TSTP Solution File: SET899+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET899+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n015.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 15:26:56 EDT 2023
% Result : Theorem 3.62s 1.27s
% Output : Proof 4.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET899+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n015.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 10:01:07 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 ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.16/1.00 Prover 1: Preprocessing ...
% 2.16/1.00 Prover 4: Preprocessing ...
% 2.16/1.05 Prover 5: Preprocessing ...
% 2.16/1.05 Prover 2: Preprocessing ...
% 2.16/1.05 Prover 0: Preprocessing ...
% 2.16/1.05 Prover 3: Preprocessing ...
% 2.16/1.05 Prover 6: Preprocessing ...
% 2.70/1.15 Prover 2: Proving ...
% 2.70/1.15 Prover 5: Proving ...
% 2.70/1.15 Prover 1: Warning: ignoring some quantifiers
% 2.70/1.15 Prover 3: Warning: ignoring some quantifiers
% 2.70/1.16 Prover 1: Constructing countermodel ...
% 2.70/1.16 Prover 4: Constructing countermodel ...
% 2.70/1.16 Prover 3: Constructing countermodel ...
% 2.70/1.17 Prover 6: Proving ...
% 2.70/1.18 Prover 0: Proving ...
% 3.62/1.26 Prover 3: proved (622ms)
% 3.62/1.26
% 3.62/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.62/1.27
% 3.62/1.27 Prover 0: proved (624ms)
% 3.62/1.27
% 3.62/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.62/1.27
% 3.62/1.27 Prover 5: proved (623ms)
% 3.62/1.27
% 3.62/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.62/1.27
% 3.62/1.27 Prover 6: proved (622ms)
% 3.62/1.27
% 3.62/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.62/1.27
% 3.62/1.27 Prover 2: proved (627ms)
% 3.62/1.27
% 3.62/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.62/1.27
% 3.62/1.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.62/1.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.62/1.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.62/1.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.62/1.28 Prover 7: Preprocessing ...
% 3.62/1.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.62/1.28 Prover 8: Preprocessing ...
% 3.62/1.29 Prover 11: Preprocessing ...
% 3.62/1.30 Prover 10: Preprocessing ...
% 4.25/1.30 Prover 13: Preprocessing ...
% 4.25/1.31 Prover 7: Warning: ignoring some quantifiers
% 4.25/1.31 Prover 7: Constructing countermodel ...
% 4.25/1.32 Prover 4: Found proof (size 17)
% 4.25/1.32 Prover 1: Found proof (size 17)
% 4.25/1.32 Prover 4: proved (683ms)
% 4.25/1.32 Prover 1: proved (684ms)
% 4.25/1.32 Prover 7: stopped
% 4.25/1.33 Prover 10: Warning: ignoring some quantifiers
% 4.25/1.33 Prover 10: Constructing countermodel ...
% 4.25/1.33 Prover 13: Warning: ignoring some quantifiers
% 4.25/1.33 Prover 10: stopped
% 4.25/1.34 Prover 13: Constructing countermodel ...
% 4.25/1.34 Prover 8: Warning: ignoring some quantifiers
% 4.25/1.34 Prover 13: stopped
% 4.25/1.34 Prover 8: Constructing countermodel ...
% 4.25/1.34 Prover 11: Constructing countermodel ...
% 4.25/1.35 Prover 11: stopped
% 4.25/1.35 Prover 8: stopped
% 4.25/1.35
% 4.25/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.25/1.35
% 4.25/1.35 % SZS output start Proof for theBenchmark
% 4.25/1.36 Assumptions after simplification:
% 4.25/1.36 ---------------------------------
% 4.25/1.36
% 4.25/1.36 (l3_zfmisc_1)
% 4.25/1.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 4.25/1.39 int] : (v5 = 0 | ~ (singleton(v2) = v3) | ~ (set_difference(v1, v3) = v4)
% 4.25/1.39 | ~ (subset(v0, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 4.25/1.39 any] : ? [v7: any] : (in(v2, v0) = v7 & subset(v0, v1) = v6 & ( ~ (v6 =
% 4.25/1.39 0) | v7 = 0)))
% 4.25/1.39
% 4.25/1.39 (t40_zfmisc_1)
% 4.25/1.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] : ? [v5:
% 4.25/1.39 $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v3 = 0) & singleton(v2) = v4 &
% 4.25/1.39 set_difference(v1, v4) = v5 & in(v2, v0) = v3 & subset(v0, v5) = v6 &
% 4.25/1.39 subset(v0, v1) = 0 & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0))
% 4.25/1.39
% 4.25/1.39 (function-axioms)
% 4.25/1.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 4.25/1.40 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 4.25/1.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 4.25/1.40 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 4.25/1.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 4.25/1.40 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 4.25/1.40 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 4.25/1.40 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 4.25/1.40 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 4.25/1.40 (empty(v2) = v0))
% 4.25/1.40
% 4.25/1.40 Further assumptions not needed in the proof:
% 4.25/1.40 --------------------------------------------
% 4.25/1.40 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 4.25/1.40
% 4.25/1.40 Those formulas are unsatisfiable:
% 4.25/1.40 ---------------------------------
% 4.25/1.40
% 4.25/1.40 Begin of proof
% 4.25/1.40 |
% 4.25/1.40 | ALPHA: (function-axioms) implies:
% 4.25/1.40 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.25/1.40 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2)
% 4.25/1.40 | = v0))
% 4.25/1.40 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.25/1.40 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.25/1.40 |
% 4.25/1.40 | DELTA: instantiating (t40_zfmisc_1) with fresh symbols all_11_0, all_11_1,
% 4.25/1.40 | all_11_2, all_11_3, all_11_4, all_11_5, all_11_6 gives:
% 4.25/1.41 | (3) ~ (all_11_0 = 0) & ~ (all_11_3 = 0) & singleton(all_11_4) = all_11_2
% 4.25/1.41 | & set_difference(all_11_5, all_11_2) = all_11_1 & in(all_11_4,
% 4.25/1.41 | all_11_6) = all_11_3 & subset(all_11_6, all_11_1) = all_11_0 &
% 4.25/1.41 | subset(all_11_6, all_11_5) = 0 & $i(all_11_1) & $i(all_11_2) &
% 4.25/1.41 | $i(all_11_4) & $i(all_11_5) & $i(all_11_6)
% 4.25/1.41 |
% 4.25/1.41 | ALPHA: (3) implies:
% 4.25/1.41 | (4) ~ (all_11_3 = 0)
% 4.25/1.41 | (5) ~ (all_11_0 = 0)
% 4.25/1.41 | (6) $i(all_11_6)
% 4.25/1.41 | (7) $i(all_11_5)
% 4.25/1.41 | (8) $i(all_11_4)
% 4.25/1.41 | (9) subset(all_11_6, all_11_5) = 0
% 4.25/1.41 | (10) subset(all_11_6, all_11_1) = all_11_0
% 4.25/1.41 | (11) in(all_11_4, all_11_6) = all_11_3
% 4.25/1.41 | (12) set_difference(all_11_5, all_11_2) = all_11_1
% 4.25/1.41 | (13) singleton(all_11_4) = all_11_2
% 4.25/1.41 |
% 4.25/1.41 | GROUND_INST: instantiating (l3_zfmisc_1) with all_11_6, all_11_5, all_11_4,
% 4.25/1.41 | all_11_2, all_11_1, all_11_0, simplifying with (6), (7), (8),
% 4.25/1.41 | (10), (12), (13) gives:
% 4.25/1.41 | (14) all_11_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_11_4, all_11_6) =
% 4.25/1.41 | v1 & subset(all_11_6, all_11_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 4.25/1.41 |
% 4.25/1.41 | BETA: splitting (14) gives:
% 4.25/1.41 |
% 4.25/1.41 | Case 1:
% 4.25/1.41 | |
% 4.25/1.41 | | (15) all_11_0 = 0
% 4.25/1.41 | |
% 4.25/1.41 | | REDUCE: (5), (15) imply:
% 4.25/1.41 | | (16) $false
% 4.25/1.41 | |
% 4.25/1.41 | | CLOSE: (16) is inconsistent.
% 4.25/1.41 | |
% 4.25/1.41 | Case 2:
% 4.25/1.41 | |
% 4.25/1.41 | | (17) ? [v0: any] : ? [v1: any] : (in(all_11_4, all_11_6) = v1 &
% 4.25/1.41 | | subset(all_11_6, all_11_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 4.25/1.41 | |
% 4.25/1.41 | | DELTA: instantiating (17) with fresh symbols all_20_0, all_20_1 gives:
% 4.25/1.42 | | (18) in(all_11_4, all_11_6) = all_20_0 & subset(all_11_6, all_11_5) =
% 4.25/1.42 | | all_20_1 & ( ~ (all_20_1 = 0) | all_20_0 = 0)
% 4.25/1.42 | |
% 4.25/1.42 | | ALPHA: (18) implies:
% 4.25/1.42 | | (19) subset(all_11_6, all_11_5) = all_20_1
% 4.25/1.42 | | (20) in(all_11_4, all_11_6) = all_20_0
% 4.25/1.42 | | (21) ~ (all_20_1 = 0) | all_20_0 = 0
% 4.25/1.42 | |
% 4.25/1.42 | | GROUND_INST: instantiating (1) with 0, all_20_1, all_11_5, all_11_6,
% 4.25/1.42 | | simplifying with (9), (19) gives:
% 4.25/1.42 | | (22) all_20_1 = 0
% 4.25/1.42 | |
% 4.25/1.42 | | GROUND_INST: instantiating (2) with all_11_3, all_20_0, all_11_6, all_11_4,
% 4.25/1.42 | | simplifying with (11), (20) gives:
% 4.25/1.42 | | (23) all_20_0 = all_11_3
% 4.25/1.42 | |
% 4.25/1.42 | | BETA: splitting (21) gives:
% 4.25/1.42 | |
% 4.25/1.42 | | Case 1:
% 4.25/1.42 | | |
% 4.25/1.42 | | | (24) ~ (all_20_1 = 0)
% 4.25/1.42 | | |
% 4.25/1.42 | | | REDUCE: (22), (24) imply:
% 4.25/1.42 | | | (25) $false
% 4.25/1.42 | | |
% 4.25/1.42 | | | CLOSE: (25) is inconsistent.
% 4.25/1.42 | | |
% 4.25/1.42 | | Case 2:
% 4.25/1.42 | | |
% 4.25/1.42 | | | (26) all_20_0 = 0
% 4.25/1.42 | | |
% 4.25/1.42 | | | COMBINE_EQS: (23), (26) imply:
% 4.25/1.42 | | | (27) all_11_3 = 0
% 4.25/1.42 | | |
% 4.25/1.42 | | | REDUCE: (4), (27) imply:
% 4.25/1.42 | | | (28) $false
% 4.25/1.42 | | |
% 4.25/1.42 | | | CLOSE: (28) is inconsistent.
% 4.25/1.42 | | |
% 4.25/1.42 | | End of split
% 4.25/1.42 | |
% 4.25/1.42 | End of split
% 4.25/1.42 |
% 4.25/1.42 End of proof
% 4.25/1.42 % SZS output end Proof for theBenchmark
% 4.25/1.42
% 4.25/1.42 799ms
%------------------------------------------------------------------------------