TSTP Solution File: SWW612_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW612_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : Fri Sep 1 00:50:54 EDT 2023
% Result : Theorem 22.50s 3.85s
% Output : Proof 52.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW612_2 : TPTP v8.1.2. Released v6.1.0.
% 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 19:19:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 5.47/1.53 Prover 0: Preprocessing ...
% 5.47/1.53 Prover 1: Preprocessing ...
% 5.47/1.53 Prover 3: Preprocessing ...
% 5.47/1.54 Prover 2: Preprocessing ...
% 5.77/1.56 Prover 5: Preprocessing ...
% 5.77/1.58 Prover 6: Preprocessing ...
% 5.77/1.60 Prover 4: Preprocessing ...
% 14.09/2.66 Prover 1: Warning: ignoring some quantifiers
% 14.09/2.75 Prover 5: Proving ...
% 14.09/2.75 Prover 4: Warning: ignoring some quantifiers
% 14.09/2.75 Prover 3: Warning: ignoring some quantifiers
% 14.09/2.76 Prover 1: Constructing countermodel ...
% 14.09/2.76 Prover 6: Proving ...
% 14.09/2.77 Prover 0: Proving ...
% 14.09/2.79 Prover 3: Constructing countermodel ...
% 14.09/2.79 Prover 4: Constructing countermodel ...
% 15.36/2.83 Prover 2: Proving ...
% 22.50/3.85 Prover 0: proved (3224ms)
% 22.50/3.85
% 22.50/3.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.50/3.85
% 22.50/3.87 Prover 2: stopped
% 22.50/3.87 Prover 6: stopped
% 22.50/3.87 Prover 5: stopped
% 22.50/3.87 Prover 3: stopped
% 22.50/3.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.50/3.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.50/3.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.50/3.87 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.50/3.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.65/4.15 Prover 8: Preprocessing ...
% 24.65/4.16 Prover 11: Preprocessing ...
% 24.65/4.16 Prover 10: Preprocessing ...
% 24.65/4.17 Prover 13: Preprocessing ...
% 24.65/4.18 Prover 7: Preprocessing ...
% 26.10/4.37 Prover 8: Warning: ignoring some quantifiers
% 26.97/4.41 Prover 10: Warning: ignoring some quantifiers
% 26.97/4.41 Prover 8: Constructing countermodel ...
% 26.97/4.45 Prover 7: Warning: ignoring some quantifiers
% 26.97/4.46 Prover 10: Constructing countermodel ...
% 26.97/4.48 Prover 7: Constructing countermodel ...
% 27.71/4.52 Prover 11: Warning: ignoring some quantifiers
% 27.71/4.53 Prover 13: Warning: ignoring some quantifiers
% 27.71/4.55 Prover 13: Constructing countermodel ...
% 27.71/4.56 Prover 11: Constructing countermodel ...
% 52.40/7.74 Prover 4: Found proof (size 92)
% 52.40/7.74 Prover 4: proved (7106ms)
% 52.40/7.74 Prover 7: stopped
% 52.40/7.74 Prover 13: stopped
% 52.40/7.74 Prover 8: stopped
% 52.40/7.74 Prover 10: stopped
% 52.40/7.74 Prover 1: stopped
% 52.40/7.75 Prover 11: stopped
% 52.40/7.75
% 52.40/7.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 52.40/7.75
% 52.40/7.75 % SZS output start Proof for theBenchmark
% 52.40/7.76 Assumptions after simplification:
% 52.40/7.76 ---------------------------------
% 52.40/7.76
% 52.40/7.76 (bertrand_postulate)
% 52.40/7.77 ! [v0: int] : ( ~ (no_prime_in1(v0, $product(2, v0)) = 0) | ? [v1: int] : (
% 52.40/7.77 ~ (v1 = 0) & prime1(v0) = v1)) & ! [v0: int] : ( ~ (prime1(v0) = 0) | ?
% 52.40/7.77 [v1: int] : ( ~ (v1 = 0) & no_prime_in1(v0, $product(2, v0)) = v1))
% 52.40/7.77
% 52.40/7.77 (bridgeL1)
% 52.40/7.77 ! [v0: int] : ! [v1: uni] : ( ~ (t2tb1(v0) = v1) | tb2t1(v1) = v0)
% 52.40/7.77
% 52.40/7.77 (bridgeR3)
% 52.40/7.77 ! [v0: uni] : ! [v1: map_int_int] : ( ~ (tb2t3(v0) = v1) | ~ uni(v0) |
% 52.40/7.77 t2tb3(v1) = v0)
% 52.40/7.77
% 52.40/7.77 (divides_plusr)
% 52.40/7.78 ? [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v3 = 0 | ~
% 52.40/7.78 (divides1(v1, $sum(v2, v0)) = v3) | ? [v4: any] : ? [v5: any] :
% 52.40/7.78 (divides1(v1, v2) = v5 & divides1(v1, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 =
% 52.40/7.78 0))))
% 52.40/7.78
% 52.40/7.78 (no_prime_in_def)
% 52.40/7.78 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = 0 | ~ (no_prime_in1(v0,
% 52.40/7.78 v1) = v2) | ? [v3: int] : ($lesseq(1, $difference(v1, v3)) & $lesseq(1,
% 52.40/7.78 $difference(v3, v0)) & prime1(v3) = 0)) & ! [v0: int] : ! [v1: int] :
% 52.40/7.78 ! [v2: int] : ( ~ ($lesseq(1, $difference(v1, v2))) | ~ ($lesseq(1,
% 52.40/7.78 $difference(v2, v0))) | ~ (no_prime_in1(v0, v1) = 0) | ~ (prime1(v2) =
% 52.40/7.78 0))
% 52.40/7.78
% 52.40/7.78 (odd_def)
% 52.40/7.78 ? [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($difference(v1, $product(2,
% 52.40/7.78 v0)) = 1) | v2 = 0 | ~ (odd1(v1) = v2)) & ! [v0: int] : ( ~
% 52.40/7.78 (odd1(v0) = 0) | ? [v1: int] : $sum($product(2, v1), v0) = -1)
% 52.40/7.78
% 52.40/7.78 (odd_divides)
% 52.40/7.78 ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ (divides1(2, v0) = v1) | odd1(v0) =
% 52.40/7.78 0) & ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ (odd1(v0) = v1) |
% 52.40/7.78 divides1(2, v0) = 0) & ! [v0: int] : ( ~ (divides1(2, v0) = 0) | ? [v1:
% 52.40/7.78 int] : ( ~ (v1 = 0) & odd1(v0) = v1)) & ! [v0: int] : ( ~ (odd1(v0) = 0)
% 52.40/7.78 | ? [v1: int] : ( ~ (v1 = 0) & divides1(2, v0) = v1))
% 52.40/7.78
% 52.40/7.78 (odd_prime)
% 52.40/7.78 ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($lesseq(3, v0)) | ~ (odd1(v0) =
% 52.40/7.78 v1) | ? [v2: int] : ( ~ (v2 = 0) & prime1(v0) = v2)) & ! [v0: int] : ( ~
% 52.40/7.78 ($lesseq(3, v0)) | ~ (prime1(v0) = 0) | odd1(v0) = 0)
% 52.40/7.78
% 52.40/7.78 (select_eq)
% 52.40/7.78 ! [v0: ty] : ! [v1: ty] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 52.40/7.78 [v5: uni] : ! [v6: uni] : (v6 = v4 | ~ (set(v1, v0, v2, v3, v4) = v5) | ~
% 52.40/7.78 (get(v1, v0, v5, v3) = v6) | ~ ty(v1) | ~ ty(v0) | ~ uni(v4) | ~ uni(v3)
% 52.40/7.78 | ~ uni(v2) | ? [v7: int] : ( ~ (v7 = 0) & sort1(v1, v4) = v7))
% 52.40/7.78
% 52.40/7.78 (t2tb_sort1)
% 52.40/7.78 ty(int) & ! [v0: int] : ! [v1: uni] : ( ~ (t2tb1(v0) = v1) | sort1(int, v1)
% 52.40/7.78 = 0)
% 52.40/7.78
% 52.40/7.78 (wP_parameter_prime_numbers)
% 52.40/7.79 ty(int) & ? [v0: uni] : ? [v1: uni] : ? [v2: uni] : ? [v3: uni] : ? [v4:
% 52.40/7.79 map_int_int] : ? [v5: uni] : ? [v6: uni] : ? [v7: int] : ? [v8: uni] :
% 52.40/7.79 ? [v9: uni] : ? [v10: map_int_int] : ? [v11: int] : ? [v12: map_int_int] :
% 52.40/7.79 ? [v13: int] : ? [v14: uni] : ? [v15: uni] : ? [v16: array_int] : ? [v17:
% 52.40/7.79 uni] : ? [v18: uni] : ? [v19: int] : ? [v20: uni] : ? [v21: int] : ?
% 52.40/7.79 [v22: uni] : ? [v23: uni] : ? [v24: map_int_int] : ? [v25: uni] : ? [v26:
% 52.40/7.79 uni] : ? [v27: int] : ? [v28: int] : ( ~ (v28 = 0) & $lesseq(1,
% 52.40/7.79 $difference(v21, v19)) & $lesseq(1, $difference($product(2, v19), v11)) &
% 52.40/7.79 $lesseq(1, $difference(v11, v19)) & $lesseq(1, $difference(v7, v13)) &
% 52.40/7.79 $lesseq(2, v13) & tb2t3(v23) = v24 & tb2t3(v9) = v10 & tb2t3(v3) = v4 &
% 52.40/7.79 t2tb3(v24) = v25 & t2tb3(v12) = v14 & t2tb3(v4) = v8 & first_primes1(v16,
% 52.40/7.79 v13) = 0 & tb2t2(v15) = v16 & no_prime_in1(v27, $sum(v21, 2)) = v28 &
% 52.40/7.79 no_prime_in1(v19, v21) = 0 & no_prime_in1(v19, v11) = 0 & mk_array1(int, v7,
% 52.40/7.79 v14) = v15 & const(int, int, v0) = v1 & set(int, int, v14, v20, v22) = v23
% 52.40/7.79 & set(int, int, v8, v5, v6) = v9 & set(int, int, v1, v0, v2) = v3 & get(int,
% 52.40/7.79 int, v25, v20) = v26 & get(int, int, v14, v17) = v18 & prime1(v21) = 0 &
% 52.40/7.79 odd1(v11) = 0 & tb2t1(v26) = v27 & tb2t1(v18) = v19 & t2tb1(v21) = v22 &
% 52.40/7.79 t2tb1($sum(v13, -1)) = v17 & t2tb1(v13) = v20 & t2tb1(3) = v6 & t2tb1(2) =
% 52.40/7.79 v2 & t2tb1(1) = v5 & t2tb1(0) = v0 & map_int_int(v24) & map_int_int(v12) &
% 52.40/7.79 map_int_int(v10) & map_int_int(v4) & array_int(v16) & uni(v26) & uni(v25) &
% 52.40/7.79 uni(v23) & uni(v22) & uni(v20) & uni(v18) & uni(v17) & uni(v15) & uni(v14) &
% 52.40/7.79 uni(v9) & uni(v8) & uni(v6) & uni(v5) & uni(v3) & uni(v2) & uni(v1) &
% 52.40/7.79 uni(v0) & ? [v29: uni] : ? [v30: int] : ? [v31: int] : ( ~ (v31 = 0) &
% 52.40/7.79 get(int, int, v14, v0) = v29 & divides1(v30, v11) = v31 & tb2t1(v29) = v30
% 52.40/7.79 & uni(v29)))
% 52.40/7.79
% 52.40/7.79 (function-axioms)
% 52.40/7.81 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 52.40/7.81 [v5: ty] : ! [v6: ty] : (v1 = v0 | ~ (set(v6, v5, v4, v3, v2) = v1) | ~
% 52.40/7.81 (set(v6, v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni]
% 52.40/7.81 : ! [v3: int] : ! [v4: uni] : ! [v5: ty] : (v1 = v0 | ~ (set2(v5, v4, v3,
% 52.40/7.81 v2) = v1) | ~ (set2(v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1:
% 52.40/7.81 uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : ! [v5: ty] : (v1 = v0 |
% 52.40/7.81 ~ (get(v5, v4, v3, v2) = v1) | ~ (get(v5, v4, v3, v2) = v0)) & ! [v0: uni]
% 52.40/7.81 : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : ! [v5: ty] : (v1
% 52.40/7.81 = v0 | ~ (tuple21(v5, v4, v3, v2) = v1) | ~ (tuple21(v5, v4, v3, v2) =
% 52.40/7.81 v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4:
% 52.40/7.81 bool1] : ! [v5: ty] : (v1 = v0 | ~ (match_bool1(v5, v4, v3, v2) = v1) | ~
% 52.40/7.81 (match_bool1(v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2:
% 52.40/7.81 uni] : ! [v3: int] : ! [v4: ty] : (v1 = v0 | ~ (make1(v4, v3, v2) = v1) |
% 52.40/7.81 ~ (make1(v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: int] :
% 52.40/7.81 ! [v3: uni] : ! [v4: ty] : (v1 = v0 | ~ (get2(v4, v3, v2) = v1) | ~
% 52.40/7.81 (get2(v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : !
% 52.40/7.81 [v3: int] : ! [v4: ty] : (v1 = v0 | ~ (mk_array1(v4, v3, v2) = v1) | ~
% 52.40/7.81 (mk_array1(v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] :
% 52.40/7.81 ! [v3: ty] : ! [v4: ty] : (v1 = v0 | ~ (const(v4, v3, v2) = v1) | ~
% 52.40/7.81 (const(v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : !
% 52.40/7.81 [v3: ty] : ! [v4: ty] : (v1 = v0 | ~ (tuple2_proj_21(v4, v3, v2) = v1) | ~
% 52.40/7.81 (tuple2_proj_21(v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2:
% 52.40/7.81 uni] : ! [v3: ty] : ! [v4: ty] : (v1 = v0 | ~ (tuple2_proj_11(v4, v3, v2)
% 52.40/7.81 = v1) | ~ (tuple2_proj_11(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 52.40/7.81 : ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3: array_int] : (v1 = v0 |
% 52.40/7.81 ~ (first_primes1(v3, v2) = v1) | ~ (first_primes1(v3, v2) = v0)) & ! [v0:
% 52.40/7.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3:
% 52.40/7.81 int] : (v1 = v0 | ~ (no_prime_in1(v3, v2) = v1) | ~ (no_prime_in1(v3, v2)
% 52.40/7.81 = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 =
% 52.40/7.81 v0 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) & ! [v0: int] : !
% 52.40/7.81 [v1: int] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (length1(v3, v2) = v1)
% 52.40/7.81 | ~ (length1(v3, v2) = v0)) & ! [v0: ty] : ! [v1: ty] : ! [v2: ty] : !
% 52.40/7.81 [v3: ty] : (v1 = v0 | ~ (map(v3, v2) = v1) | ~ (map(v3, v2) = v0)) & ! [v0:
% 52.40/7.81 uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~
% 52.40/7.81 (contents(v3, v2) = v1) | ~ (contents(v3, v2) = v0)) & ! [v0: uni] : !
% 52.40/7.81 [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (mk_ref(v3, v2) = v1) |
% 52.40/7.81 ~ (mk_ref(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 52.40/7.81 MultipleValueBool] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~
% 52.40/7.81 (divides1(v3, v2) = v1) | ~ (divides1(v3, v2) = v0)) & ! [v0:
% 52.40/7.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: lpintcm_intrp] :
% 52.40/7.81 ! [v3: lpintcm_intrp] : (v1 = v0 | ~ (lex1(v3, v2) = v1) | ~ (lex1(v3, v2) =
% 52.40/7.81 v0)) & ! [v0: ty] : ! [v1: ty] : ! [v2: ty] : ! [v3: ty] : (v1 = v0 |
% 52.40/7.81 ~ (tuple2(v3, v2) = v1) | ~ (tuple2(v3, v2) = v0)) & ! [v0:
% 52.40/7.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3:
% 52.40/7.81 int] : (v1 = v0 | ~ (lt_nat1(v3, v2) = v1) | ~ (lt_nat1(v3, v2) = v0)) &
% 52.40/7.81 ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~
% 52.40/7.81 (div2(v3, v2) = v1) | ~ (div2(v3, v2) = v0)) & ! [v0: int] : ! [v1: int]
% 52.40/7.81 : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ (mod2(v3, v2) = v1) | ~
% 52.40/7.81 (mod2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 52.40/7.81 MultipleValueBool] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (sort1(v3,
% 52.40/7.81 v2) = v1) | ~ (sort1(v3, v2) = v0)) & ! [v0: map_int_int] : ! [v1:
% 52.40/7.81 map_int_int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t3(v2) = v1) | ~ (tb2t3(v2)
% 52.40/7.81 = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: map_int_int] : (v1 = v0 |
% 52.40/7.81 ~ (t2tb3(v2) = v1) | ~ (t2tb3(v2) = v0)) & ! [v0: array_int] : ! [v1:
% 52.40/7.81 array_int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t2(v2) = v1) | ~ (tb2t2(v2) =
% 52.40/7.81 v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: array_int] : (v1 = v0 | ~
% 52.40/7.81 (t2tb2(v2) = v1) | ~ (t2tb2(v2) = v0)) & ! [v0: ty] : ! [v1: ty] : !
% 52.40/7.81 [v2: ty] : (v1 = v0 | ~ (array(v2) = v1) | ~ (array(v2) = v0)) & ! [v0: ty]
% 52.40/7.81 : ! [v1: ty] : ! [v2: ty] : (v1 = v0 | ~ (ref(v2) = v1) | ~ (ref(v2) =
% 52.40/7.81 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 52.40/7.81 int] : (v1 = v0 | ~ (prime1(v2) = v1) | ~ (prime1(v2) = v0)) & ! [v0:
% 52.40/7.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : (v1 = v0 |
% 52.40/7.81 ~ (odd1(v2) = v1) | ~ (odd1(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 52.40/7.81 [v1: MultipleValueBool] : ! [v2: int] : (v1 = v0 | ~ (even1(v2) = v1) | ~
% 52.40/7.81 (even1(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: uni] : (v1 = v0 |
% 52.40/7.81 ~ (tb2t1(v2) = v1) | ~ (tb2t1(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : !
% 52.40/7.81 [v2: int] : (v1 = v0 | ~ (t2tb1(v2) = v1) | ~ (t2tb1(v2) = v0)) & ! [v0:
% 52.40/7.81 lpintcm_intrp] : ! [v1: lpintcm_intrp] : ! [v2: uni] : (v1 = v0 | ~
% 52.40/7.81 (tb2t(v2) = v1) | ~ (tb2t(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : !
% 52.40/7.81 [v2: lpintcm_intrp] : (v1 = v0 | ~ (t2tb(v2) = v1) | ~ (t2tb(v2) = v0)) & !
% 52.40/7.81 [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (abs1(v2) = v1) | ~
% 52.40/7.81 (abs1(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~
% 52.40/7.81 (witness1(v2) = v1) | ~ (witness1(v2) = v0))
% 52.40/7.81
% 52.40/7.81 Further assumptions not needed in the proof:
% 52.40/7.81 --------------------------------------------
% 52.40/7.81 abs_def, abs_le, abs_pos, array_inversion1, bool_inversion, bridgeL, bridgeL2,
% 52.40/7.81 bridgeL3, bridgeR, bridgeR1, bridgeR2, compatOrderMult, const, const_sort1,
% 52.40/7.81 contents_def1, contents_sort1, div_1, div_bound, div_inf, div_mod, div_mult,
% 52.40/7.81 div_mult1, div_sign_neg, div_sign_pos, divides_0, divides_1_n, divides_antisym,
% 52.40/7.81 divides_bounds, divides_def, divides_factorl, divides_factorr, divides_left,
% 52.40/7.81 divides_minusr, divides_mod_computer, divides_mod_euclidean, divides_multl,
% 52.40/7.81 divides_multr, divides_n_1, divides_oppl, divides_oppl_rev, divides_oppr,
% 52.40/7.81 divides_oppr_rev, divides_refl, divides_right, divides_trans, elts_def1,
% 52.40/7.81 elts_sort1, even_2k, even_def, even_divides, even_even, even_not_odd, even_odd,
% 52.40/7.81 even_or_odd, even_prime, exists_prime, first_primes_def, get_def, get_sort2,
% 52.40/7.81 get_sort3, length_def1, lex_1, lex_2, lex_inversion, lt_nat_def, make_def,
% 52.40/7.81 make_sort1, match_bool_False, match_bool_True, match_bool_sort1, mk_array_sort1,
% 52.40/7.81 mk_ref_sort1, mod_1, mod_bound, mod_divides_computer, mod_divides_euclidean,
% 52.40/7.81 mod_inf, mod_mult, mod_mult1, mod_sign_neg, mod_sign_pos, not_prime_1, odd_2k1,
% 52.40/7.81 odd_even, odd_not_even, odd_odd, prime_2, prime_3, prime_def, prime_divisors,
% 52.40/7.81 ref_inversion1, rounds_toward_zero, select_neq, set_def, set_sort2, set_sort3,
% 52.40/7.81 small_divisors, t2tb_sort, t2tb_sort2, t2tb_sort3, true_False, tuple0_inversion,
% 52.40/7.81 tuple2_inversion1, tuple2_proj_1_def1, tuple2_proj_1_sort1, tuple2_proj_2_def1,
% 52.40/7.81 tuple2_proj_2_sort1, tuple2_sort1, witness_sort1
% 52.40/7.81
% 52.40/7.81 Those formulas are unsatisfiable:
% 52.40/7.81 ---------------------------------
% 52.40/7.81
% 52.40/7.81 Begin of proof
% 52.40/7.81 |
% 52.40/7.81 | ALPHA: (t2tb_sort1) implies:
% 52.40/7.81 | (1) ! [v0: int] : ! [v1: uni] : ( ~ (t2tb1(v0) = v1) | sort1(int, v1) =
% 52.40/7.81 | 0)
% 52.40/7.81 |
% 52.40/7.81 | ALPHA: (odd_def) implies:
% 52.40/7.82 | (2) ! [v0: int] : ( ~ (odd1(v0) = 0) | ? [v1: int] : $sum($product(2,
% 52.40/7.82 | v1), v0) = -1)
% 52.40/7.82 |
% 52.40/7.82 | ALPHA: (odd_divides) implies:
% 52.40/7.82 | (3) ! [v0: int] : ( ~ (odd1(v0) = 0) | ? [v1: int] : ( ~ (v1 = 0) &
% 52.40/7.82 | divides1(2, v0) = v1))
% 52.40/7.82 |
% 52.40/7.82 | ALPHA: (odd_prime) implies:
% 52.40/7.82 | (4) ! [v0: int] : ( ~ ($lesseq(3, v0)) | ~ (prime1(v0) = 0) | odd1(v0) =
% 52.40/7.82 | 0)
% 52.40/7.82 |
% 52.40/7.82 | ALPHA: (no_prime_in_def) implies:
% 52.40/7.82 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = 0 | ~
% 52.40/7.82 | (no_prime_in1(v0, v1) = v2) | ? [v3: int] : ($lesseq(1,
% 52.40/7.82 | $difference(v1, v3)) & $lesseq(1, $difference(v3, v0)) &
% 52.40/7.82 | prime1(v3) = 0))
% 52.40/7.82 |
% 52.40/7.82 | ALPHA: (bertrand_postulate) implies:
% 52.40/7.82 | (6) ! [v0: int] : ( ~ (prime1(v0) = 0) | ? [v1: int] : ( ~ (v1 = 0) &
% 52.40/7.82 | no_prime_in1(v0, $product(2, v0)) = v1))
% 52.40/7.82 |
% 52.40/7.82 | ALPHA: (wP_parameter_prime_numbers) implies:
% 52.40/7.82 | (7) ty(int)
% 52.40/7.82 | (8) ? [v0: uni] : ? [v1: uni] : ? [v2: uni] : ? [v3: uni] : ? [v4:
% 52.40/7.82 | map_int_int] : ? [v5: uni] : ? [v6: uni] : ? [v7: int] : ? [v8:
% 52.40/7.82 | uni] : ? [v9: uni] : ? [v10: map_int_int] : ? [v11: int] : ?
% 52.40/7.82 | [v12: map_int_int] : ? [v13: int] : ? [v14: uni] : ? [v15: uni] : ?
% 52.40/7.82 | [v16: array_int] : ? [v17: uni] : ? [v18: uni] : ? [v19: int] : ?
% 52.40/7.82 | [v20: uni] : ? [v21: int] : ? [v22: uni] : ? [v23: uni] : ? [v24:
% 52.40/7.82 | map_int_int] : ? [v25: uni] : ? [v26: uni] : ? [v27: int] : ?
% 52.40/7.82 | [v28: int] : ( ~ (v28 = 0) & $lesseq(1, $difference(v21, v19)) &
% 52.40/7.82 | $lesseq(1, $difference($product(2, v19), v11)) & $lesseq(1,
% 52.40/7.82 | $difference(v11, v19)) & $lesseq(1, $difference(v7, v13)) &
% 52.40/7.82 | $lesseq(2, v13) & tb2t3(v23) = v24 & tb2t3(v9) = v10 & tb2t3(v3) = v4
% 52.40/7.82 | & t2tb3(v24) = v25 & t2tb3(v12) = v14 & t2tb3(v4) = v8 &
% 52.40/7.82 | first_primes1(v16, v13) = 0 & tb2t2(v15) = v16 & no_prime_in1(v27,
% 52.40/7.82 | $sum(v21, 2)) = v28 & no_prime_in1(v19, v21) = 0 &
% 52.40/7.82 | no_prime_in1(v19, v11) = 0 & mk_array1(int, v7, v14) = v15 &
% 52.40/7.82 | const(int, int, v0) = v1 & set(int, int, v14, v20, v22) = v23 &
% 52.40/7.82 | set(int, int, v8, v5, v6) = v9 & set(int, int, v1, v0, v2) = v3 &
% 52.40/7.82 | get(int, int, v25, v20) = v26 & get(int, int, v14, v17) = v18 &
% 52.40/7.82 | prime1(v21) = 0 & odd1(v11) = 0 & tb2t1(v26) = v27 & tb2t1(v18) = v19
% 52.40/7.82 | & t2tb1(v21) = v22 & t2tb1($sum(v13, -1)) = v17 & t2tb1(v13) = v20 &
% 52.40/7.82 | t2tb1(3) = v6 & t2tb1(2) = v2 & t2tb1(1) = v5 & t2tb1(0) = v0 &
% 52.40/7.82 | map_int_int(v24) & map_int_int(v12) & map_int_int(v10) &
% 52.40/7.82 | map_int_int(v4) & array_int(v16) & uni(v26) & uni(v25) & uni(v23) &
% 52.40/7.82 | uni(v22) & uni(v20) & uni(v18) & uni(v17) & uni(v15) & uni(v14) &
% 52.40/7.82 | uni(v9) & uni(v8) & uni(v6) & uni(v5) & uni(v3) & uni(v2) & uni(v1) &
% 52.40/7.82 | uni(v0) & ? [v29: uni] : ? [v30: int] : ? [v31: int] : ( ~ (v31 =
% 52.40/7.82 | 0) & get(int, int, v14, v0) = v29 & divides1(v30, v11) = v31 &
% 52.40/7.82 | tb2t1(v29) = v30 & uni(v29)))
% 52.40/7.82 |
% 52.40/7.82 | ALPHA: (function-axioms) implies:
% 52.40/7.82 | (9) ! [v0: int] : ! [v1: int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t1(v2) =
% 52.40/7.82 | v1) | ~ (tb2t1(v2) = v0))
% 52.40/7.82 | (10) ! [v0: uni] : ! [v1: uni] : ! [v2: map_int_int] : (v1 = v0 | ~
% 52.40/7.82 | (t2tb3(v2) = v1) | ~ (t2tb3(v2) = v0))
% 52.40/7.83 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni]
% 52.40/7.83 | : ! [v3: ty] : (v1 = v0 | ~ (sort1(v3, v2) = v1) | ~ (sort1(v3, v2)
% 52.40/7.83 | = v0))
% 52.40/7.83 |
% 52.40/7.83 | DELTA: instantiating (divides_plusr) with fresh symbol all_149_0 gives:
% 52.40/7.83 | (12) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = 0 | ~
% 52.40/7.83 | (divides1(v0, $sum(v1, all_149_0)) = v2) | ? [v3: any] : ? [v4:
% 52.40/7.83 | any] : (divides1(v0, v1) = v4 & divides1(v0, all_149_0) = v3 & ( ~
% 52.40/7.83 | (v4 = 0) | ~ (v3 = 0))))
% 52.40/7.83 |
% 52.40/7.83 | DELTA: instantiating (8) with fresh symbols all_159_0, all_159_1, all_159_2,
% 52.40/7.83 | all_159_3, all_159_4, all_159_5, all_159_6, all_159_7, all_159_8,
% 52.40/7.83 | all_159_9, all_159_10, all_159_11, all_159_12, all_159_13, all_159_14,
% 52.40/7.83 | all_159_15, all_159_16, all_159_17, all_159_18, all_159_19, all_159_20,
% 52.40/7.83 | all_159_21, all_159_22, all_159_23, all_159_24, all_159_25, all_159_26,
% 52.40/7.83 | all_159_27, all_159_28 gives:
% 52.40/7.83 | (13) ~ (all_159_0 = 0) & $lesseq(1, $difference(all_159_7, all_159_9)) &
% 52.40/7.83 | $lesseq(1, $difference($product(2, all_159_9), all_159_17)) &
% 52.40/7.83 | $lesseq(1, $difference(all_159_17, all_159_9)) & $lesseq(1,
% 52.40/7.83 | $difference(all_159_21, all_159_15)) & $lesseq(2, all_159_15) &
% 52.40/7.83 | tb2t3(all_159_5) = all_159_4 & tb2t3(all_159_19) = all_159_18 &
% 52.40/7.83 | tb2t3(all_159_25) = all_159_24 & t2tb3(all_159_4) = all_159_3 &
% 52.40/7.83 | t2tb3(all_159_16) = all_159_14 & t2tb3(all_159_24) = all_159_20 &
% 52.40/7.83 | first_primes1(all_159_12, all_159_15) = 0 & tb2t2(all_159_13) =
% 52.40/7.83 | all_159_12 & no_prime_in1(all_159_1, $sum(all_159_7, 2)) = all_159_0 &
% 52.40/7.83 | no_prime_in1(all_159_9, all_159_7) = 0 & no_prime_in1(all_159_9,
% 52.40/7.83 | all_159_17) = 0 & mk_array1(int, all_159_21, all_159_14) =
% 52.40/7.83 | all_159_13 & const(int, int, all_159_28) = all_159_27 & set(int, int,
% 52.40/7.83 | all_159_14, all_159_8, all_159_6) = all_159_5 & set(int, int,
% 52.40/7.83 | all_159_20, all_159_23, all_159_22) = all_159_19 & set(int, int,
% 52.40/7.83 | all_159_27, all_159_28, all_159_26) = all_159_25 & get(int, int,
% 52.40/7.83 | all_159_3, all_159_8) = all_159_2 & get(int, int, all_159_14,
% 52.40/7.83 | all_159_11) = all_159_10 & prime1(all_159_7) = 0 & odd1(all_159_17)
% 52.40/7.83 | = 0 & tb2t1(all_159_2) = all_159_1 & tb2t1(all_159_10) = all_159_9 &
% 52.40/7.83 | t2tb1(all_159_7) = all_159_6 & t2tb1($sum(all_159_15, -1)) =
% 52.40/7.83 | all_159_11 & t2tb1(all_159_15) = all_159_8 & t2tb1(3) = all_159_22 &
% 52.40/7.83 | t2tb1(2) = all_159_26 & t2tb1(1) = all_159_23 & t2tb1(0) = all_159_28
% 52.40/7.83 | & map_int_int(all_159_4) & map_int_int(all_159_16) &
% 52.40/7.83 | map_int_int(all_159_18) & map_int_int(all_159_24) &
% 52.40/7.83 | array_int(all_159_12) & uni(all_159_2) & uni(all_159_3) &
% 52.40/7.83 | uni(all_159_5) & uni(all_159_6) & uni(all_159_8) & uni(all_159_10) &
% 52.40/7.83 | uni(all_159_11) & uni(all_159_13) & uni(all_159_14) & uni(all_159_19)
% 52.40/7.83 | & uni(all_159_20) & uni(all_159_22) & uni(all_159_23) &
% 52.40/7.83 | uni(all_159_25) & uni(all_159_26) & uni(all_159_27) & uni(all_159_28)
% 52.40/7.83 | & ? [v0: uni] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = 0) & get(int,
% 52.40/7.83 | int, all_159_14, all_159_28) = v0 & divides1(v1, all_159_17) = v2
% 52.40/7.83 | & tb2t1(v0) = v1 & uni(v0))
% 52.40/7.83 |
% 52.40/7.83 | ALPHA: (13) implies:
% 52.40/7.83 | (14) ~ (all_159_0 = 0)
% 52.40/7.83 | (15) $lesseq(1, $difference(all_159_17, all_159_9))
% 52.40/7.83 | (16) $lesseq(1, $difference($product(2, all_159_9), all_159_17))
% 52.40/7.83 | (17) $lesseq(1, $difference(all_159_7, all_159_9))
% 52.40/7.83 | (18) uni(all_159_14)
% 52.87/7.83 | (19) uni(all_159_8)
% 52.87/7.83 | (20) uni(all_159_6)
% 52.87/7.83 | (21) uni(all_159_5)
% 52.87/7.83 | (22) t2tb1(all_159_7) = all_159_6
% 52.87/7.83 | (23) tb2t1(all_159_2) = all_159_1
% 52.87/7.83 | (24) odd1(all_159_17) = 0
% 52.87/7.83 | (25) prime1(all_159_7) = 0
% 52.87/7.83 | (26) get(int, int, all_159_3, all_159_8) = all_159_2
% 52.87/7.83 | (27) set(int, int, all_159_14, all_159_8, all_159_6) = all_159_5
% 52.87/7.83 | (28) no_prime_in1(all_159_1, $sum(all_159_7, 2)) = all_159_0
% 52.87/7.83 | (29) t2tb3(all_159_4) = all_159_3
% 52.87/7.83 | (30) tb2t3(all_159_5) = all_159_4
% 52.87/7.83 |
% 52.87/7.84 | GROUND_INST: instantiating (2) with all_159_17, simplifying with (24) gives:
% 52.87/7.84 | (31) ? [v0: int] : $sum($product(2, v0), all_159_17) = -1
% 52.87/7.84 |
% 52.87/7.84 | DELTA: instantiating (31) with fresh symbol all_168_0 gives:
% 52.87/7.84 | (32) $sum($product(2, all_168_0), all_159_17) = -1
% 52.87/7.84 |
% 52.87/7.84 | COL_REDUCE: introducing fresh symbol sc_170_0_0 defined by:
% 52.87/7.84 | (33) all_168_0 = sc_170_0_0
% 52.87/7.84 |
% 52.87/7.84 | COMBINE_EQS: (32), (33) imply:
% 52.87/7.84 | (34) $sum(all_159_17, $product(2, sc_170_0_0)) = -1
% 52.87/7.84 |
% 52.87/7.84 | REDUCE: (16), (34) imply:
% 52.87/7.84 | (35) $lesseq(0, $sum(all_159_9, sc_170_0_0))
% 52.87/7.84 |
% 52.87/7.84 | SIMP: (35) implies:
% 52.87/7.84 | (36) $lesseq(0, $sum(all_159_9, sc_170_0_0))
% 52.87/7.84 |
% 52.87/7.84 | REDUCE: (15), (34) imply:
% 52.87/7.84 | (37) $lesseq(2, $difference($product(-1, all_159_9), $product(2,
% 52.87/7.84 | sc_170_0_0)))
% 52.87/7.84 |
% 52.87/7.84 | COMBINE_INEQS: (36), (37) imply:
% 52.87/7.84 | (38) $lesseq(sc_170_0_0, -2)
% 52.87/7.84 |
% 52.87/7.84 | COMBINE_INEQS: (36), (38) imply:
% 52.87/7.84 | (39) $lesseq(2, all_159_9)
% 52.87/7.84 |
% 52.87/7.84 | COMBINE_INEQS: (37), (39) imply:
% 52.87/7.84 | (40) $lesseq(sc_170_0_0, -2)
% 52.87/7.84 |
% 52.87/7.84 | REDUCE: (24), (34) imply:
% 52.87/7.84 | (41) odd1($difference(-1, $product(2, sc_170_0_0))) = 0
% 52.87/7.84 |
% 52.87/7.84 | GROUND_INST: instantiating (bridgeL1) with all_159_7, all_159_6, simplifying
% 52.87/7.84 | with (22) gives:
% 52.87/7.84 | (42) tb2t1(all_159_6) = all_159_7
% 52.87/7.84 |
% 52.87/7.84 | GROUND_INST: instantiating (1) with all_159_7, all_159_6, simplifying with
% 52.87/7.84 | (22) gives:
% 52.87/7.84 | (43) sort1(int, all_159_6) = 0
% 52.87/7.84 |
% 52.87/7.84 | GROUND_INST: instantiating (3) with $difference(-1, $product(2, sc_170_0_0)),
% 52.87/7.84 | simplifying with (41) gives:
% 52.87/7.84 | (44) ? [v0: int] : ( ~ (v0 = 0) & divides1(2, $difference(-1, $product(2,
% 52.87/7.84 | sc_170_0_0))) = v0)
% 52.87/7.84 |
% 52.87/7.84 | GROUND_INST: instantiating (4) with all_159_7, simplifying with (25) gives:
% 52.87/7.84 | (45) ~ ($lesseq(3, all_159_7)) | odd1(all_159_7) = 0
% 52.87/7.84 |
% 52.87/7.84 | GROUND_INST: instantiating (6) with all_159_7, simplifying with (25) gives:
% 52.87/7.84 | (46) ? [v0: int] : ( ~ (v0 = 0) & no_prime_in1(all_159_7, $product(2,
% 52.87/7.84 | all_159_7)) = v0)
% 52.87/7.84 |
% 52.87/7.84 | GROUND_INST: instantiating (5) with all_159_1, $sum(all_159_7, 2), all_159_0,
% 52.87/7.84 | simplifying with (28) gives:
% 52.87/7.84 | (47) all_159_0 = 0 | ? [v0: int] : ($lesseq(-1, $difference(all_159_7,
% 52.87/7.84 | v0)) & $lesseq(1, $difference(v0, all_159_1)) & prime1(v0) = 0)
% 52.87/7.84 |
% 52.87/7.84 | GROUND_INST: instantiating (bridgeR3) with all_159_5, all_159_4, simplifying
% 52.87/7.84 | with (21), (30) gives:
% 52.87/7.84 | (48) t2tb3(all_159_4) = all_159_5
% 52.87/7.84 |
% 52.87/7.84 | DELTA: instantiating (44) with fresh symbol all_189_0 gives:
% 52.87/7.84 | (49) ~ (all_189_0 = 0) & divides1(2, $difference(-1, $product(2,
% 52.87/7.84 | sc_170_0_0))) = all_189_0
% 52.87/7.84 |
% 52.87/7.84 | ALPHA: (49) implies:
% 52.87/7.84 | (50) ~ (all_189_0 = 0)
% 52.87/7.84 | (51) divides1(2, $difference(-1, $product(2, sc_170_0_0))) = all_189_0
% 52.87/7.84 |
% 52.87/7.84 | DELTA: instantiating (46) with fresh symbol all_195_0 gives:
% 52.87/7.84 | (52) ~ (all_195_0 = 0) & no_prime_in1(all_159_7, $product(2, all_159_7)) =
% 52.87/7.84 | all_195_0
% 52.87/7.84 |
% 52.87/7.84 | ALPHA: (52) implies:
% 52.87/7.84 | (53) ~ (all_195_0 = 0)
% 52.87/7.84 | (54) no_prime_in1(all_159_7, $product(2, all_159_7)) = all_195_0
% 52.87/7.84 |
% 52.87/7.84 | BETA: splitting (45) gives:
% 52.87/7.84 |
% 52.87/7.84 | Case 1:
% 52.87/7.84 | |
% 52.87/7.84 | | (55) odd1(all_159_7) = 0
% 52.87/7.84 | |
% 52.87/7.85 | | BETA: splitting (47) gives:
% 52.87/7.85 | |
% 52.87/7.85 | | Case 1:
% 52.87/7.85 | | |
% 52.87/7.85 | | | (56) all_159_0 = 0
% 52.87/7.85 | | |
% 52.87/7.85 | | | REDUCE: (14), (56) imply:
% 52.87/7.85 | | | (57) $false
% 52.87/7.85 | | |
% 52.87/7.85 | | | CLOSE: (57) is inconsistent.
% 52.87/7.85 | | |
% 52.87/7.85 | | Case 2:
% 52.87/7.85 | | |
% 52.87/7.85 | | | (58) ? [v0: int] : ($lesseq(-1, $difference(all_159_7, v0)) &
% 52.87/7.85 | | | $lesseq(1, $difference(v0, all_159_1)) & prime1(v0) = 0)
% 52.87/7.85 | | |
% 52.87/7.85 | | | DELTA: instantiating (58) with fresh symbol all_266_0 gives:
% 52.87/7.85 | | | (59) $lesseq(-1, $difference(all_159_7, all_266_0)) & $lesseq(1,
% 52.87/7.85 | | | $difference(all_266_0, all_159_1)) & prime1(all_266_0) = 0
% 52.87/7.85 | | |
% 52.87/7.85 | | | ALPHA: (59) implies:
% 52.87/7.85 | | | (60) $lesseq(1, $difference(all_266_0, all_159_1))
% 52.87/7.85 | | | (61) $lesseq(-1, $difference(all_159_7, all_266_0))
% 52.87/7.85 | | | (62) prime1(all_266_0) = 0
% 52.87/7.85 | | |
% 52.87/7.85 | | | GROUND_INST: instantiating (2) with all_159_7, simplifying with (55)
% 52.87/7.85 | | | gives:
% 52.87/7.85 | | | (63) ? [v0: int] : $sum($product(2, v0), all_159_7) = -1
% 52.87/7.85 | | |
% 52.87/7.85 | | | GROUND_INST: instantiating (10) with all_159_3, all_159_5, all_159_4,
% 52.87/7.85 | | | simplifying with (29), (48) gives:
% 52.87/7.85 | | | (64) all_159_3 = all_159_5
% 52.87/7.85 | | |
% 52.87/7.85 | | | DELTA: instantiating (63) with fresh symbol all_284_0 gives:
% 52.87/7.85 | | | (65) $sum($product(2, all_284_0), all_159_7) = -1
% 52.87/7.85 | | |
% 52.87/7.85 | | | COL_REDUCE: introducing fresh symbol sc_286_0_0 defined by:
% 52.87/7.85 | | | (66) all_284_0 = sc_286_0_0
% 52.87/7.85 | | |
% 52.87/7.85 | | | COMBINE_EQS: (65), (66) imply:
% 52.87/7.85 | | | (67) $sum(all_159_7, $product(2, sc_286_0_0)) = -1
% 52.87/7.85 | | |
% 52.87/7.85 | | | REDUCE: (61), (67) imply:
% 52.87/7.85 | | | (68) $lesseq(all_266_0, $product(-2, sc_286_0_0))
% 52.87/7.85 | | |
% 52.87/7.85 | | | REDUCE: (54), (67) imply:
% 52.87/7.85 | | | (69) no_prime_in1($difference(-1, $product(2, sc_286_0_0)),
% 52.87/7.85 | | | $difference(-2, $product(4, sc_286_0_0))) = all_195_0
% 52.87/7.85 | | |
% 52.87/7.85 | | | REDUCE: (26), (64) imply:
% 52.87/7.85 | | | (70) get(int, int, all_159_5, all_159_8) = all_159_2
% 52.87/7.85 | | |
% 52.87/7.85 | | | REDUCE: (42), (67) imply:
% 52.87/7.85 | | | (71) tb2t1(all_159_6) = $difference(-1, $product(2, sc_286_0_0))
% 52.87/7.85 | | |
% 52.87/7.85 | | | GROUND_INST: instantiating (12) with 2, $sum($difference($product(-2,
% 52.87/7.85 | | | sc_170_0_0), all_149_0), -1), all_189_0, simplifying
% 52.87/7.85 | | | with (51) gives:
% 52.87/7.85 | | | (72) all_189_0 = 0 | ? [v0: any] : ? [v1: any] : (divides1(2,
% 52.87/7.85 | | | $sum($difference($product(-2, sc_170_0_0), all_149_0), -1)) =
% 52.87/7.85 | | | v1 & divides1(2, all_149_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 52.87/7.85 | | |
% 52.87/7.85 | | | GROUND_INST: instantiating (4) with all_266_0, simplifying with (62)
% 52.87/7.85 | | | gives:
% 52.87/7.85 | | | (73) ~ ($lesseq(3, all_266_0)) | odd1(all_266_0) = 0
% 52.87/7.85 | | |
% 52.87/7.85 | | | GROUND_INST: instantiating (select_eq) with int, int, all_159_14,
% 52.87/7.85 | | | all_159_8, all_159_6, all_159_5, all_159_2, simplifying with
% 52.87/7.85 | | | (7), (18), (19), (20), (27), (70) gives:
% 52.87/7.85 | | | (74) all_159_2 = all_159_6 | ? [v0: int] : ( ~ (v0 = 0) & sort1(int,
% 52.87/7.85 | | | all_159_6) = v0)
% 52.87/7.85 | | |
% 52.87/7.85 | | | GROUND_INST: instantiating (5) with $difference(-1, $product(2,
% 52.87/7.85 | | | sc_286_0_0)), $difference(-2, $product(4, sc_286_0_0)),
% 52.87/7.85 | | | all_195_0, simplifying with (69) gives:
% 52.87/7.86 | | | (75) all_195_0 = 0 | ? [v0: int] : ($lesseq(3,
% 52.87/7.86 | | | $difference($product(-1, v0), $product(4, sc_286_0_0))) &
% 52.87/7.86 | | | $lesseq(0, $sum(v0, $product(2, sc_286_0_0))) & prime1(v0) = 0)
% 52.87/7.86 | | |
% 52.87/7.86 | | | BETA: splitting (74) gives:
% 52.87/7.86 | | |
% 52.87/7.86 | | | Case 1:
% 52.87/7.86 | | | |
% 52.87/7.86 | | | | (76) all_159_2 = all_159_6
% 52.87/7.86 | | | |
% 52.87/7.86 | | | | REDUCE: (23), (76) imply:
% 52.87/7.86 | | | | (77) tb2t1(all_159_6) = all_159_1
% 52.87/7.86 | | | |
% 52.87/7.86 | | | | BETA: splitting (75) gives:
% 52.87/7.86 | | | |
% 52.87/7.86 | | | | Case 1:
% 52.87/7.86 | | | | |
% 52.87/7.86 | | | | | (78) all_195_0 = 0
% 52.87/7.86 | | | | |
% 52.87/7.86 | | | | | REDUCE: (53), (78) imply:
% 52.87/7.86 | | | | | (79) $false
% 52.87/7.86 | | | | |
% 52.87/7.86 | | | | | CLOSE: (79) is inconsistent.
% 52.87/7.86 | | | | |
% 52.87/7.86 | | | | Case 2:
% 52.87/7.86 | | | | |
% 52.87/7.86 | | | | | (80) ? [v0: int] : ($lesseq(3, $difference($product(-1, v0),
% 52.87/7.86 | | | | | $product(4, sc_286_0_0))) & $lesseq(0, $sum(v0,
% 52.87/7.86 | | | | | $product(2, sc_286_0_0))) & prime1(v0) = 0)
% 52.87/7.86 | | | | |
% 52.87/7.86 | | | | | DELTA: instantiating (80) with fresh symbol all_520_0 gives:
% 52.87/7.86 | | | | | (81) $lesseq(3, $difference($product(-1, all_520_0), $product(4,
% 52.87/7.86 | | | | | sc_286_0_0))) & $lesseq(0, $sum(all_520_0, $product(2,
% 52.87/7.86 | | | | | sc_286_0_0))) & prime1(all_520_0) = 0
% 52.87/7.86 | | | | |
% 52.87/7.86 | | | | | ALPHA: (81) implies:
% 52.87/7.86 | | | | | (82) $lesseq(0, $sum(all_520_0, $product(2, sc_286_0_0)))
% 52.87/7.86 | | | | | (83) $lesseq(3, $difference($product(-1, all_520_0), $product(4,
% 52.87/7.86 | | | | | sc_286_0_0)))
% 52.87/7.86 | | | | |
% 52.87/7.86 | | | | | BETA: splitting (72) gives:
% 52.87/7.86 | | | | |
% 52.87/7.86 | | | | | Case 1:
% 52.87/7.86 | | | | | |
% 52.87/7.86 | | | | | | (84) all_189_0 = 0
% 52.87/7.86 | | | | | |
% 52.87/7.86 | | | | | | REDUCE: (50), (84) imply:
% 52.87/7.86 | | | | | | (85) $false
% 52.87/7.86 | | | | | |
% 52.87/7.86 | | | | | | CLOSE: (85) is inconsistent.
% 52.87/7.86 | | | | | |
% 52.87/7.86 | | | | | Case 2:
% 52.87/7.86 | | | | | |
% 52.87/7.86 | | | | | |
% 52.87/7.86 | | | | | | GROUND_INST: instantiating (9) with $difference(-1, $product(2,
% 52.87/7.86 | | | | | | sc_286_0_0)), all_159_1, all_159_6, simplifying
% 52.87/7.86 | | | | | | with (71), (77) gives:
% 52.87/7.86 | | | | | | (86) $sum(all_159_1, $product(2, sc_286_0_0)) = -1
% 52.87/7.86 | | | | | |
% 52.87/7.86 | | | | | | REDUCE: (60), (86) imply:
% 52.87/7.86 | | | | | | (87) $lesseq(0, $sum(all_266_0, $product(2, sc_286_0_0)))
% 52.87/7.86 | | | | | |
% 52.87/7.86 | | | | | | ANTI_SYMM: (68), (87) imply:
% 52.87/7.86 | | | | | | (88) $sum(all_266_0, $product(2, sc_286_0_0)) = 0
% 52.87/7.86 | | | | | |
% 52.87/7.86 | | | | | | BETA: splitting (73) gives:
% 52.87/7.86 | | | | | |
% 52.87/7.86 | | | | | | Case 1:
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | | (89) odd1(all_266_0) = 0
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | | REDUCE: (88), (89) imply:
% 52.87/7.86 | | | | | | | (90) odd1($product(-2, sc_286_0_0)) = 0
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | | GROUND_INST: instantiating (2) with $product(-2, sc_286_0_0),
% 52.87/7.86 | | | | | | | simplifying with (90) gives:
% 52.87/7.86 | | | | | | | (91) $false
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | | CLOSE: (91) is inconsistent.
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | Case 2:
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | | (92) $lesseq(all_266_0, 2)
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | | REDUCE: (88), (92) imply:
% 52.87/7.86 | | | | | | | (93) $lesseq(-1, sc_286_0_0)
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | | SIMP: (93) implies:
% 52.87/7.86 | | | | | | | (94) $lesseq(-1, sc_286_0_0)
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | | COMBINE_INEQS: (82), (83) imply:
% 52.87/7.86 | | | | | | | (95) $lesseq(sc_286_0_0, -2)
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | | SIMP: (95) implies:
% 52.87/7.86 | | | | | | | (96) $lesseq(sc_286_0_0, -2)
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | | COMBINE_INEQS: (94), (96) imply:
% 52.87/7.86 | | | | | | | (97) $false
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | | CLOSE: (97) is inconsistent.
% 52.87/7.86 | | | | | | |
% 52.87/7.86 | | | | | | End of split
% 52.87/7.86 | | | | | |
% 52.87/7.86 | | | | | End of split
% 52.87/7.86 | | | | |
% 52.87/7.86 | | | | End of split
% 52.87/7.86 | | | |
% 52.87/7.86 | | | Case 2:
% 52.87/7.86 | | | |
% 52.87/7.86 | | | | (98) ? [v0: int] : ( ~ (v0 = 0) & sort1(int, all_159_6) = v0)
% 52.87/7.86 | | | |
% 52.87/7.86 | | | | DELTA: instantiating (98) with fresh symbol all_490_0 gives:
% 52.87/7.86 | | | | (99) ~ (all_490_0 = 0) & sort1(int, all_159_6) = all_490_0
% 52.87/7.86 | | | |
% 52.87/7.86 | | | | ALPHA: (99) implies:
% 52.87/7.86 | | | | (100) ~ (all_490_0 = 0)
% 52.87/7.86 | | | | (101) sort1(int, all_159_6) = all_490_0
% 52.87/7.86 | | | |
% 52.87/7.86 | | | | GROUND_INST: instantiating (11) with 0, all_490_0, all_159_6, int,
% 52.87/7.86 | | | | simplifying with (43), (101) gives:
% 52.87/7.86 | | | | (102) all_490_0 = 0
% 52.87/7.86 | | | |
% 52.87/7.86 | | | | REDUCE: (100), (102) imply:
% 52.87/7.86 | | | | (103) $false
% 52.87/7.86 | | | |
% 52.87/7.86 | | | | CLOSE: (103) is inconsistent.
% 52.87/7.86 | | | |
% 52.87/7.86 | | | End of split
% 52.87/7.86 | | |
% 52.87/7.86 | | End of split
% 52.87/7.86 | |
% 52.87/7.86 | Case 2:
% 52.87/7.86 | |
% 52.87/7.86 | | (104) $lesseq(all_159_7, 2)
% 52.87/7.86 | |
% 52.87/7.86 | | COMBINE_INEQS: (17), (104) imply:
% 52.87/7.86 | | (105) $lesseq(all_159_9, 1)
% 52.87/7.86 | |
% 52.87/7.86 | | COMBINE_INEQS: (36), (105) imply:
% 52.87/7.86 | | (106) $lesseq(-1, sc_170_0_0)
% 52.87/7.86 | |
% 52.87/7.86 | | COMBINE_INEQS: (38), (106) imply:
% 52.87/7.86 | | (107) $false
% 52.87/7.86 | |
% 52.87/7.86 | | CLOSE: (107) is inconsistent.
% 52.87/7.86 | |
% 52.87/7.86 | End of split
% 52.87/7.86 |
% 52.87/7.86 End of proof
% 52.87/7.86 % SZS output end Proof for theBenchmark
% 52.87/7.86
% 52.87/7.86 7256ms
%------------------------------------------------------------------------------