TSTP Solution File: KLE150+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE150+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n003.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 05:34:42 EDT 2023
% Result : Theorem 9.10s 1.91s
% Output : Proof 12.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE150+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 11:00:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.54/1.02 Prover 1: Preprocessing ...
% 2.54/1.03 Prover 4: Preprocessing ...
% 2.71/1.06 Prover 0: Preprocessing ...
% 2.71/1.06 Prover 6: Preprocessing ...
% 2.71/1.06 Prover 3: Preprocessing ...
% 2.71/1.06 Prover 2: Preprocessing ...
% 2.71/1.06 Prover 5: Preprocessing ...
% 4.78/1.34 Prover 3: Constructing countermodel ...
% 4.78/1.34 Prover 6: Constructing countermodel ...
% 5.08/1.37 Prover 1: Constructing countermodel ...
% 5.08/1.39 Prover 4: Constructing countermodel ...
% 5.08/1.42 Prover 0: Proving ...
% 5.08/1.42 Prover 5: Proving ...
% 5.67/1.47 Prover 3: gave up
% 5.67/1.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.94/1.48 Prover 2: Proving ...
% 5.94/1.48 Prover 1: gave up
% 5.94/1.50 Prover 7: Preprocessing ...
% 5.94/1.50 Prover 6: gave up
% 5.94/1.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.94/1.51 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.39/1.54 Prover 8: Preprocessing ...
% 6.39/1.54 Prover 9: Preprocessing ...
% 6.55/1.61 Prover 8: Warning: ignoring some quantifiers
% 7.03/1.62 Prover 7: Constructing countermodel ...
% 7.03/1.62 Prover 8: Constructing countermodel ...
% 7.33/1.67 Prover 9: Constructing countermodel ...
% 7.33/1.69 Prover 8: gave up
% 7.33/1.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.33/1.73 Prover 10: Preprocessing ...
% 8.22/1.79 Prover 10: Constructing countermodel ...
% 8.22/1.83 Prover 10: gave up
% 8.22/1.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.22/1.87 Prover 11: Preprocessing ...
% 9.10/1.90 Prover 0: proved (1291ms)
% 9.10/1.91
% 9.10/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.10/1.91
% 9.10/1.91 Prover 9: stopped
% 9.10/1.91 Prover 5: stopped
% 9.10/1.92 Prover 2: stopped
% 9.10/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.10/1.92 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.10/1.92 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.10/1.93 Prover 16: Preprocessing ...
% 9.10/1.94 Prover 19: Preprocessing ...
% 9.10/1.95 Prover 13: Preprocessing ...
% 9.56/1.96 Prover 11: Constructing countermodel ...
% 9.56/1.99 Prover 16: Warning: ignoring some quantifiers
% 9.56/2.00 Prover 16: Constructing countermodel ...
% 9.56/2.02 Prover 19: Warning: ignoring some quantifiers
% 9.56/2.02 Prover 13: Warning: ignoring some quantifiers
% 9.56/2.03 Prover 19: Constructing countermodel ...
% 9.56/2.03 Prover 13: Constructing countermodel ...
% 10.34/2.07 Prover 13: gave up
% 10.34/2.07 Prover 19: gave up
% 11.91/2.36 Prover 11: Found proof (size 42)
% 11.91/2.36 Prover 11: proved (526ms)
% 11.91/2.36 Prover 7: stopped
% 11.91/2.36 Prover 16: stopped
% 12.70/2.36 Prover 4: stopped
% 12.70/2.36
% 12.70/2.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.70/2.36
% 12.70/2.37 % SZS output start Proof for theBenchmark
% 12.70/2.37 Assumptions after simplification:
% 12.70/2.37 ---------------------------------
% 12.70/2.37
% 12.70/2.37 (additive_associativity)
% 12.88/2.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 12.88/2.40 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 12.88/2.40 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 &
% 12.88/2.40 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 12.88/2.40 : ! [v4: $i] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~
% 12.88/2.40 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 &
% 12.88/2.40 addition(v2, v1) = v5 & $i(v5) & $i(v4)))
% 12.88/2.40
% 12.88/2.40 (additive_commutativity)
% 12.88/2.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~
% 12.88/2.40 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 12.88/2.40 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 12.88/2.40 (addition(v1, v0) = v2 & $i(v2)))
% 12.88/2.40
% 12.88/2.40 (distributivity1)
% 12.88/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 12.88/2.41 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 12.88/2.41 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 12.88/2.41 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) &
% 12.88/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 12.88/2.41 (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ $i(v2) | ~
% 12.88/2.41 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v0, v2) =
% 12.88/2.41 v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 12.88/2.41 & $i(v4)))
% 12.88/2.41
% 12.88/2.41 (goals)
% 12.88/2.41 $i(one) & $i(zero) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (
% 12.88/2.41 ~ (v3 = v2) & strong_iteration(v1) = v2 & multiplication(v0, zero) = v1 &
% 12.88/2.41 addition(one, v1) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 12.88/2.41
% 12.88/2.41 (infty_unfold1)
% 12.88/2.41 $i(one) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 12.88/2.41 $i(v0) | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1
% 12.88/2.41 & $i(v2) & $i(v1)))
% 12.88/2.41
% 12.88/2.41 (isolation)
% 12.88/2.41 $i(zero) & ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~
% 12.88/2.41 $i(v0) | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & multiplication(v1,
% 12.88/2.41 zero) = v3 & addition(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & !
% 12.88/2.41 [v0: $i] : ! [v1: $i] : ( ~ (star(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 12.88/2.41 [v3: $i] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 &
% 12.88/2.41 addition(v1, v3) = v2 & $i(v3) & $i(v2)))
% 12.88/2.41
% 12.88/2.41 (left_annihilation)
% 12.88/2.41 $i(zero) & ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero,
% 12.88/2.41 v0) = v1) | ~ $i(v0))
% 12.88/2.41
% 12.88/2.41 (multiplicative_associativity)
% 12.88/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 12.88/2.42 (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ $i(v2)
% 12.88/2.42 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1, v2) = v5 &
% 12.88/2.42 multiplication(v0, v5) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1:
% 12.88/2.42 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (multiplication(v1, v2)
% 12.88/2.42 = v3) | ~ (multiplication(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 12.88/2.42 $i(v0) | ? [v5: $i] : (multiplication(v5, v2) = v4 & multiplication(v0, v1)
% 12.88/2.42 = v5 & $i(v5) & $i(v4)))
% 12.88/2.42
% 12.88/2.42 (multiplicative_right_identity)
% 12.88/2.42 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 12.88/2.42 v1) | ~ $i(v0))
% 12.88/2.42
% 12.88/2.42 (function-axioms)
% 12.88/2.42 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.88/2.42 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 12.88/2.42 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.88/2.42 (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0:
% 12.88/2.42 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3,
% 12.88/2.42 v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 12.88/2.42 [v2: $i] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~
% 12.88/2.42 (strong_iteration(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 12.88/2.42 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0))
% 12.88/2.42
% 12.88/2.42 Further assumptions not needed in the proof:
% 12.88/2.42 --------------------------------------------
% 12.88/2.42 additive_identity, distributivity2, idempotence, infty_coinduction,
% 12.88/2.42 multiplicative_left_identity, order, star_induction1, star_induction2,
% 12.88/2.42 star_unfold1, star_unfold2
% 12.88/2.42
% 12.88/2.42 Those formulas are unsatisfiable:
% 12.88/2.42 ---------------------------------
% 12.88/2.42
% 12.88/2.42 Begin of proof
% 12.88/2.42 |
% 12.88/2.42 | ALPHA: (additive_commutativity) implies:
% 12.88/2.42 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 12.88/2.42 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 12.88/2.42 |
% 12.88/2.42 | ALPHA: (additive_associativity) implies:
% 12.88/2.42 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 12.88/2.43 | ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) |
% 12.88/2.43 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 &
% 12.88/2.43 | addition(v1, v0) = v5 & $i(v5) & $i(v4)))
% 12.88/2.43 |
% 12.88/2.43 | ALPHA: (multiplicative_associativity) implies:
% 12.88/2.43 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 12.88/2.43 | ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 12.88/2.43 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (multiplication(v1,
% 12.88/2.43 | v2) = v5 & multiplication(v0, v5) = v4 & $i(v5) & $i(v4)))
% 12.88/2.43 |
% 12.88/2.43 | ALPHA: (multiplicative_right_identity) implies:
% 12.88/2.43 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 12.88/2.43 | v1) | ~ $i(v0))
% 12.88/2.43 |
% 12.88/2.43 | ALPHA: (distributivity1) implies:
% 12.88/2.43 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 12.88/2.43 | ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~
% 12.88/2.43 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] :
% 12.88/2.43 | (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 &
% 12.88/2.43 | addition(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 12.88/2.43 |
% 12.88/2.43 | ALPHA: (left_annihilation) implies:
% 12.88/2.43 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = zero | ~ (multiplication(zero, v0) =
% 12.88/2.43 | v1) | ~ $i(v0))
% 12.88/2.43 |
% 12.88/2.43 | ALPHA: (infty_unfold1) implies:
% 12.88/2.43 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ $i(v0)
% 12.88/2.43 | | ? [v2: $i] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1
% 12.88/2.43 | & $i(v2) & $i(v1)))
% 12.88/2.43 |
% 12.88/2.43 | ALPHA: (isolation) implies:
% 12.88/2.43 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (strong_iteration(v0) = v1) | ~ $i(v0)
% 12.88/2.43 | | ? [v2: $i] : ? [v3: $i] : (star(v0) = v2 & multiplication(v1,
% 12.88/2.43 | zero) = v3 & addition(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 12.88/2.43 |
% 12.88/2.43 | ALPHA: (goals) implies:
% 12.88/2.43 | (9) $i(zero)
% 12.88/2.43 | (10) $i(one)
% 12.88/2.43 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2)
% 12.88/2.43 | & strong_iteration(v1) = v2 & multiplication(v0, zero) = v1 &
% 12.88/2.43 | addition(one, v1) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 12.88/2.43 |
% 12.88/2.43 | ALPHA: (function-axioms) implies:
% 12.88/2.43 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.88/2.43 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 12.88/2.43 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.88/2.43 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 12.88/2.43 |
% 12.88/2.44 | DELTA: instantiating (11) with fresh symbols all_22_0, all_22_1, all_22_2,
% 12.88/2.44 | all_22_3 gives:
% 12.88/2.44 | (14) ~ (all_22_0 = all_22_1) & strong_iteration(all_22_2) = all_22_1 &
% 12.88/2.44 | multiplication(all_22_3, zero) = all_22_2 & addition(one, all_22_2) =
% 12.88/2.44 | all_22_0 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & $i(all_22_3)
% 12.88/2.44 |
% 12.88/2.44 | ALPHA: (14) implies:
% 12.88/2.44 | (15) ~ (all_22_0 = all_22_1)
% 12.88/2.44 | (16) $i(all_22_3)
% 12.88/2.44 | (17) $i(all_22_2)
% 12.88/2.44 | (18) addition(one, all_22_2) = all_22_0
% 12.88/2.44 | (19) multiplication(all_22_3, zero) = all_22_2
% 12.88/2.44 | (20) strong_iteration(all_22_2) = all_22_1
% 12.88/2.44 |
% 12.88/2.44 | GROUND_INST: instantiating (1) with all_22_2, one, all_22_0, simplifying with
% 12.88/2.44 | (10), (17), (18) gives:
% 12.88/2.44 | (21) addition(all_22_2, one) = all_22_0 & $i(all_22_0)
% 12.88/2.44 |
% 12.88/2.44 | ALPHA: (21) implies:
% 12.88/2.44 | (22) addition(all_22_2, one) = all_22_0
% 12.88/2.44 |
% 12.88/2.44 | GROUND_INST: instantiating (8) with all_22_2, all_22_1, simplifying with (17),
% 12.88/2.44 | (20) gives:
% 12.88/2.44 | (23) ? [v0: $i] : ? [v1: $i] : (star(all_22_2) = v0 &
% 12.88/2.44 | multiplication(all_22_1, zero) = v1 & addition(v0, v1) = all_22_1 &
% 12.88/2.44 | $i(v1) & $i(v0) & $i(all_22_1))
% 12.88/2.44 |
% 12.88/2.44 | GROUND_INST: instantiating (7) with all_22_2, all_22_1, simplifying with (17),
% 12.88/2.44 | (20) gives:
% 12.88/2.44 | (24) ? [v0: $i] : (multiplication(all_22_2, all_22_1) = v0 & addition(v0,
% 12.88/2.44 | one) = all_22_1 & $i(v0) & $i(all_22_1))
% 12.88/2.44 |
% 12.88/2.44 | DELTA: instantiating (24) with fresh symbol all_30_0 gives:
% 12.88/2.44 | (25) multiplication(all_22_2, all_22_1) = all_30_0 & addition(all_30_0,
% 12.88/2.44 | one) = all_22_1 & $i(all_30_0) & $i(all_22_1)
% 12.88/2.44 |
% 12.88/2.44 | ALPHA: (25) implies:
% 12.88/2.44 | (26) $i(all_30_0)
% 12.88/2.44 | (27) addition(all_30_0, one) = all_22_1
% 12.88/2.44 | (28) multiplication(all_22_2, all_22_1) = all_30_0
% 12.88/2.44 |
% 12.88/2.44 | DELTA: instantiating (23) with fresh symbols all_32_0, all_32_1 gives:
% 12.88/2.44 | (29) star(all_22_2) = all_32_1 & multiplication(all_22_1, zero) = all_32_0
% 12.88/2.44 | & addition(all_32_1, all_32_0) = all_22_1 & $i(all_32_0) &
% 12.88/2.44 | $i(all_32_1) & $i(all_22_1)
% 12.88/2.44 |
% 12.88/2.44 | ALPHA: (29) implies:
% 12.88/2.44 | (30) $i(all_32_1)
% 12.88/2.44 | (31) $i(all_32_0)
% 12.88/2.44 | (32) addition(all_32_1, all_32_0) = all_22_1
% 12.88/2.44 |
% 12.88/2.44 | GROUND_INST: instantiating (1) with all_32_0, all_32_1, all_22_1, simplifying
% 12.88/2.44 | with (30), (31), (32) gives:
% 12.88/2.44 | (33) addition(all_32_0, all_32_1) = all_22_1 & $i(all_22_1)
% 12.88/2.44 |
% 12.88/2.44 | ALPHA: (33) implies:
% 12.88/2.44 | (34) $i(all_22_1)
% 12.88/2.44 |
% 12.88/2.45 | GROUND_INST: instantiating (3) with all_22_3, zero, all_22_1, all_22_2,
% 12.88/2.45 | all_30_0, simplifying with (9), (16), (19), (28), (34) gives:
% 12.88/2.45 | (35) ? [v0: $i] : (multiplication(all_22_3, v0) = all_30_0 &
% 12.88/2.45 | multiplication(zero, all_22_1) = v0 & $i(v0) & $i(all_30_0))
% 12.88/2.45 |
% 12.88/2.45 | GROUND_INST: instantiating (5) with all_22_2, all_30_0, one, all_22_1,
% 12.88/2.45 | all_30_0, simplifying with (10), (17), (26), (27), (28) gives:
% 12.88/2.45 | (36) ? [v0: $i] : ? [v1: $i] : (multiplication(all_22_2, all_30_0) = v0 &
% 12.88/2.45 | multiplication(all_22_2, one) = v1 & addition(v0, v1) = all_30_0 &
% 12.88/2.45 | $i(v1) & $i(v0))
% 12.88/2.45 |
% 12.88/2.45 | DELTA: instantiating (35) with fresh symbol all_42_0 gives:
% 12.88/2.45 | (37) multiplication(all_22_3, all_42_0) = all_30_0 & multiplication(zero,
% 12.88/2.45 | all_22_1) = all_42_0 & $i(all_42_0) & $i(all_30_0)
% 12.88/2.45 |
% 12.88/2.45 | ALPHA: (37) implies:
% 12.88/2.45 | (38) multiplication(zero, all_22_1) = all_42_0
% 12.88/2.45 | (39) multiplication(all_22_3, all_42_0) = all_30_0
% 12.88/2.45 |
% 12.88/2.45 | DELTA: instantiating (36) with fresh symbols all_48_0, all_48_1 gives:
% 12.88/2.45 | (40) multiplication(all_22_2, all_30_0) = all_48_1 &
% 12.88/2.45 | multiplication(all_22_2, one) = all_48_0 & addition(all_48_1,
% 12.88/2.45 | all_48_0) = all_30_0 & $i(all_48_0) & $i(all_48_1)
% 12.88/2.45 |
% 12.88/2.45 | ALPHA: (40) implies:
% 12.88/2.45 | (41) $i(all_48_1)
% 12.88/2.45 | (42) $i(all_48_0)
% 12.88/2.45 | (43) addition(all_48_1, all_48_0) = all_30_0
% 12.88/2.45 | (44) multiplication(all_22_2, one) = all_48_0
% 12.88/2.45 |
% 12.88/2.45 | GROUND_INST: instantiating (2) with one, all_48_0, all_48_1, all_30_0,
% 12.88/2.45 | all_22_1, simplifying with (10), (27), (41), (42), (43) gives:
% 12.88/2.45 | (45) ? [v0: $i] : (addition(all_48_0, one) = v0 & addition(all_48_1, v0) =
% 12.88/2.45 | all_22_1 & $i(v0) & $i(all_22_1))
% 12.88/2.45 |
% 12.88/2.45 | GROUND_INST: instantiating (6) with all_22_1, all_42_0, simplifying with (34),
% 12.88/2.45 | (38) gives:
% 12.88/2.45 | (46) all_42_0 = zero
% 12.88/2.45 |
% 12.88/2.45 | GROUND_INST: instantiating (4) with all_22_2, all_48_0, simplifying with (17),
% 12.88/2.45 | (44) gives:
% 12.88/2.45 | (47) all_48_0 = all_22_2
% 12.88/2.45 |
% 12.88/2.45 | DELTA: instantiating (45) with fresh symbol all_86_0 gives:
% 12.88/2.45 | (48) addition(all_48_0, one) = all_86_0 & addition(all_48_1, all_86_0) =
% 12.88/2.45 | all_22_1 & $i(all_86_0) & $i(all_22_1)
% 12.88/2.45 |
% 12.88/2.45 | ALPHA: (48) implies:
% 12.88/2.45 | (49) addition(all_48_0, one) = all_86_0
% 12.88/2.45 |
% 12.88/2.45 | REDUCE: (39), (46) imply:
% 12.88/2.45 | (50) multiplication(all_22_3, zero) = all_30_0
% 12.88/2.45 |
% 12.88/2.45 | REDUCE: (47), (49) imply:
% 12.88/2.45 | (51) addition(all_22_2, one) = all_86_0
% 12.88/2.45 |
% 12.88/2.45 | GROUND_INST: instantiating (12) with all_22_0, all_86_0, one, all_22_2,
% 12.88/2.45 | simplifying with (22), (51) gives:
% 12.88/2.45 | (52) all_86_0 = all_22_0
% 12.88/2.45 |
% 12.88/2.45 | GROUND_INST: instantiating (13) with all_22_2, all_30_0, zero, all_22_3,
% 12.88/2.45 | simplifying with (19), (50) gives:
% 12.88/2.45 | (53) all_30_0 = all_22_2
% 12.88/2.45 |
% 12.88/2.45 | REDUCE: (27), (53) imply:
% 12.88/2.45 | (54) addition(all_22_2, one) = all_22_1
% 12.88/2.45 |
% 12.88/2.46 | GROUND_INST: instantiating (12) with all_22_0, all_22_1, one, all_22_2,
% 12.88/2.46 | simplifying with (22), (54) gives:
% 12.88/2.46 | (55) all_22_0 = all_22_1
% 12.88/2.46 |
% 12.88/2.46 | REDUCE: (15), (55) imply:
% 12.88/2.46 | (56) $false
% 12.88/2.46 |
% 12.88/2.46 | CLOSE: (56) is inconsistent.
% 12.88/2.46 |
% 12.88/2.46 End of proof
% 12.88/2.46 % SZS output end Proof for theBenchmark
% 12.88/2.46
% 12.88/2.46 1864ms
%------------------------------------------------------------------------------