TSTP Solution File: SET925+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET925+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 : n023.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 15:27:03 EDT 2023
% Result : Theorem 3.92s 1.21s
% Output : Proof 4.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET925+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 15:37:56 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.60 ________ _____
% 0.18/0.60 ___ __ \_________(_)________________________________
% 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.60
% 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.60 (2023-06-19)
% 0.18/0.60
% 0.18/0.60 (c) Philipp Rümmer, 2009-2023
% 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.60 Amanda Stjerna.
% 0.18/0.60 Free software under BSD-3-Clause.
% 0.18/0.60
% 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.60
% 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.63/0.61 Running up to 7 provers in parallel.
% 0.71/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.71/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.71/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.71/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.71/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.71/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.71/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.01/0.93 Prover 4: Preprocessing ...
% 2.01/0.93 Prover 1: Preprocessing ...
% 2.01/0.97 Prover 6: Preprocessing ...
% 2.01/0.97 Prover 5: Preprocessing ...
% 2.01/0.97 Prover 3: Preprocessing ...
% 2.01/0.97 Prover 2: Preprocessing ...
% 2.01/0.97 Prover 0: Preprocessing ...
% 3.05/1.09 Prover 6: Constructing countermodel ...
% 3.05/1.10 Prover 2: Proving ...
% 3.05/1.10 Prover 5: Proving ...
% 3.05/1.10 Prover 3: Constructing countermodel ...
% 3.05/1.10 Prover 1: Constructing countermodel ...
% 3.05/1.11 Prover 4: Constructing countermodel ...
% 3.05/1.11 Prover 0: Proving ...
% 3.92/1.21 Prover 3: proved (586ms)
% 3.92/1.21
% 3.92/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.92/1.21
% 3.92/1.22 Prover 6: stopped
% 3.92/1.22 Prover 5: stopped
% 3.92/1.22 Prover 2: proved (591ms)
% 3.92/1.22
% 3.92/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.92/1.22
% 3.92/1.22 Prover 0: proved (596ms)
% 3.92/1.22
% 3.92/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.92/1.22
% 3.92/1.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.92/1.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.92/1.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.92/1.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.92/1.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.10/1.23 Prover 7: Preprocessing ...
% 4.10/1.24 Prover 11: Preprocessing ...
% 4.10/1.24 Prover 8: Preprocessing ...
% 4.10/1.24 Prover 13: Preprocessing ...
% 4.10/1.25 Prover 10: Preprocessing ...
% 4.10/1.26 Prover 7: Constructing countermodel ...
% 4.10/1.27 Prover 8: Warning: ignoring some quantifiers
% 4.10/1.28 Prover 13: Warning: ignoring some quantifiers
% 4.10/1.28 Prover 1: Found proof (size 23)
% 4.10/1.28 Prover 1: proved (662ms)
% 4.10/1.28 Prover 10: Constructing countermodel ...
% 4.10/1.28 Prover 7: stopped
% 4.10/1.28 Prover 4: stopped
% 4.10/1.28 Prover 8: Constructing countermodel ...
% 4.10/1.28 Prover 13: Constructing countermodel ...
% 4.10/1.29 Prover 10: stopped
% 4.10/1.29 Prover 8: stopped
% 4.10/1.29 Prover 13: stopped
% 4.10/1.29 Prover 11: Constructing countermodel ...
% 4.10/1.30 Prover 11: stopped
% 4.10/1.30
% 4.10/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.10/1.30
% 4.10/1.30 % SZS output start Proof for theBenchmark
% 4.10/1.31 Assumptions after simplification:
% 4.10/1.31 ---------------------------------
% 4.10/1.31
% 4.10/1.31 (l36_zfmisc_1)
% 4.72/1.34 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 =
% 4.72/1.34 empty_set | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~
% 4.72/1.34 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & !
% 4.72/1.34 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~
% 4.72/1.34 (set_difference(v2, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | in(v0, v1) =
% 4.72/1.34 0)
% 4.72/1.34
% 4.72/1.34 (t68_zfmisc_1)
% 4.72/1.34 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 4.72/1.34 [v4: any] : (singleton(v0) = v2 & set_difference(v2, v1) = v3 & in(v0, v1) =
% 4.72/1.34 v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v3 = empty_set)) |
% 4.72/1.34 (v3 = empty_set & ~ (v4 = 0))))
% 4.72/1.34
% 4.72/1.34 (function-axioms)
% 4.72/1.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 4.72/1.35 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 4.72/1.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 4.72/1.35 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 4.72/1.35 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 4.72/1.35 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 4.72/1.35 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 4.72/1.35 (empty(v2) = v0))
% 4.72/1.35
% 4.72/1.35 Further assumptions not needed in the proof:
% 4.72/1.35 --------------------------------------------
% 4.72/1.35 antisymmetry_r2_hidden, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0
% 4.72/1.35
% 4.72/1.35 Those formulas are unsatisfiable:
% 4.72/1.35 ---------------------------------
% 4.72/1.35
% 4.72/1.35 Begin of proof
% 4.72/1.35 |
% 4.72/1.35 | ALPHA: (l36_zfmisc_1) implies:
% 4.72/1.35 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~
% 4.72/1.35 | (set_difference(v2, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | in(v0,
% 4.72/1.35 | v1) = 0)
% 4.72/1.35 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set
% 4.72/1.35 | | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~
% 4.72/1.35 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 4.72/1.35 |
% 4.72/1.35 | ALPHA: (t68_zfmisc_1) implies:
% 4.72/1.36 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 4.72/1.36 | (singleton(v0) = v2 & set_difference(v2, v1) = v3 & in(v0, v1) = v4 &
% 4.72/1.36 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v3 = empty_set)) |
% 4.72/1.36 | (v3 = empty_set & ~ (v4 = 0))))
% 4.72/1.36 |
% 4.72/1.36 | ALPHA: (function-axioms) implies:
% 4.72/1.36 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.72/1.36 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.72/1.36 |
% 4.72/1.36 | DELTA: instantiating (3) with fresh symbols all_10_0, all_10_1, all_10_2,
% 4.72/1.36 | all_10_3, all_10_4 gives:
% 4.72/1.36 | (5) singleton(all_10_4) = all_10_2 & set_difference(all_10_2, all_10_3) =
% 4.72/1.36 | all_10_1 & in(all_10_4, all_10_3) = all_10_0 & $i(all_10_1) &
% 4.72/1.36 | $i(all_10_2) & $i(all_10_3) & $i(all_10_4) & ((all_10_0 = 0 & ~
% 4.72/1.36 | (all_10_1 = empty_set)) | (all_10_1 = empty_set & ~ (all_10_0 =
% 4.72/1.36 | 0)))
% 4.72/1.36 |
% 4.72/1.36 | ALPHA: (5) implies:
% 4.72/1.36 | (6) $i(all_10_4)
% 4.72/1.36 | (7) $i(all_10_3)
% 4.72/1.36 | (8) in(all_10_4, all_10_3) = all_10_0
% 4.72/1.36 | (9) set_difference(all_10_2, all_10_3) = all_10_1
% 4.72/1.36 | (10) singleton(all_10_4) = all_10_2
% 4.72/1.36 | (11) (all_10_0 = 0 & ~ (all_10_1 = empty_set)) | (all_10_1 = empty_set &
% 4.72/1.36 | ~ (all_10_0 = 0))
% 4.72/1.36 |
% 4.72/1.37 | GROUND_INST: instantiating (2) with all_10_4, all_10_3, all_10_2, all_10_1,
% 4.72/1.37 | simplifying with (6), (7), (9), (10) gives:
% 4.72/1.37 | (12) all_10_1 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & in(all_10_4,
% 4.72/1.37 | all_10_3) = v0)
% 4.72/1.37 |
% 4.72/1.37 | BETA: splitting (11) gives:
% 4.72/1.37 |
% 4.72/1.37 | Case 1:
% 4.72/1.37 | |
% 4.72/1.37 | | (13) all_10_0 = 0 & ~ (all_10_1 = empty_set)
% 4.72/1.37 | |
% 4.72/1.37 | | ALPHA: (13) implies:
% 4.72/1.37 | | (14) all_10_0 = 0
% 4.72/1.37 | | (15) ~ (all_10_1 = empty_set)
% 4.72/1.37 | |
% 4.72/1.37 | | REDUCE: (8), (14) imply:
% 4.72/1.37 | | (16) in(all_10_4, all_10_3) = 0
% 4.72/1.37 | |
% 4.72/1.37 | | BETA: splitting (12) gives:
% 4.72/1.37 | |
% 4.72/1.37 | | Case 1:
% 4.72/1.37 | | |
% 4.72/1.37 | | | (17) all_10_1 = empty_set
% 4.72/1.37 | | |
% 4.72/1.37 | | | REDUCE: (15), (17) imply:
% 4.72/1.37 | | | (18) $false
% 4.72/1.37 | | |
% 4.72/1.37 | | | CLOSE: (18) is inconsistent.
% 4.72/1.37 | | |
% 4.72/1.37 | | Case 2:
% 4.72/1.37 | | |
% 4.72/1.37 | | | (19) ? [v0: int] : ( ~ (v0 = 0) & in(all_10_4, all_10_3) = v0)
% 4.72/1.37 | | |
% 4.72/1.37 | | | DELTA: instantiating (19) with fresh symbol all_23_0 gives:
% 4.72/1.37 | | | (20) ~ (all_23_0 = 0) & in(all_10_4, all_10_3) = all_23_0
% 4.72/1.37 | | |
% 4.72/1.37 | | | ALPHA: (20) implies:
% 4.72/1.37 | | | (21) ~ (all_23_0 = 0)
% 4.72/1.37 | | | (22) in(all_10_4, all_10_3) = all_23_0
% 4.72/1.37 | | |
% 4.72/1.38 | | | GROUND_INST: instantiating (4) with 0, all_23_0, all_10_3, all_10_4,
% 4.72/1.38 | | | simplifying with (16), (22) gives:
% 4.72/1.38 | | | (23) all_23_0 = 0
% 4.72/1.38 | | |
% 4.72/1.38 | | | REDUCE: (21), (23) imply:
% 4.72/1.38 | | | (24) $false
% 4.72/1.38 | | |
% 4.72/1.38 | | | CLOSE: (24) is inconsistent.
% 4.72/1.38 | | |
% 4.72/1.38 | | End of split
% 4.72/1.38 | |
% 4.72/1.38 | Case 2:
% 4.72/1.38 | |
% 4.72/1.38 | | (25) all_10_1 = empty_set & ~ (all_10_0 = 0)
% 4.72/1.38 | |
% 4.72/1.38 | | ALPHA: (25) implies:
% 4.72/1.38 | | (26) all_10_1 = empty_set
% 4.72/1.38 | | (27) ~ (all_10_0 = 0)
% 4.72/1.38 | |
% 4.72/1.38 | | REDUCE: (9), (26) imply:
% 4.72/1.38 | | (28) set_difference(all_10_2, all_10_3) = empty_set
% 4.72/1.38 | |
% 4.72/1.38 | | GROUND_INST: instantiating (1) with all_10_4, all_10_3, all_10_2,
% 4.72/1.38 | | simplifying with (6), (7), (10), (28) gives:
% 4.72/1.38 | | (29) in(all_10_4, all_10_3) = 0
% 4.72/1.38 | |
% 4.72/1.38 | | GROUND_INST: instantiating (4) with all_10_0, 0, all_10_3, all_10_4,
% 4.72/1.38 | | simplifying with (8), (29) gives:
% 4.72/1.38 | | (30) all_10_0 = 0
% 4.72/1.38 | |
% 4.72/1.38 | | REDUCE: (27), (30) imply:
% 4.72/1.38 | | (31) $false
% 4.72/1.38 | |
% 4.72/1.38 | | CLOSE: (31) is inconsistent.
% 4.72/1.38 | |
% 4.72/1.38 | End of split
% 4.72/1.38 |
% 4.72/1.38 End of proof
% 4.72/1.38 % SZS output end Proof for theBenchmark
% 4.72/1.38
% 4.72/1.38 782ms
%------------------------------------------------------------------------------