TSTP Solution File: SET027+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET027+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 : n005.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 15:23:15 EDT 2023
% Result : Theorem 3.87s 1.35s
% Output : Proof 5.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET027+3 : TPTP v8.1.2. Released v2.2.0.
% 0.05/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Aug 26 10:42:38 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.60 ________ _____
% 0.16/0.60 ___ __ \_________(_)________________________________
% 0.16/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.60
% 0.16/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.60 (2023-06-19)
% 0.16/0.60
% 0.16/0.60 (c) Philipp Rümmer, 2009-2023
% 0.16/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.60 Amanda Stjerna.
% 0.16/0.60 Free software under BSD-3-Clause.
% 0.16/0.60
% 0.16/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.60
% 0.16/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.62 Running up to 7 provers in parallel.
% 0.16/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.16/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 1.52/1.01 Prover 1: Preprocessing ...
% 1.52/1.01 Prover 4: Preprocessing ...
% 2.02/1.06 Prover 3: Preprocessing ...
% 2.02/1.06 Prover 2: Preprocessing ...
% 2.02/1.06 Prover 0: Preprocessing ...
% 2.02/1.06 Prover 6: Preprocessing ...
% 2.02/1.06 Prover 5: Preprocessing ...
% 2.82/1.16 Prover 5: Proving ...
% 2.82/1.16 Prover 2: Proving ...
% 2.89/1.17 Prover 0: Proving ...
% 2.89/1.17 Prover 6: Proving ...
% 2.89/1.18 Prover 1: Constructing countermodel ...
% 2.89/1.18 Prover 3: Constructing countermodel ...
% 2.89/1.18 Prover 4: Constructing countermodel ...
% 3.87/1.35 Prover 3: proved (722ms)
% 3.87/1.35
% 3.87/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.87/1.35
% 3.87/1.35 Prover 6: stopped
% 3.87/1.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.87/1.36 Prover 2: stopped
% 3.87/1.36 Prover 5: stopped
% 3.87/1.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.87/1.36 Prover 0: proved (740ms)
% 3.87/1.36
% 3.87/1.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.87/1.36
% 3.87/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.87/1.38 Prover 7: Preprocessing ...
% 3.87/1.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.87/1.38 Prover 11: Preprocessing ...
% 3.87/1.38 Prover 10: Preprocessing ...
% 3.87/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.87/1.39 Prover 13: Preprocessing ...
% 3.87/1.39 Prover 10: Warning: ignoring some quantifiers
% 3.87/1.39 Prover 8: Preprocessing ...
% 3.87/1.39 Prover 10: Constructing countermodel ...
% 3.87/1.41 Prover 7: Warning: ignoring some quantifiers
% 3.87/1.41 Prover 7: Constructing countermodel ...
% 3.87/1.42 Prover 13: Warning: ignoring some quantifiers
% 3.87/1.42 Prover 4: Found proof (size 20)
% 3.87/1.42 Prover 4: proved (790ms)
% 3.87/1.42 Prover 13: Constructing countermodel ...
% 3.87/1.42 Prover 7: stopped
% 3.87/1.42 Prover 10: stopped
% 3.87/1.42 Prover 13: stopped
% 4.55/1.43 Prover 1: Found proof (size 17)
% 4.55/1.43 Prover 1: proved (800ms)
% 4.55/1.44 Prover 11: Constructing countermodel ...
% 4.55/1.44 Prover 11: stopped
% 4.55/1.44 Prover 8: Warning: ignoring some quantifiers
% 4.55/1.45 Prover 8: Constructing countermodel ...
% 4.55/1.45 Prover 8: stopped
% 4.55/1.45
% 4.55/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.55/1.45
% 4.55/1.46 % SZS output start Proof for theBenchmark
% 4.55/1.46 Assumptions after simplification:
% 4.55/1.46 ---------------------------------
% 4.55/1.46
% 4.55/1.46 (prove_transitivity_of_subset)
% 4.86/1.51 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 4.86/1.51 subset(v1, v2) = 0 & subset(v0, v2) = v3 & subset(v0, v1) = 0 & $i(v2) &
% 4.86/1.51 $i(v1) & $i(v0))
% 4.86/1.51
% 4.86/1.51 (subset_defn)
% 4.86/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.86/1.52 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 4.86/1.52 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 4.86/1.52 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 4.86/1.52 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 4.86/1.52 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 4.86/1.52 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 4.86/1.52 ~ $i(v0) | member(v2, v1) = 0)
% 4.86/1.52
% 4.86/1.52 (function-axioms)
% 4.86/1.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.86/1.52 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 4.86/1.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 4.86/1.52 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 4.86/1.52
% 4.86/1.52 Further assumptions not needed in the proof:
% 4.86/1.52 --------------------------------------------
% 4.86/1.53 reflexivity_of_subset
% 4.86/1.53
% 4.86/1.53 Those formulas are unsatisfiable:
% 4.86/1.53 ---------------------------------
% 4.86/1.53
% 4.86/1.53 Begin of proof
% 4.86/1.53 |
% 4.86/1.53 | ALPHA: (subset_defn) implies:
% 4.86/1.53 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 4.86/1.53 | (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v2,
% 4.86/1.53 | v1) = 0)
% 4.86/1.53 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 4.86/1.53 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 4.86/1.53 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 4.86/1.54 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.86/1.54 | (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~
% 4.86/1.54 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) =
% 4.86/1.54 | v4))
% 4.86/1.54 |
% 4.86/1.54 | ALPHA: (function-axioms) implies:
% 4.86/1.54 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.86/1.54 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 4.86/1.54 | = v0))
% 4.86/1.54 |
% 4.86/1.54 | DELTA: instantiating (prove_transitivity_of_subset) with fresh symbols
% 4.86/1.54 | all_5_0, all_5_1, all_5_2, all_5_3 gives:
% 4.86/1.54 | (5) ~ (all_5_0 = 0) & subset(all_5_2, all_5_1) = 0 & subset(all_5_3,
% 4.86/1.54 | all_5_1) = all_5_0 & subset(all_5_3, all_5_2) = 0 & $i(all_5_1) &
% 4.86/1.54 | $i(all_5_2) & $i(all_5_3)
% 4.86/1.54 |
% 4.86/1.54 | ALPHA: (5) implies:
% 4.86/1.54 | (6) ~ (all_5_0 = 0)
% 4.86/1.54 | (7) $i(all_5_3)
% 4.86/1.54 | (8) $i(all_5_2)
% 4.86/1.54 | (9) $i(all_5_1)
% 4.86/1.54 | (10) subset(all_5_3, all_5_2) = 0
% 4.86/1.54 | (11) subset(all_5_3, all_5_1) = all_5_0
% 4.86/1.54 | (12) subset(all_5_2, all_5_1) = 0
% 4.86/1.54 |
% 4.86/1.55 | GROUND_INST: instantiating (2) with all_5_3, all_5_1, all_5_0, simplifying
% 4.86/1.55 | with (7), (9), (11) gives:
% 4.86/1.55 | (13) all_5_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 4.86/1.55 | all_5_1) = v1 & member(v0, all_5_3) = 0 & $i(v0))
% 4.86/1.55 |
% 4.86/1.55 | BETA: splitting (13) gives:
% 4.86/1.55 |
% 4.86/1.55 | Case 1:
% 4.86/1.55 | |
% 4.86/1.55 | | (14) all_5_0 = 0
% 4.86/1.55 | |
% 4.86/1.55 | | REDUCE: (6), (14) imply:
% 4.86/1.55 | | (15) $false
% 4.86/1.55 | |
% 4.86/1.55 | | CLOSE: (15) is inconsistent.
% 4.86/1.55 | |
% 4.86/1.55 | Case 2:
% 4.86/1.55 | |
% 4.86/1.55 | | (16) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_5_1) = v1
% 4.86/1.55 | | & member(v0, all_5_3) = 0 & $i(v0))
% 4.86/1.55 | |
% 4.86/1.55 | | DELTA: instantiating (16) with fresh symbols all_14_0, all_14_1 gives:
% 4.86/1.55 | | (17) ~ (all_14_0 = 0) & member(all_14_1, all_5_1) = all_14_0 &
% 4.86/1.55 | | member(all_14_1, all_5_3) = 0 & $i(all_14_1)
% 4.86/1.55 | |
% 4.86/1.55 | | ALPHA: (17) implies:
% 4.86/1.56 | | (18) ~ (all_14_0 = 0)
% 4.86/1.56 | | (19) $i(all_14_1)
% 4.86/1.56 | | (20) member(all_14_1, all_5_3) = 0
% 4.86/1.56 | | (21) member(all_14_1, all_5_1) = all_14_0
% 4.86/1.56 | |
% 4.86/1.56 | | GROUND_INST: instantiating (1) with all_5_3, all_5_2, all_14_1, simplifying
% 4.86/1.56 | | with (7), (8), (10), (19), (20) gives:
% 4.86/1.56 | | (22) member(all_14_1, all_5_2) = 0
% 4.86/1.56 | |
% 5.19/1.56 | | GROUND_INST: instantiating (3) with all_5_2, all_5_1, all_14_1, all_14_0,
% 5.19/1.56 | | simplifying with (8), (9), (12), (19), (21) gives:
% 5.19/1.56 | | (23) all_14_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_14_1,
% 5.19/1.56 | | all_5_2) = v0)
% 5.19/1.56 | |
% 5.19/1.56 | | BETA: splitting (23) gives:
% 5.19/1.56 | |
% 5.19/1.56 | | Case 1:
% 5.19/1.56 | | |
% 5.19/1.56 | | | (24) all_14_0 = 0
% 5.19/1.56 | | |
% 5.19/1.56 | | | REDUCE: (18), (24) imply:
% 5.19/1.56 | | | (25) $false
% 5.19/1.56 | | |
% 5.19/1.56 | | | CLOSE: (25) is inconsistent.
% 5.19/1.56 | | |
% 5.19/1.56 | | Case 2:
% 5.19/1.56 | | |
% 5.19/1.56 | | | (26) ? [v0: int] : ( ~ (v0 = 0) & member(all_14_1, all_5_2) = v0)
% 5.19/1.56 | | |
% 5.19/1.56 | | | DELTA: instantiating (26) with fresh symbol all_26_0 gives:
% 5.19/1.56 | | | (27) ~ (all_26_0 = 0) & member(all_14_1, all_5_2) = all_26_0
% 5.19/1.56 | | |
% 5.19/1.56 | | | ALPHA: (27) implies:
% 5.19/1.56 | | | (28) ~ (all_26_0 = 0)
% 5.19/1.57 | | | (29) member(all_14_1, all_5_2) = all_26_0
% 5.19/1.57 | | |
% 5.19/1.57 | | | GROUND_INST: instantiating (4) with 0, all_26_0, all_5_2, all_14_1,
% 5.19/1.57 | | | simplifying with (22), (29) gives:
% 5.19/1.57 | | | (30) all_26_0 = 0
% 5.19/1.57 | | |
% 5.19/1.57 | | | REDUCE: (28), (30) imply:
% 5.19/1.57 | | | (31) $false
% 5.19/1.57 | | |
% 5.19/1.57 | | | CLOSE: (31) is inconsistent.
% 5.19/1.57 | | |
% 5.19/1.57 | | End of split
% 5.19/1.57 | |
% 5.19/1.57 | End of split
% 5.19/1.57 |
% 5.19/1.57 End of proof
% 5.19/1.57 % SZS output end Proof for theBenchmark
% 5.19/1.57
% 5.19/1.57 966ms
%------------------------------------------------------------------------------