/3.23 |
% 17.87/3.23 | ALPHA: (holds(conseq(307), 490, 0)) implies:
% 18.04/3.23 | (9) $i(vd486)
% 18.04/3.23 | (10) $i(vd488)
% 18.04/3.23 | (11) ? [v0: int] : ( ~ (v0 = 0) & greater(vd486, vd488) = v0)
% 18.04/3.23 |
% 18.04/3.23 | ALPHA: (function-axioms) implies:
% 18.04/3.23 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.04/3.23 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 18.04/3.23 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 18.04/3.23 | : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) =
% 18.04/3.23 | v0))
% 18.04/3.23 |
% 18.04/3.23 | DELTA: instantiating (11) with fresh symbol all_53_0 gives:
% 18.04/3.23 | (14) ~ (all_53_0 = 0) & greater(vd486, vd488) = all_53_0
% 18.04/3.23 |
% 18.04/3.23 | ALPHA: (14) implies:
% 18.04/3.23 | (15) ~ (all_53_0 = 0)
% 18.04/3.23 | (16) greater(vd486, vd488) = all_53_0
% 18.04/3.23 |
% 18.04/3.23 | DELTA: instantiating (2) with fresh symbols all_55_0, all_55_1 gives:
% 18.04/3.24 | (17) vmul(vd488, vd487) = all_55_0 & vmul(vd486, vd487) = all_55_1 &
% 18.04/3.24 | greater(all_55_1, all_55_0) = 0 & $i(all_55_0) & $i(all_55_1)
% 18.04/3.24 |
% 18.04/3.24 | ALPHA: (17) implies:
% 18.04/3.24 | (18) $i(all_55_1)
% 18.04/3.24 | (19) $i(all_55_0)
% 18.04/3.24 | (20) greater(all_55_1, all_55_0) = 0
% 18.04/3.24 | (21) vmul(vd486, vd487) = all_55_1
% 18.04/3.24 | (22) vmul(vd488, vd487) = all_55_0
% 18.04/3.24 |
% 18.04/3.24 | GROUND_INST: instantiating (7) with vd486, vd488, all_53_0, simplifying with
% 18.04/3.24 | (9), (10), (16) gives:
% 18.04/3.24 | (23) all_53_0 = 0 | vd488 = vd486 | less(vd486, vd488) = 0
% 18.04/3.24 |
% 18.04/3.24 | GROUND_INST: instantiating (6) with all_55_1, all_55_0, simplifying with (18),
% 18.04/3.24 | (19), (20) gives:
% 18.04/3.24 | (24) less(all_55_0, all_55_1) = 0
% 18.04/3.24 |
% 18.04/3.24 | GROUND_INST: instantiating (8) with all_55_1, all_55_0, simplifying with (18),
% 18.04/3.24 | (19), (20) gives:
% 18.04/3.24 | (25) ? [v0: int] : ( ~ (v0 = 0) & less(all_55_1, all_55_0) = v0)
% 18.04/3.24 |
% 18.04/3.24 | GROUND_INST: instantiating (3) with vd487, vd486, all_55_1, simplifying with
% 18.04/3.24 | (1), (9), (21) gives:
% 18.04/3.24 | (26) vmul(vd487, vd486) = all_55_1 & $i(all_55_1)
% 18.04/3.24 |
% 18.04/3.24 | ALPHA: (26) implies:
% 18.04/3.24 | (27) vmul(vd487, vd486) = all_55_1
% 18.04/3.24 |
% 18.04/3.24 | GROUND_INST: instantiating (3) with vd487, vd488, all_55_0, simplifying with
% 18.04/3.24 | (1), (10), (22) gives:
% 18.04/3.24 | (28) vmul(vd487, vd488) = all_55_0 & $i(all_55_0)
% 18.04/3.24 |
% 18.04/3.24 | ALPHA: (28) implies:
% 18.04/3.24 | (29) vmul(vd487, vd488) = all_55_0
% 18.04/3.24 |
% 18.04/3.24 | DELTA: instantiating (25) with fresh symbol all_66_0 gives:
% 18.04/3.24 | (30) ~ (all_66_0 = 0) & less(all_55_1, all_55_0) = all_66_0
% 18.04/3.24 |
% 18.04/3.24 | ALPHA: (30) implies:
% 18.04/3.24 | (31) ~ (all_66_0 = 0)
% 18.04/3.24 | (32) less(all_55_1, all_55_0) = all_66_0
% 18.04/3.24 |
% 18.04/3.24 | GROUND_INST: instantiating (ass(cond(299, 0), 0)) with vd487, vd486, vd488,
% 18.04/3.24 | all_55_1, all_55_0, all_66_0, simplifying with (1), (9), (10),
% 18.04/3.24 | (21), (22), (32) gives:
% 18.04/3.24 | (33) all_66_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & less(vd486, vd488) = v0)
% 18.04/3.24 |
% 18.04/3.24 | GROUND_INST: instantiating (5) with all_55_1, all_55_1, all_55_0, all_66_0,
% 18.04/3.24 | all_66_0, simplifying with (18), (19), (32) gives:
% 18.04/3.24 | (34) all_66_0 = 0 | ? [v0: MultipleValueBool] : ? [v1: any] : ? [v2:
% 18.04/3.24 | any] : (leq(all_55_1, all_55_0) = v1 & leq(all_55_1, all_55_1) = v0
% 18.04/3.24 | & less(all_55_1, all_55_1) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0)))
% 18.04/3.24 |
% 18.04/3.24 | GROUND_INST: instantiating (4) with all_55_1, all_55_0, all_55_1, 0, all_66_0,
% 18.04/3.24 | simplifying with (18), (19), (24), (32) gives:
% 18.04/3.24 | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] : (leq(all_55_0, all_55_1)
% 18.04/3.24 | = v1 & leq(all_55_1, all_55_0) = v0 & less(all_55_1, all_55_1) = v2
% 18.04/3.24 | & (v2 = 0 | ( ~ (v0 = 0) & ( ~ (v1 = 0) | ~ (all_66_0 = 0)))))
% 18.04/3.24 |
% 18.04/3.25 | GROUND_INST: instantiating (4) with all_55_0, all_55_1, all_55_0, all_66_0, 0,
% 18.04/3.25 | simplifying with (18), (19), (24), (32) gives:
% 18.04/3.25 | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : (leq(all_55_0, all_55_1)
% 18.04/3.25 | = v0 & leq(all_55_1, all_55_0) = v1 & less(all_55_0, all_55_0) = v2
% 18.04/3.25 | & (v2 = 0 | ( ~ (v1 = 0) & ( ~ (v0 = 0) | ~ (all_66_0 = 0)))))
% 18.04/3.25 |
% 18.04/3.25 | DELTA: instantiating (36) with fresh symbols all_152_0, all_152_1, all_152_2
% 18.04/3.25 | gives:
% 18.04/3.25 | (37) leq(all_55_0, all_55_1) = all_152_2 & leq(all_55_1, all_55_0) =
% 18.04/3.25 | all_152_1 & less(all_55_0, all_55_0) = all_152_0 & (all_152_0 = 0 | (
% 18.04/3.25 | ~ (all_152_1 = 0) & ( ~ (all_152_2 = 0) | ~ (all_66_0 = 0))))
% 18.04/3.25 |
% 18.04/3.25 | ALPHA: (37) implies:
% 18.04/3.25 | (38) less(all_55_0, all_55_0) = all_152_0
% 18.04/3.25 |
% 18.04/3.25 | DELTA: instantiating (35) with fresh symbols all_154_0, all_154_1, all_154_2
% 18.04/3.25 | gives:
% 18.04/3.25 | (39) leq(all_55_0, all_55_1) = all_154_1 & leq(all_55_1, all_55_0) =
% 18.04/3.25 | all_154_2 & less(all_55_1, all_55_1) = all_154_0 & (all_154_0 = 0 | (
% 18.04/3.25 | ~ (all_154_2 = 0) & ( ~ (all_154_1 = 0) | ~ (all_66_0 = 0))))
% 18.04/3.25 |
% 18.04/3.25 | ALPHA: (39) implies:
% 18.04/3.25 | (40) less(all_55_1, all_55_1) = all_154_0
% 18.04/3.25 |
% 18.04/3.25 | BETA: splitting (33) gives:
% 18.04/3.25 |
% 18.04/3.25 | Case 1:
% 18.04/3.25 | |
% 18.04/3.25 | | (41) all_66_0 = 0
% 18.04/3.25 | |
% 18.04/3.25 | | REDUCE: (31), (41) imply:
% 18.04/3.25 | | (42) $false
% 18.04/3.25 | |
% 18.04/3.25 | | CLOSE: (42) is inconsistent.
% 18.04/3.25 | |
% 18.04/3.25 | Case 2:
% 18.04/3.25 | |
% 18.04/3.25 | | (43) ? [v0: int] : ( ~ (v0 = 0) & less(vd486, vd488) = v0)
% 18.04/3.25 | |
% 18.04/3.25 | | DELTA: instantiating (43) with fresh symbol all_160_0 gives:
% 18.04/3.25 | | (44) ~ (all_160_0 = 0) & less(vd486, vd488) = all_160_0
% 18.04/3.25 | |
% 18.04/3.25 | | ALPHA: (44) implies:
% 18.04/3.25 | | (45) ~ (all_160_0 = 0)
% 18.04/3.25 | | (46) less(vd486, vd488) = all_160_0
% 18.04/3.25 | |
% 18.04/3.25 | | BETA: splitting (34) gives:
% 18.04/3.25 | |
% 18.04/3.25 | | Case 1:
% 18.04/3.25 | | |
% 18.04/3.25 | | | (47) all_66_0 = 0
% 18.04/3.25 | | |
% 18.04/3.25 | | | REDUCE: (31), (47) imply:
% 18.04/3.25 | | | (48) $false
% 18.04/3.25 | | |
% 18.04/3.25 | | | CLOSE: (48) is inconsistent.
% 18.04/3.25 | | |
% 18.04/3.25 | | Case 2:
% 18.04/3.25 | | |
% 18.04/3.25 | | | (49) ? [v0: MultipleValueBool] : ? [v1: any] : ? [v2: any] :
% 18.04/3.25 | | | (leq(all_55_1, all_55_0) = v1 & leq(all_55_1, all_55_1) = v0 &
% 18.04/3.25 | | | less(all_55_1, all_55_1) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0)))
% 18.04/3.25 | | |
% 18.04/3.25 | | | DELTA: instantiating (49) with fresh symbols all_170_0, all_170_1,
% 18.04/3.25 | | | all_170_2 gives:
% 18.04/3.25 | | | (50) leq(all_55_1, all_55_0) = all_170_1 & leq(all_55_1, all_55_1) =
% 18.04/3.25 | | | all_170_2 & less(all_55_1, all_55_1) = all_170_0 & ( ~ (all_170_0
% 18.04/3.25 | | | = 0) | ~ (all_170_1 = 0))
% 18.04/3.25 | | |
% 18.04/3.25 | | | ALPHA: (50) implies:
% 18.04/3.25 | | | (51) less(all_55_1, all_55_1) = all_170_0
% 18.04/3.25 | | |
% 18.04/3.25 | | | BETA: splitting (23) gives:
% 18.04/3.25 | | |
% 18.04/3.25 | | | Case 1:
% 18.04/3.25 | | | |
% 18.04/3.25 | | | | (52) less(vd486, vd488) = 0
% 18.04/3.25 | | | |
% 18.04/3.25 | | | | GROUND_INST: instantiating (13) with 0, all_160_0, vd488, vd486,
% 18.04/3.25 | | | | simplifying with (46), (52) gives:
% 18.04/3.25 | | | | (53) all_160_0 = 0
% 18.04/3.25 | | | |
% 18.04/3.25 | | | | REDUCE: (45), (53) imply:
% 18.04/3.25 | | | | (54) $false
% 18.04/3.25 | | | |
% 18.04/3.25 | | | | CLOSE: (54) is inconsistent.
% 18.04/3.25 | | | |
% 18.04/3.25 | | | Case 2:
% 18.04/3.25 | | | |
% 18.04/3.25 | | | | (55) all_53_0 = 0 | vd488 = vd486
% 18.04/3.25 | | | |
% 18.04/3.25 | | | | BETA: splitting (55) gives:
% 18.04/3.25 | | | |
% 18.04/3.25 | | | | Case 1:
% 18.04/3.25 | | | | |
% 18.04/3.25 | | | | | (56) all_53_0 = 0
% 18.04/3.25 | | | | |
% 18.04/3.25 | | | | | REDUCE: (15), (56) imply:
% 18.04/3.25 | | | | | (57) $false
% 18.04/3.25 | | | | |
% 18.04/3.25 | | | | | CLOSE: (57) is inconsistent.
% 18.04/3.25 | | | | |
% 18.04/3.25 | | | | Case 2:
% 18.04/3.25 | | | | |
% 18.04/3.25 | | | | | (58) vd488 = vd486
% 18.04/3.25 | | | | |
% 18.04/3.25 | | | | | REDUCE: (29), (58) imply:
% 18.04/3.25 | | | | | (59) vmul(vd487, vd486) = all_55_0
% 18.04/3.25 | | | | |
% 18.04/3.26 | | | | | GROUND_INST: instantiating (12) with all_55_1, all_55_0, vd486, vd487,
% 18.04/3.26 | | | | | simplifying with (27), (59) gives:
% 18.04/3.26 | | | | | (60) all_55_0 = all_55_1
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | GROUND_INST: instantiating (13) with all_154_0, all_170_0, all_55_1,
% 18.04/3.26 | | | | | all_55_1, simplifying with (40), (51) gives:
% 18.04/3.26 | | | | | (61) all_170_0 = all_154_0
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | REDUCE: (38), (60) imply:
% 18.04/3.26 | | | | | (62) less(all_55_1, all_55_1) = all_152_0
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | REDUCE: (24), (60) imply:
% 18.04/3.26 | | | | | (63) less(all_55_1, all_55_1) = 0
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | REDUCE: (32), (60) imply:
% 18.04/3.26 | | | | | (64) less(all_55_1, all_55_1) = all_66_0
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | GROUND_INST: instantiating (13) with all_154_0, all_66_0, all_55_1,
% 18.04/3.26 | | | | | all_55_1, simplifying with (40), (64) gives:
% 18.04/3.26 | | | | | (65) all_154_0 = all_66_0
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | GROUND_INST: instantiating (13) with all_154_0, all_152_0, all_55_1,
% 18.04/3.26 | | | | | all_55_1, simplifying with (40), (62) gives:
% 18.04/3.26 | | | | | (66) all_154_0 = all_152_0
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | GROUND_INST: instantiating (13) with 0, all_152_0, all_55_1, all_55_1,
% 18.04/3.26 | | | | | simplifying with (62), (63) gives:
% 18.04/3.26 | | | | | (67) all_152_0 = 0
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | COMBINE_EQS: (65), (66) imply:
% 18.04/3.26 | | | | | (68) all_152_0 = all_66_0
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | SIMP: (68) implies:
% 18.04/3.26 | | | | | (69) all_152_0 = all_66_0
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | COMBINE_EQS: (67), (69) imply:
% 18.04/3.26 | | | | | (70) all_66_0 = 0
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | REDUCE: (31), (70) imply:
% 18.04/3.26 | | | | | (71) $false
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | | CLOSE: (71) is inconsistent.
% 18.04/3.26 | | | | |
% 18.04/3.26 | | | | End of split
% 18.04/3.26 | | | |
% 18.04/3.26 | | | End of split
% 18.04/3.26 | | |
% 18.04/3.26 | | End of split
% 18.04/3.26 | |
% 18.04/3.26 | End of split
% 18.04/3.26 |
% 18.04/3.26 End of proof
% 18.04/3.26 % SZS output end Proof for theBenchmark
% 18.04/3.26
% 18.04/3.26 2629ms
%------------------------------------------------------------------------------