TSTP Solution File: SWV488+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV488+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 22:56:42 EDT 2023
% Result : Theorem 6.44s 1.72s
% Output : Proof 9.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWV488+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 09:33:06 EDT 2023
% 0.19/0.33 % CPUTime :
% 0.61/0.63 ________ _____
% 0.61/0.63 ___ __ \_________(_)________________________________
% 0.61/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.61/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.61/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.61/0.63
% 0.61/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.61/0.63 (2023-06-19)
% 0.61/0.63
% 0.61/0.63 (c) Philipp Rümmer, 2009-2023
% 0.61/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.61/0.63 Amanda Stjerna.
% 0.61/0.63 Free software under BSD-3-Clause.
% 0.61/0.63
% 0.61/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.61/0.63
% 0.61/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.61/0.65 Running up to 7 provers in parallel.
% 0.61/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.60/1.11 Prover 4: Preprocessing ...
% 2.60/1.11 Prover 1: Preprocessing ...
% 2.60/1.16 Prover 6: Preprocessing ...
% 2.60/1.16 Prover 5: Preprocessing ...
% 2.60/1.16 Prover 0: Preprocessing ...
% 2.60/1.16 Prover 3: Preprocessing ...
% 2.60/1.16 Prover 2: Preprocessing ...
% 5.20/1.53 Prover 1: Constructing countermodel ...
% 5.20/1.54 Prover 3: Constructing countermodel ...
% 5.64/1.54 Prover 6: Proving ...
% 5.64/1.55 Prover 5: Proving ...
% 5.75/1.57 Prover 2: Proving ...
% 6.44/1.72 Prover 3: proved (1051ms)
% 6.44/1.72
% 6.44/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.44/1.72
% 6.44/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.44/1.73 Prover 5: stopped
% 6.44/1.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.44/1.74 Prover 2: stopped
% 6.44/1.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.09/1.74 Prover 6: stopped
% 7.09/1.75 Prover 7: Preprocessing ...
% 7.09/1.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.09/1.76 Prover 8: Preprocessing ...
% 7.09/1.77 Prover 10: Preprocessing ...
% 7.44/1.79 Prover 11: Preprocessing ...
% 7.44/1.80 Prover 7: Warning: ignoring some quantifiers
% 7.44/1.82 Prover 7: Constructing countermodel ...
% 7.44/1.83 Prover 10: Warning: ignoring some quantifiers
% 7.44/1.84 Prover 10: Constructing countermodel ...
% 7.44/1.84 Prover 1: Found proof (size 31)
% 7.44/1.84 Prover 1: proved (1177ms)
% 7.44/1.85 Prover 10: stopped
% 7.44/1.85 Prover 11: stopped
% 7.44/1.86 Prover 7: stopped
% 7.44/1.87 Prover 8: Warning: ignoring some quantifiers
% 7.44/1.87 Prover 8: Constructing countermodel ...
% 7.44/1.88 Prover 8: stopped
% 9.17/2.05 Prover 4: Constructing countermodel ...
% 9.17/2.06 Prover 4: stopped
% 9.35/2.11 Prover 0: Proving ...
% 9.35/2.11 Prover 0: stopped
% 9.35/2.11
% 9.35/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.35/2.11
% 9.35/2.11 % SZS output start Proof for theBenchmark
% 9.35/2.12 Assumptions after simplification:
% 9.35/2.12 ---------------------------------
% 9.35/2.12
% 9.35/2.12 (qii)
% 9.60/2.15 $i(n) & $i(real_zero) & $i(real_one) & $i(int_one) & $i(int_zero) & ! [v0:
% 9.60/2.15 $i] : ! [v1: $i] : ( ~ (int_leq(v1, n) = 0) | ~ (int_leq(v0, n) = 0) | ~
% 9.60/2.15 $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (int_leq(int_one, v1) =
% 9.60/2.15 v3 & int_leq(int_one, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))) | ( ! [v2:
% 9.60/2.15 $i] : ( ~ (int_less(int_zero, v2) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~
% 9.60/2.15 (v3 = v1) & plus(v0, v2) = v3 & $i(v3)) | ! [v3: $i] : ! [v4: $i] :
% 9.60/2.15 ! [v5: $i] : (v5 = real_zero | ~ (a(v3, v4) = v5) | ~ (plus(v3, v2) =
% 9.60/2.15 v4) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : (int_leq(v3, v0) =
% 9.60/2.15 v7 & int_leq(int_one, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & !
% 9.60/2.15 [v2: $i] : ( ~ (int_less(int_zero, v2) = 0) | ~ $i(v2) | ? [v3: $i] : (
% 9.60/2.15 ~ (v3 = v0) & plus(v1, v2) = v3 & $i(v3)) | ! [v3: $i] : ! [v4: $i]
% 9.60/2.15 : ! [v5: $i] : (v5 = real_zero | ~ (a(v4, v3) = v5) | ~ (plus(v3, v2)
% 9.60/2.15 = v4) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : (int_leq(v3, v1) =
% 9.60/2.15 v7 & int_leq(int_one, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & !
% 9.60/2.15 [v2: $i] : ( ~ (int_leq(int_one, v2) = 0) | ~ $i(v2) | ? [v3: any] : ?
% 9.60/2.15 [v4: $i] : (a(v2, v2) = v4 & int_leq(v2, v1) = v3 & $i(v4) & ( ~ (v3 =
% 9.60/2.15 0) | v4 = real_one)))))
% 9.60/2.15
% 9.60/2.15 (real_constants)
% 9.60/2.15 ~ (real_zero = real_one) & $i(real_zero) & $i(real_one)
% 9.60/2.15
% 9.60/2.15 (uti)
% 9.60/2.15 $i(n) & $i(real_zero) & $i(int_one) & ? [v0: $i] : (a(v0, v0) = real_zero &
% 9.60/2.15 int_leq(v0, v0) = 0 & int_leq(v0, n) = 0 & int_leq(int_one, v0) = 0 &
% 9.60/2.15 $i(v0))
% 9.60/2.15
% 9.60/2.15 (function-axioms)
% 9.60/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (a(v3,
% 9.60/2.16 v2) = v1) | ~ (a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.60/2.16 $i] : ! [v3: $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) =
% 9.60/2.16 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.60/2.16 $i] : ! [v3: $i] : (v1 = v0 | ~ (int_less(v3, v2) = v1) | ~ (int_less(v3,
% 9.60/2.16 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 9.60/2.16 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (int_leq(v3, v2) = v1) | ~
% 9.60/2.16 (int_leq(v3, v2) = v0))
% 9.60/2.16
% 9.60/2.16 Further assumptions not needed in the proof:
% 9.60/2.16 --------------------------------------------
% 9.60/2.16 int_leq, int_less_irreflexive, int_less_total, int_less_transitive,
% 9.60/2.16 int_zero_one, one_successor_of_zero, plus_and_inverse, plus_and_order1,
% 9.60/2.16 plus_commutative, plus_zero
% 9.60/2.16
% 9.60/2.16 Those formulas are unsatisfiable:
% 9.60/2.16 ---------------------------------
% 9.60/2.16
% 9.60/2.16 Begin of proof
% 9.60/2.16 |
% 9.60/2.16 | ALPHA: (real_constants) implies:
% 9.60/2.16 | (1) ~ (real_zero = real_one)
% 9.60/2.16 |
% 9.60/2.16 | ALPHA: (qii) implies:
% 9.60/2.17 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (int_leq(v1, n) = 0) | ~ (int_leq(v0,
% 9.60/2.17 | n) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 9.60/2.17 | (int_leq(int_one, v1) = v3 & int_leq(int_one, v0) = v2 & ( ~ (v3 = 0)
% 9.60/2.17 | | ~ (v2 = 0))) | ( ! [v2: $i] : ( ~ (int_less(int_zero, v2) = 0)
% 9.60/2.17 | | ~ $i(v2) | ? [v3: $i] : ( ~ (v3 = v1) & plus(v0, v2) = v3 &
% 9.60/2.17 | $i(v3)) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 =
% 9.60/2.17 | real_zero | ~ (a(v3, v4) = v5) | ~ (plus(v3, v2) = v4) | ~
% 9.60/2.17 | $i(v3) | ? [v6: any] : ? [v7: any] : (int_leq(v3, v0) = v7 &
% 9.60/2.17 | int_leq(int_one, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) &
% 9.60/2.17 | ! [v2: $i] : ( ~ (int_less(int_zero, v2) = 0) | ~ $i(v2) | ? [v3:
% 9.60/2.17 | $i] : ( ~ (v3 = v0) & plus(v1, v2) = v3 & $i(v3)) | ! [v3: $i]
% 9.60/2.17 | : ! [v4: $i] : ! [v5: $i] : (v5 = real_zero | ~ (a(v4, v3) =
% 9.60/2.17 | v5) | ~ (plus(v3, v2) = v4) | ~ $i(v3) | ? [v6: any] : ?
% 9.60/2.17 | [v7: any] : (int_leq(v3, v1) = v7 & int_leq(int_one, v3) = v6 &
% 9.60/2.17 | ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v2: $i] : ( ~
% 9.60/2.17 | (int_leq(int_one, v2) = 0) | ~ $i(v2) | ? [v3: any] : ? [v4:
% 9.60/2.17 | $i] : (a(v2, v2) = v4 & int_leq(v2, v1) = v3 & $i(v4) & ( ~ (v3
% 9.60/2.17 | = 0) | v4 = real_one)))))
% 9.60/2.17 |
% 9.60/2.17 | ALPHA: (uti) implies:
% 9.60/2.17 | (3) ? [v0: $i] : (a(v0, v0) = real_zero & int_leq(v0, v0) = 0 &
% 9.60/2.17 | int_leq(v0, n) = 0 & int_leq(int_one, v0) = 0 & $i(v0))
% 9.60/2.17 |
% 9.60/2.17 | ALPHA: (function-axioms) implies:
% 9.60/2.17 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.60/2.17 | ! [v3: $i] : (v1 = v0 | ~ (int_leq(v3, v2) = v1) | ~ (int_leq(v3,
% 9.60/2.17 | v2) = v0))
% 9.60/2.17 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.60/2.17 | (a(v3, v2) = v1) | ~ (a(v3, v2) = v0))
% 9.60/2.17 |
% 9.60/2.17 | DELTA: instantiating (3) with fresh symbol all_14_0 gives:
% 9.60/2.17 | (6) a(all_14_0, all_14_0) = real_zero & int_leq(all_14_0, all_14_0) = 0 &
% 9.60/2.17 | int_leq(all_14_0, n) = 0 & int_leq(int_one, all_14_0) = 0 &
% 9.60/2.17 | $i(all_14_0)
% 9.60/2.17 |
% 9.60/2.17 | ALPHA: (6) implies:
% 9.60/2.17 | (7) $i(all_14_0)
% 9.60/2.17 | (8) int_leq(int_one, all_14_0) = 0
% 9.60/2.17 | (9) int_leq(all_14_0, n) = 0
% 9.60/2.17 | (10) int_leq(all_14_0, all_14_0) = 0
% 9.60/2.17 | (11) a(all_14_0, all_14_0) = real_zero
% 9.60/2.17 |
% 9.60/2.18 | GROUND_INST: instantiating (2) with all_14_0, all_14_0, simplifying with (7),
% 9.60/2.18 | (9) gives:
% 9.60/2.18 | (12) ? [v0: any] : ? [v1: any] : (int_leq(int_one, all_14_0) = v1 &
% 9.60/2.18 | int_leq(int_one, all_14_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ( !
% 9.60/2.18 | [v0: $i] : ( ~ (int_less(int_zero, v0) = 0) | ~ $i(v0) | ? [v1:
% 9.60/2.18 | any] : ( ~ (v1 = all_14_0) & plus(all_14_0, v0) = v1 & $i(v1)) |
% 9.60/2.18 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = real_zero | ~
% 9.60/2.18 | (a(v2, v1) = v3) | ~ (plus(v1, v0) = v2) | ~ $i(v1) | ? [v4:
% 9.60/2.18 | any] : ? [v5: any] : (int_leq(v1, all_14_0) = v5 &
% 9.60/2.18 | int_leq(int_one, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) &
% 9.60/2.18 | ! [v0: $i] : ( ~ (int_less(int_zero, v0) = 0) | ~ $i(v0) | ? [v1:
% 9.60/2.18 | any] : ( ~ (v1 = all_14_0) & plus(all_14_0, v0) = v1 & $i(v1)) |
% 9.60/2.18 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = real_zero | ~
% 9.60/2.18 | (a(v1, v2) = v3) | ~ (plus(v1, v0) = v2) | ~ $i(v1) | ? [v4:
% 9.60/2.18 | any] : ? [v5: any] : (int_leq(v1, all_14_0) = v5 &
% 9.60/2.18 | int_leq(int_one, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) &
% 9.60/2.18 | ! [v0: $i] : ( ~ (int_leq(int_one, v0) = 0) | ~ $i(v0) | ? [v1:
% 9.60/2.18 | any] : ? [v2: $i] : (a(v0, v0) = v2 & int_leq(v0, all_14_0) =
% 9.60/2.18 | v1 & $i(v2) & ( ~ (v1 = 0) | v2 = real_one))))
% 9.60/2.18 |
% 9.60/2.18 | BETA: splitting (12) gives:
% 9.60/2.18 |
% 9.60/2.18 | Case 1:
% 9.60/2.18 | |
% 9.60/2.18 | | (13) ? [v0: any] : ? [v1: any] : (int_leq(int_one, all_14_0) = v1 &
% 9.60/2.18 | | int_leq(int_one, all_14_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 9.60/2.18 | |
% 9.60/2.18 | | DELTA: instantiating (13) with fresh symbols all_27_0, all_27_1 gives:
% 9.60/2.18 | | (14) int_leq(int_one, all_14_0) = all_27_0 & int_leq(int_one, all_14_0) =
% 9.60/2.18 | | all_27_1 & ( ~ (all_27_0 = 0) | ~ (all_27_1 = 0))
% 9.60/2.18 | |
% 9.60/2.18 | | ALPHA: (14) implies:
% 9.60/2.18 | | (15) int_leq(int_one, all_14_0) = all_27_1
% 9.60/2.18 | | (16) int_leq(int_one, all_14_0) = all_27_0
% 9.60/2.18 | | (17) ~ (all_27_0 = 0) | ~ (all_27_1 = 0)
% 9.60/2.18 | |
% 9.60/2.18 | | GROUND_INST: instantiating (4) with 0, all_27_0, all_14_0, int_one,
% 9.60/2.18 | | simplifying with (8), (16) gives:
% 9.60/2.18 | | (18) all_27_0 = 0
% 9.60/2.18 | |
% 9.60/2.18 | | GROUND_INST: instantiating (4) with all_27_1, all_27_0, all_14_0, int_one,
% 9.60/2.18 | | simplifying with (15), (16) gives:
% 9.60/2.18 | | (19) all_27_0 = all_27_1
% 9.60/2.18 | |
% 9.60/2.18 | | COMBINE_EQS: (18), (19) imply:
% 9.60/2.18 | | (20) all_27_1 = 0
% 9.60/2.18 | |
% 9.60/2.18 | | BETA: splitting (17) gives:
% 9.60/2.18 | |
% 9.60/2.18 | | Case 1:
% 9.60/2.18 | | |
% 9.60/2.18 | | | (21) ~ (all_27_0 = 0)
% 9.60/2.18 | | |
% 9.60/2.18 | | | REDUCE: (18), (21) imply:
% 9.60/2.18 | | | (22) $false
% 9.60/2.19 | | |
% 9.60/2.19 | | | CLOSE: (22) is inconsistent.
% 9.60/2.19 | | |
% 9.60/2.19 | | Case 2:
% 9.60/2.19 | | |
% 9.60/2.19 | | | (23) ~ (all_27_1 = 0)
% 9.60/2.19 | | |
% 9.60/2.19 | | | REDUCE: (20), (23) imply:
% 9.60/2.19 | | | (24) $false
% 9.60/2.19 | | |
% 9.60/2.19 | | | CLOSE: (24) is inconsistent.
% 9.60/2.19 | | |
% 9.60/2.19 | | End of split
% 9.60/2.19 | |
% 9.60/2.19 | Case 2:
% 9.60/2.19 | |
% 9.60/2.19 | | (25) ! [v0: $i] : ( ~ (int_less(int_zero, v0) = 0) | ~ $i(v0) | ? [v1:
% 9.60/2.19 | | any] : ( ~ (v1 = all_14_0) & plus(all_14_0, v0) = v1 & $i(v1)) |
% 9.60/2.19 | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = real_zero | ~
% 9.60/2.19 | | (a(v2, v1) = v3) | ~ (plus(v1, v0) = v2) | ~ $i(v1) | ? [v4:
% 9.60/2.19 | | any] : ? [v5: any] : (int_leq(v1, all_14_0) = v5 &
% 9.60/2.19 | | int_leq(int_one, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) &
% 9.60/2.19 | | ! [v0: $i] : ( ~ (int_less(int_zero, v0) = 0) | ~ $i(v0) | ? [v1:
% 9.60/2.19 | | any] : ( ~ (v1 = all_14_0) & plus(all_14_0, v0) = v1 & $i(v1)) |
% 9.60/2.19 | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = real_zero | ~
% 9.60/2.19 | | (a(v1, v2) = v3) | ~ (plus(v1, v0) = v2) | ~ $i(v1) | ? [v4:
% 9.60/2.19 | | any] : ? [v5: any] : (int_leq(v1, all_14_0) = v5 &
% 9.60/2.19 | | int_leq(int_one, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) &
% 9.60/2.19 | | ! [v0: $i] : ( ~ (int_leq(int_one, v0) = 0) | ~ $i(v0) | ? [v1:
% 9.60/2.19 | | any] : ? [v2: $i] : (a(v0, v0) = v2 & int_leq(v0, all_14_0) =
% 9.60/2.19 | | v1 & $i(v2) & ( ~ (v1 = 0) | v2 = real_one)))
% 9.60/2.19 | |
% 9.60/2.19 | | ALPHA: (25) implies:
% 9.60/2.19 | | (26) ! [v0: $i] : ( ~ (int_leq(int_one, v0) = 0) | ~ $i(v0) | ? [v1:
% 9.60/2.19 | | any] : ? [v2: $i] : (a(v0, v0) = v2 & int_leq(v0, all_14_0) =
% 9.60/2.19 | | v1 & $i(v2) & ( ~ (v1 = 0) | v2 = real_one)))
% 9.60/2.19 | |
% 9.60/2.19 | | GROUND_INST: instantiating (26) with all_14_0, simplifying with (7), (8)
% 9.60/2.19 | | gives:
% 9.60/2.19 | | (27) ? [v0: any] : ? [v1: $i] : (a(all_14_0, all_14_0) = v1 &
% 9.60/2.19 | | int_leq(all_14_0, all_14_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 9.60/2.19 | | real_one))
% 9.60/2.19 | |
% 9.60/2.19 | | DELTA: instantiating (27) with fresh symbols all_28_0, all_28_1 gives:
% 9.60/2.19 | | (28) a(all_14_0, all_14_0) = all_28_0 & int_leq(all_14_0, all_14_0) =
% 9.60/2.19 | | all_28_1 & $i(all_28_0) & ( ~ (all_28_1 = 0) | all_28_0 = real_one)
% 9.60/2.19 | |
% 9.60/2.19 | | ALPHA: (28) implies:
% 9.60/2.19 | | (29) int_leq(all_14_0, all_14_0) = all_28_1
% 9.60/2.19 | | (30) a(all_14_0, all_14_0) = all_28_0
% 9.60/2.19 | | (31) ~ (all_28_1 = 0) | all_28_0 = real_one
% 9.60/2.19 | |
% 9.60/2.19 | | GROUND_INST: instantiating (4) with 0, all_28_1, all_14_0, all_14_0,
% 9.60/2.19 | | simplifying with (10), (29) gives:
% 9.60/2.19 | | (32) all_28_1 = 0
% 9.60/2.19 | |
% 9.60/2.19 | | GROUND_INST: instantiating (5) with real_zero, all_28_0, all_14_0, all_14_0,
% 9.60/2.19 | | simplifying with (11), (30) gives:
% 9.60/2.19 | | (33) all_28_0 = real_zero
% 9.60/2.19 | |
% 9.60/2.19 | | BETA: splitting (31) gives:
% 9.60/2.19 | |
% 9.60/2.19 | | Case 1:
% 9.60/2.19 | | |
% 9.60/2.20 | | | (34) ~ (all_28_1 = 0)
% 9.60/2.20 | | |
% 9.60/2.20 | | | REDUCE: (32), (34) imply:
% 9.60/2.20 | | | (35) $false
% 9.60/2.20 | | |
% 9.60/2.20 | | | CLOSE: (35) is inconsistent.
% 9.60/2.20 | | |
% 9.60/2.20 | | Case 2:
% 9.60/2.20 | | |
% 9.60/2.20 | | | (36) all_28_0 = real_one
% 9.60/2.20 | | |
% 9.60/2.20 | | | COMBINE_EQS: (33), (36) imply:
% 9.60/2.20 | | | (37) real_zero = real_one
% 9.60/2.20 | | |
% 9.60/2.20 | | | REDUCE: (1), (37) imply:
% 9.60/2.20 | | | (38) $false
% 9.60/2.20 | | |
% 9.60/2.20 | | | CLOSE: (38) is inconsistent.
% 9.60/2.20 | | |
% 9.60/2.20 | | End of split
% 9.60/2.20 | |
% 9.60/2.20 | End of split
% 9.60/2.20 |
% 9.60/2.20 End of proof
% 9.60/2.20 % SZS output end Proof for theBenchmark
% 9.60/2.20
% 9.60/2.20 1561ms
%------------------------------------------------------------------------------