TSTP Solution File: SET574+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET574+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n012.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 15:25:21 EDT 2023
% Result : Theorem 3.29s 1.26s
% Output : Proof 3.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET574+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 09:35:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.64 Running up to 7 provers in parallel.
% 0.19/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.94/1.04 Prover 1: Preprocessing ...
% 1.94/1.04 Prover 4: Preprocessing ...
% 1.94/1.08 Prover 5: Preprocessing ...
% 1.94/1.08 Prover 0: Preprocessing ...
% 1.94/1.08 Prover 6: Preprocessing ...
% 1.94/1.08 Prover 2: Preprocessing ...
% 1.94/1.08 Prover 3: Preprocessing ...
% 2.58/1.16 Prover 2: Constructing countermodel ...
% 2.58/1.16 Prover 5: Proving ...
% 2.58/1.17 Prover 6: Proving ...
% 2.58/1.17 Prover 3: Constructing countermodel ...
% 2.58/1.18 Prover 1: Constructing countermodel ...
% 2.58/1.18 Prover 4: Constructing countermodel ...
% 2.58/1.19 Prover 0: Proving ...
% 3.29/1.25 Prover 0: proved (606ms)
% 3.29/1.26
% 3.29/1.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.29/1.26
% 3.29/1.26 Prover 2: proved (610ms)
% 3.29/1.26
% 3.29/1.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.29/1.26
% 3.29/1.26 Prover 3: stopped
% 3.29/1.27 Prover 6: stopped
% 3.29/1.27 Prover 5: stopped
% 3.29/1.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.29/1.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.29/1.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.29/1.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.29/1.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.29/1.28 Prover 13: Preprocessing ...
% 3.29/1.28 Prover 11: Preprocessing ...
% 3.29/1.28 Prover 8: Preprocessing ...
% 3.29/1.28 Prover 7: Preprocessing ...
% 3.29/1.29 Prover 10: Preprocessing ...
% 3.99/1.30 Prover 7: Constructing countermodel ...
% 3.99/1.31 Prover 13: Constructing countermodel ...
% 3.99/1.31 Prover 10: Constructing countermodel ...
% 3.99/1.32 Prover 4: Found proof (size 15)
% 3.99/1.32 Prover 4: proved (669ms)
% 3.99/1.32 Prover 13: stopped
% 3.99/1.32 Prover 7: stopped
% 3.99/1.32 Prover 1: Found proof (size 14)
% 3.99/1.32 Prover 1: proved (673ms)
% 3.99/1.32 Prover 10: stopped
% 3.99/1.33 Prover 8: Warning: ignoring some quantifiers
% 3.99/1.33 Prover 11: Constructing countermodel ...
% 3.99/1.33 Prover 8: Constructing countermodel ...
% 3.99/1.34 Prover 8: stopped
% 3.99/1.34 Prover 11: stopped
% 3.99/1.34
% 3.99/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.99/1.34
% 3.99/1.34 % SZS output start Proof for theBenchmark
% 3.99/1.34 Assumptions after simplification:
% 3.99/1.34 ---------------------------------
% 3.99/1.34
% 3.99/1.34 (intersect_defn)
% 3.99/1.38 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~
% 3.99/1.38 (intersect(v0, v1) = v2) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v1) |
% 3.99/1.38 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v0) = v4)) & ! [v0:
% 3.99/1.38 $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ (intersect(v0,
% 3.99/1.38 v1) = v2) | ~ (member(v3, v0) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0)
% 3.99/1.38 | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0: $i] : !
% 3.99/1.38 [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 3.99/1.38 (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2)))
% 3.99/1.38
% 3.99/1.38 (prove_th13)
% 3.99/1.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 3.99/1.39 intersect(v1, v2) = v3 & member(v0, v2) = 0 & member(v0, v1) = 0 & $i(v2) &
% 3.99/1.39 $i(v1) & $i(v0))
% 3.99/1.39
% 3.99/1.39 (function-axioms)
% 3.99/1.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 3.99/1.39 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) =
% 3.99/1.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 3.99/1.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 3.99/1.39 = v0))
% 3.99/1.39
% 3.99/1.39 Further assumptions not needed in the proof:
% 3.99/1.39 --------------------------------------------
% 3.99/1.39 symmetry_of_intersect
% 3.99/1.39
% 3.99/1.39 Those formulas are unsatisfiable:
% 3.99/1.39 ---------------------------------
% 3.99/1.39
% 3.99/1.39 Begin of proof
% 3.99/1.39 |
% 3.99/1.39 | ALPHA: (intersect_defn) implies:
% 3.99/1.39 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~
% 3.99/1.39 | (intersect(v0, v1) = v2) | ~ (member(v3, v0) = 0) | ~ $i(v3) | ~
% 3.99/1.39 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) =
% 3.99/1.39 | v4))
% 3.99/1.39 |
% 3.99/1.39 | ALPHA: (function-axioms) implies:
% 3.99/1.40 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 3.99/1.40 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 3.99/1.40 | = v0))
% 3.99/1.40 |
% 3.99/1.40 | DELTA: instantiating (prove_th13) with fresh symbols all_5_0, all_5_1,
% 3.99/1.40 | all_5_2, all_5_3 gives:
% 3.99/1.40 | (3) ~ (all_5_0 = 0) & intersect(all_5_2, all_5_1) = all_5_0 &
% 3.99/1.40 | member(all_5_3, all_5_1) = 0 & member(all_5_3, all_5_2) = 0 &
% 3.99/1.40 | $i(all_5_1) & $i(all_5_2) & $i(all_5_3)
% 3.99/1.40 |
% 3.99/1.40 | ALPHA: (3) implies:
% 3.99/1.40 | (4) ~ (all_5_0 = 0)
% 3.99/1.40 | (5) $i(all_5_3)
% 3.99/1.40 | (6) $i(all_5_2)
% 3.99/1.40 | (7) $i(all_5_1)
% 3.99/1.40 | (8) member(all_5_3, all_5_2) = 0
% 3.99/1.40 | (9) member(all_5_3, all_5_1) = 0
% 3.99/1.40 | (10) intersect(all_5_2, all_5_1) = all_5_0
% 3.99/1.40 |
% 3.99/1.40 | GROUND_INST: instantiating (1) with all_5_2, all_5_1, all_5_0, all_5_3,
% 3.99/1.40 | simplifying with (5), (6), (7), (8), (10) gives:
% 3.99/1.40 | (11) all_5_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_5_3, all_5_1) =
% 3.99/1.40 | v0)
% 3.99/1.40 |
% 3.99/1.40 | BETA: splitting (11) gives:
% 3.99/1.40 |
% 3.99/1.40 | Case 1:
% 3.99/1.40 | |
% 3.99/1.40 | | (12) all_5_0 = 0
% 3.99/1.40 | |
% 3.99/1.40 | | REDUCE: (4), (12) imply:
% 3.99/1.40 | | (13) $false
% 3.99/1.41 | |
% 3.99/1.41 | | CLOSE: (13) is inconsistent.
% 3.99/1.41 | |
% 3.99/1.41 | Case 2:
% 3.99/1.41 | |
% 3.99/1.41 | | (14) ? [v0: int] : ( ~ (v0 = 0) & member(all_5_3, all_5_1) = v0)
% 3.99/1.41 | |
% 3.99/1.41 | | DELTA: instantiating (14) with fresh symbol all_20_0 gives:
% 3.99/1.41 | | (15) ~ (all_20_0 = 0) & member(all_5_3, all_5_1) = all_20_0
% 3.99/1.41 | |
% 3.99/1.41 | | ALPHA: (15) implies:
% 3.99/1.41 | | (16) ~ (all_20_0 = 0)
% 3.99/1.41 | | (17) member(all_5_3, all_5_1) = all_20_0
% 3.99/1.41 | |
% 3.99/1.41 | | GROUND_INST: instantiating (2) with 0, all_20_0, all_5_1, all_5_3,
% 3.99/1.41 | | simplifying with (9), (17) gives:
% 3.99/1.41 | | (18) all_20_0 = 0
% 3.99/1.41 | |
% 3.99/1.41 | | REDUCE: (16), (18) imply:
% 3.99/1.41 | | (19) $false
% 3.99/1.41 | |
% 3.99/1.41 | | CLOSE: (19) is inconsistent.
% 3.99/1.41 | |
% 3.99/1.41 | End of split
% 3.99/1.41 |
% 3.99/1.41 End of proof
% 3.99/1.41 % SZS output end Proof for theBenchmark
% 3.99/1.41
% 3.99/1.41 788ms
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