TSTP Solution File: SWW581_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW581_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 : 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 : Fri Sep 1 00:50:47 EDT 2023
% Result : Theorem 7.54s 2.00s
% Output : Proof 10.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW581_2 : TPTP v8.1.2. Released v6.1.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Aug 27 17:38:40 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.62 ________ _____
% 0.18/0.62 ___ __ \_________(_)________________________________
% 0.18/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.62
% 0.18/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.62 (2023-06-19)
% 0.18/0.62
% 0.18/0.62 (c) Philipp Rümmer, 2009-2023
% 0.18/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.62 Amanda Stjerna.
% 0.18/0.62 Free software under BSD-3-Clause.
% 0.18/0.62
% 0.18/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.62
% 0.18/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.64 Running up to 7 provers in parallel.
% 0.18/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.18/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 3.05/1.28 Prover 3: Preprocessing ...
% 3.05/1.28 Prover 6: Preprocessing ...
% 3.05/1.28 Prover 5: Preprocessing ...
% 3.05/1.28 Prover 0: Preprocessing ...
% 3.05/1.28 Prover 1: Preprocessing ...
% 3.05/1.28 Prover 2: Preprocessing ...
% 3.05/1.28 Prover 4: Preprocessing ...
% 5.83/1.69 Prover 4: Warning: ignoring some quantifiers
% 5.83/1.71 Prover 1: Warning: ignoring some quantifiers
% 5.83/1.73 Prover 1: Constructing countermodel ...
% 5.83/1.73 Prover 2: Proving ...
% 5.83/1.74 Prover 4: Constructing countermodel ...
% 5.83/1.75 Prover 3: Warning: ignoring some quantifiers
% 6.35/1.76 Prover 6: Proving ...
% 6.35/1.76 Prover 5: Proving ...
% 6.44/1.77 Prover 3: Constructing countermodel ...
% 6.74/1.81 Prover 0: Proving ...
% 7.54/1.98 Prover 3: proved (1309ms)
% 7.54/1.99
% 7.54/2.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.54/2.00
% 7.54/2.00 Prover 2: stopped
% 7.54/2.01 Prover 0: stopped
% 7.54/2.01 Prover 6: stopped
% 7.54/2.01 Prover 5: stopped
% 7.54/2.03 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.54/2.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.54/2.03 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.54/2.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.54/2.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.54/2.09 Prover 13: Preprocessing ...
% 7.54/2.10 Prover 7: Preprocessing ...
% 7.54/2.10 Prover 11: Preprocessing ...
% 7.99/2.10 Prover 8: Preprocessing ...
% 7.99/2.12 Prover 10: Preprocessing ...
% 9.13/2.20 Prover 13: Warning: ignoring some quantifiers
% 9.13/2.21 Prover 7: Warning: ignoring some quantifiers
% 9.37/2.22 Prover 10: Warning: ignoring some quantifiers
% 9.37/2.22 Prover 13: Constructing countermodel ...
% 9.37/2.22 Prover 8: Warning: ignoring some quantifiers
% 9.37/2.22 Prover 7: Constructing countermodel ...
% 9.37/2.23 Prover 11: Warning: ignoring some quantifiers
% 9.37/2.23 Prover 8: Constructing countermodel ...
% 9.49/2.24 Prover 11: Constructing countermodel ...
% 9.49/2.24 Prover 10: Constructing countermodel ...
% 10.33/2.40 Prover 1: Found proof (size 22)
% 10.33/2.40 Prover 1: proved (1741ms)
% 10.33/2.40 Prover 8: stopped
% 10.33/2.40 Prover 11: stopped
% 10.33/2.40 Prover 10: stopped
% 10.33/2.40 Prover 4: Found proof (size 18)
% 10.33/2.40 Prover 4: proved (1731ms)
% 10.33/2.40 Prover 7: stopped
% 10.33/2.40 Prover 13: stopped
% 10.33/2.40
% 10.33/2.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.33/2.40
% 10.33/2.41 % SZS output start Proof for theBenchmark
% 10.33/2.41 Assumptions after simplification:
% 10.33/2.41 ---------------------------------
% 10.33/2.41
% 10.33/2.41 (factn)
% 10.33/2.44 ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, v0)) | ~ (fact($sum(v0, -1)) =
% 10.33/2.44 v1) | ? [v2: int] : (fact(v0) = v2 & $product(v0, v1) = v2))
% 10.33/2.44
% 10.33/2.44 (wP_parameter_routine)
% 10.33/2.44 ? [v0: int] : ($lesseq(0, v0) & ? [v1: int] : ? [v2: int] : ($lesseq(1,
% 10.33/2.44 $difference(v0, v2)) & $lesseq(0, v2) & fact(v2) = v1 & ? [v3: int] :
% 10.33/2.44 ($product($sum(v2, 1), v1) = v3 & ? [v4: int] : ( ~ (v4 = v3) &
% 10.33/2.44 fact($sum(v2, 1)) = v4))))
% 10.33/2.45
% 10.33/2.45 (function-axioms)
% 10.33/2.46 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: bool] : !
% 10.33/2.46 [v5: ty] : (v1 = v0 | ~ (match_bool(v5, v4, v3, v2) = v1) | ~
% 10.33/2.46 (match_bool(v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2:
% 10.33/2.46 uni] : ! [v3: ty] : (v1 = v0 | ~ (contents(v3, v2) = v1) | ~
% 10.33/2.46 (contents(v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : !
% 10.33/2.46 [v3: ty] : (v1 = v0 | ~ (mk_ref(v3, v2) = v1) | ~ (mk_ref(v3, v2) = v0)) &
% 10.33/2.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni] : !
% 10.33/2.46 [v3: ty] : (v1 = v0 | ~ (sort(v3, v2) = v1) | ~ (sort(v3, v2) = v0)) & !
% 10.33/2.46 [v0: ty] : ! [v1: ty] : ! [v2: ty] : (v1 = v0 | ~ (ref(v2) = v1) | ~
% 10.33/2.46 (ref(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~
% 10.33/2.46 (fact(v2) = v1) | ~ (fact(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : !
% 10.33/2.46 [v2: ty] : (v1 = v0 | ~ (witness(v2) = v1) | ~ (witness(v2) = v0))
% 10.33/2.46
% 10.33/2.46 Further assumptions not needed in the proof:
% 10.33/2.46 --------------------------------------------
% 10.33/2.46 bool_inversion, compatOrderMult, contents_def, contents_sort, fact0,
% 10.33/2.46 match_bool_False, match_bool_True, match_bool_sort, mk_ref_sort, ref_inversion,
% 10.33/2.46 true_False, tuple0_inversion, witness_sort
% 10.33/2.46
% 10.33/2.46 Those formulas are unsatisfiable:
% 10.33/2.46 ---------------------------------
% 10.33/2.46
% 10.33/2.46 Begin of proof
% 10.33/2.46 |
% 10.33/2.46 | ALPHA: (function-axioms) implies:
% 10.33/2.46 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (fact(v2) =
% 10.33/2.46 | v1) | ~ (fact(v2) = v0))
% 10.33/2.46 |
% 10.33/2.46 | DELTA: instantiating (wP_parameter_routine) with fresh symbol all_24_0 gives:
% 10.79/2.47 | (2) $lesseq(0, all_24_0) & ? [v0: int] : ? [v1: int] : ($lesseq(1,
% 10.79/2.47 | $difference(all_24_0, v1)) & $lesseq(0, v1) & fact(v1) = v0 & ?
% 10.79/2.47 | [v2: int] : ($product($sum(v1, 1), v0) = v2 & ? [v3: int] : ( ~ (v3
% 10.79/2.47 | = v2) & fact($sum(v1, 1)) = v3)))
% 10.79/2.47 |
% 10.79/2.47 | ALPHA: (2) implies:
% 10.79/2.47 | (3) ? [v0: int] : ? [v1: int] : ($lesseq(1, $difference(all_24_0, v1)) &
% 10.79/2.47 | $lesseq(0, v1) & fact(v1) = v0 & ? [v2: int] : ($product($sum(v1,
% 10.79/2.47 | 1), v0) = v2 & ? [v3: int] : ( ~ (v3 = v2) & fact($sum(v1, 1))
% 10.79/2.47 | = v3)))
% 10.79/2.47 |
% 10.79/2.47 | DELTA: instantiating (3) with fresh symbols all_27_0, all_27_1 gives:
% 10.79/2.47 | (4) $lesseq(1, $difference(all_24_0, all_27_0)) & $lesseq(0, all_27_0) &
% 10.79/2.47 | fact(all_27_0) = all_27_1 & ? [v0: int] : ($product($sum(all_27_0, 1),
% 10.79/2.47 | all_27_1) = v0 & ? [v1: int] : ( ~ (v1 = v0) & fact($sum(all_27_0,
% 10.79/2.47 | 1)) = v1))
% 10.79/2.47 |
% 10.79/2.47 | ALPHA: (4) implies:
% 10.79/2.47 | (5) $lesseq(0, all_27_0)
% 10.79/2.47 | (6) fact(all_27_0) = all_27_1
% 10.79/2.48 | (7) ? [v0: int] : ($product($sum(all_27_0, 1), all_27_1) = v0 & ? [v1:
% 10.79/2.48 | int] : ( ~ (v1 = v0) & fact($sum(all_27_0, 1)) = v1))
% 10.79/2.48 |
% 10.79/2.48 | DELTA: instantiating (7) with fresh symbol all_30_0 gives:
% 10.79/2.48 | (8) $product($sum(all_27_0, 1), all_27_1) = all_30_0 & ? [v0: int] : ( ~
% 10.79/2.48 | (v0 = all_30_0) & fact($sum(all_27_0, 1)) = v0)
% 10.79/2.48 |
% 10.79/2.48 | ALPHA: (8) implies:
% 10.79/2.48 | (9) $product($sum(all_27_0, 1), all_27_1) = all_30_0
% 10.79/2.48 | (10) ? [v0: int] : ( ~ (v0 = all_30_0) & fact($sum(all_27_0, 1)) = v0)
% 10.79/2.48 |
% 10.79/2.48 | DELTA: instantiating (10) with fresh symbol all_32_0 gives:
% 10.85/2.48 | (11) ~ (all_32_0 = all_30_0) & fact($sum(all_27_0, 1)) = all_32_0
% 10.85/2.48 |
% 10.85/2.48 | ALPHA: (11) implies:
% 10.85/2.48 | (12) ~ (all_32_0 = all_30_0)
% 10.85/2.48 | (13) fact($sum(all_27_0, 1)) = all_32_0
% 10.85/2.48 |
% 10.85/2.48 | GROUND_INST: instantiating (factn) with $sum(all_27_0, 1), all_27_1,
% 10.85/2.48 | simplifying with (6) gives:
% 10.85/2.48 | (14) ~ ($lesseq(0, all_27_0)) | ? [v0: int] : (fact($sum(all_27_0, 1)) =
% 10.85/2.48 | v0 & $product($sum(all_27_0, 1), all_27_1) = v0)
% 10.85/2.49 |
% 10.85/2.49 | BETA: splitting (14) gives:
% 10.85/2.49 |
% 10.85/2.49 | Case 1:
% 10.85/2.49 | |
% 10.85/2.49 | | (15) $lesseq(all_27_0, -1)
% 10.85/2.49 | |
% 10.85/2.49 | | COMBINE_INEQS: (5), (15) imply:
% 10.85/2.49 | | (16) $false
% 10.85/2.49 | |
% 10.85/2.49 | | CLOSE: (16) is inconsistent.
% 10.85/2.49 | |
% 10.85/2.49 | Case 2:
% 10.85/2.49 | |
% 10.85/2.49 | | (17) ? [v0: int] : (fact($sum(all_27_0, 1)) = v0 &
% 10.85/2.49 | | $product($sum(all_27_0, 1), all_27_1) = v0)
% 10.85/2.49 | |
% 10.85/2.49 | | DELTA: instantiating (17) with fresh symbol all_54_0 gives:
% 10.85/2.49 | | (18) fact($sum(all_27_0, 1)) = all_54_0 & $product($sum(all_27_0, 1),
% 10.85/2.49 | | all_27_1) = all_54_0
% 10.85/2.49 | |
% 10.85/2.49 | | ALPHA: (18) implies:
% 10.85/2.49 | | (19) $product($sum(all_27_0, 1), all_27_1) = all_54_0
% 10.85/2.49 | | (20) fact($sum(all_27_0, 1)) = all_54_0
% 10.85/2.49 | |
% 10.85/2.49 | | THEORY_AXIOM GroebnerMultiplication:
% 10.85/2.50 | | (21) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v3 = v2
% 10.85/2.50 | | | ~ ($product($sum(v1, 1), v0) = v3) | ~ ($product($sum(v1, 1),
% 10.85/2.50 | | v0) = v2))
% 10.85/2.50 | |
% 10.85/2.50 | | GROUND_INST: instantiating (21) with all_27_1, all_27_0, all_30_0, all_54_0,
% 10.85/2.50 | | simplifying with (9), (19) gives:
% 10.85/2.50 | | (22) all_54_0 = all_30_0
% 10.85/2.50 | |
% 10.85/2.50 | | REDUCE: (20), (22) imply:
% 10.85/2.50 | | (23) fact($sum(all_27_0, 1)) = all_30_0
% 10.85/2.50 | |
% 10.85/2.50 | | GROUND_INST: instantiating (1) with all_32_0, all_30_0, $sum(all_27_0, 1),
% 10.85/2.50 | | simplifying with (13), (23) gives:
% 10.85/2.50 | | (24) all_32_0 = all_30_0
% 10.85/2.50 | |
% 10.85/2.50 | | REDUCE: (12), (24) imply:
% 10.85/2.50 | | (25) $false
% 10.85/2.50 | |
% 10.85/2.50 | | CLOSE: (25) is inconsistent.
% 10.85/2.50 | |
% 10.85/2.50 | End of split
% 10.85/2.50 |
% 10.85/2.50 End of proof
% 10.85/2.50 % SZS output end Proof for theBenchmark
% 10.85/2.50
% 10.85/2.50 1874ms
%------------------------------------------------------------------------------