TSTP Solution File: SET879+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET879+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 : n006.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 15:26:53 EDT 2023
% Result : Theorem 4.20s 1.41s
% Output : Proof 6.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET879+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.18/0.34 % Computer : n006.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Sat Aug 26 13:10:22 EDT 2023
% 0.18/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 2.09/0.98 Prover 4: Preprocessing ...
% 2.09/0.99 Prover 1: Preprocessing ...
% 2.09/1.03 Prover 6: Preprocessing ...
% 2.09/1.03 Prover 0: Preprocessing ...
% 2.09/1.03 Prover 5: Preprocessing ...
% 2.09/1.03 Prover 2: Preprocessing ...
% 2.09/1.03 Prover 3: Preprocessing ...
% 3.39/1.17 Prover 1: Warning: ignoring some quantifiers
% 3.39/1.17 Prover 3: Warning: ignoring some quantifiers
% 3.39/1.18 Prover 1: Constructing countermodel ...
% 3.39/1.19 Prover 4: Warning: ignoring some quantifiers
% 3.39/1.19 Prover 6: Proving ...
% 3.39/1.19 Prover 5: Proving ...
% 3.39/1.19 Prover 2: Proving ...
% 3.39/1.19 Prover 3: Constructing countermodel ...
% 3.39/1.19 Prover 4: Constructing countermodel ...
% 3.39/1.21 Prover 0: Proving ...
% 4.20/1.40 Prover 0: proved (788ms)
% 4.20/1.40
% 4.20/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.20/1.41
% 4.20/1.41 Prover 2: proved (788ms)
% 4.20/1.41
% 4.20/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.20/1.41
% 4.20/1.41 Prover 3: stopped
% 4.20/1.41 Prover 6: stopped
% 4.20/1.41 Prover 5: stopped
% 4.20/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.20/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.20/1.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.20/1.42 Prover 4: Found proof (size 28)
% 4.20/1.42 Prover 4: proved (792ms)
% 4.20/1.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.20/1.42 Prover 7: Preprocessing ...
% 4.20/1.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.20/1.42 Prover 8: Preprocessing ...
% 4.20/1.43 Prover 11: Preprocessing ...
% 4.20/1.43 Prover 1: Found proof (size 32)
% 4.20/1.43 Prover 1: proved (815ms)
% 4.20/1.43 Prover 10: Preprocessing ...
% 4.20/1.45 Prover 11: stopped
% 4.20/1.45 Prover 13: Preprocessing ...
% 5.45/1.46 Prover 7: Warning: ignoring some quantifiers
% 5.45/1.46 Prover 10: Warning: ignoring some quantifiers
% 5.45/1.47 Prover 13: stopped
% 5.45/1.47 Prover 10: Constructing countermodel ...
% 5.45/1.47 Prover 7: Constructing countermodel ...
% 5.45/1.47 Prover 8: Warning: ignoring some quantifiers
% 5.45/1.47 Prover 7: stopped
% 5.45/1.47 Prover 10: stopped
% 5.45/1.47 Prover 8: Constructing countermodel ...
% 5.45/1.48 Prover 8: stopped
% 5.45/1.48
% 5.45/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.45/1.48
% 5.66/1.48 % SZS output start Proof for theBenchmark
% 5.66/1.48 Assumptions after simplification:
% 5.66/1.48 ---------------------------------
% 5.66/1.49
% 5.66/1.49 (d1_tarski)
% 5.66/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 5.66/1.52 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : !
% 5.66/1.52 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) =
% 5.66/1.52 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 5.66/1.52 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 5.66/1.52 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 =
% 5.66/1.52 0 | v3 = v1)))
% 5.66/1.52
% 5.66/1.52 (l34_zfmisc_1)
% 5.66/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 5.66/1.52 (set_difference(v2, v1) = v3) | ~ (singleton(v0) = v2) | ~ $i(v1) | ~
% 5.66/1.52 $i(v0) | in(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 5.66/1.52 0 | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 5.66/1.52 (set_difference(v3, v1) = v3 & singleton(v0) = v3 & $i(v3))) & ! [v0: $i] :
% 5.66/1.52 ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v2, v1) = v2) | ~
% 5.66/1.52 (singleton(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 5.66/1.52 in(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~
% 5.66/1.52 $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 5.66/1.52 set_difference(v2, v1) = v3 & singleton(v0) = v2 & $i(v3) & $i(v2)))
% 5.66/1.52
% 5.66/1.53 (t20_zfmisc_1)
% 5.66/1.53 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 5.66/1.53 (set_difference(v2, v3) = v4 & singleton(v1) = v3 & singleton(v0) = v2 &
% 5.66/1.53 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v4 = v2 & v1 = v0) | ( ~ (v4
% 5.66/1.53 = v2) & ~ (v1 = v0))))
% 5.66/1.53
% 5.66/1.53 (function-axioms)
% 5.66/1.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.66/1.53 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 5.66/1.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 5.66/1.53 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 5.66/1.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 5.66/1.53 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 5.66/1.53 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 5.66/1.53
% 5.66/1.53 Further assumptions not needed in the proof:
% 5.66/1.53 --------------------------------------------
% 5.66/1.53 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0
% 5.66/1.53
% 5.66/1.53 Those formulas are unsatisfiable:
% 5.66/1.53 ---------------------------------
% 5.66/1.53
% 5.66/1.53 Begin of proof
% 5.66/1.53 |
% 5.66/1.53 | ALPHA: (d1_tarski) implies:
% 5.66/1.54 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0)
% 5.66/1.54 | = v1) | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 5.66/1.54 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 5.66/1.54 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 5.66/1.54 |
% 5.66/1.54 | ALPHA: (l34_zfmisc_1) implies:
% 5.66/1.54 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v2, v1) =
% 5.66/1.54 | v2) | ~ (singleton(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 5.66/1.54 | int] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 5.95/1.54 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 5.95/1.54 | (set_difference(v2, v1) = v3) | ~ (singleton(v0) = v2) | ~ $i(v1) |
% 5.95/1.54 | ~ $i(v0) | in(v0, v1) = 0)
% 5.95/1.54 |
% 5.95/1.54 | ALPHA: (function-axioms) implies:
% 5.95/1.54 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 5.95/1.54 | = v1) | ~ (singleton(v2) = v0))
% 5.95/1.54 |
% 5.95/1.54 | DELTA: instantiating (t20_zfmisc_1) with fresh symbols all_12_0, all_12_1,
% 5.95/1.54 | all_12_2, all_12_3, all_12_4 gives:
% 5.95/1.55 | (6) set_difference(all_12_2, all_12_1) = all_12_0 & singleton(all_12_3) =
% 5.95/1.55 | all_12_1 & singleton(all_12_4) = all_12_2 & $i(all_12_0) & $i(all_12_1)
% 5.95/1.55 | & $i(all_12_2) & $i(all_12_3) & $i(all_12_4) & ((all_12_0 = all_12_2 &
% 5.95/1.55 | all_12_3 = all_12_4) | ( ~ (all_12_0 = all_12_2) & ~ (all_12_3 =
% 5.95/1.55 | all_12_4)))
% 5.95/1.55 |
% 5.95/1.55 | ALPHA: (6) implies:
% 5.95/1.55 | (7) $i(all_12_4)
% 5.95/1.55 | (8) $i(all_12_3)
% 5.95/1.55 | (9) $i(all_12_1)
% 5.95/1.55 | (10) singleton(all_12_4) = all_12_2
% 5.95/1.55 | (11) singleton(all_12_3) = all_12_1
% 5.95/1.55 | (12) set_difference(all_12_2, all_12_1) = all_12_0
% 5.95/1.55 | (13) (all_12_0 = all_12_2 & all_12_3 = all_12_4) | ( ~ (all_12_0 =
% 5.95/1.55 | all_12_2) & ~ (all_12_3 = all_12_4))
% 5.95/1.55 |
% 5.95/1.55 | GROUND_INST: instantiating (4) with all_12_4, all_12_1, all_12_2, all_12_0,
% 5.95/1.55 | simplifying with (7), (9), (10), (12) gives:
% 5.95/1.55 | (14) all_12_0 = all_12_2 | in(all_12_4, all_12_1) = 0
% 5.95/1.55 |
% 5.95/1.55 | BETA: splitting (13) gives:
% 5.95/1.55 |
% 5.95/1.55 | Case 1:
% 5.95/1.55 | |
% 5.95/1.55 | | (15) all_12_0 = all_12_2 & all_12_3 = all_12_4
% 5.95/1.55 | |
% 5.95/1.55 | | ALPHA: (15) implies:
% 5.95/1.55 | | (16) all_12_3 = all_12_4
% 5.95/1.55 | | (17) all_12_0 = all_12_2
% 5.95/1.55 | |
% 5.95/1.55 | | REDUCE: (12), (17) imply:
% 5.95/1.56 | | (18) set_difference(all_12_2, all_12_1) = all_12_2
% 5.95/1.56 | |
% 5.95/1.56 | | REDUCE: (11), (16) imply:
% 5.95/1.56 | | (19) singleton(all_12_4) = all_12_1
% 5.95/1.56 | |
% 5.95/1.56 | | GROUND_INST: instantiating (5) with all_12_2, all_12_1, all_12_4,
% 5.95/1.56 | | simplifying with (10), (19) gives:
% 5.95/1.56 | | (20) all_12_1 = all_12_2
% 5.95/1.56 | |
% 5.95/1.56 | | REDUCE: (18), (20) imply:
% 5.95/1.56 | | (21) set_difference(all_12_2, all_12_2) = all_12_2
% 5.95/1.56 | |
% 5.95/1.56 | | REDUCE: (9), (20) imply:
% 6.03/1.56 | | (22) $i(all_12_2)
% 6.03/1.56 | |
% 6.03/1.56 | | GROUND_INST: instantiating (3) with all_12_4, all_12_2, all_12_2,
% 6.03/1.56 | | simplifying with (7), (10), (21), (22) gives:
% 6.03/1.56 | | (23) ? [v0: int] : ( ~ (v0 = 0) & in(all_12_4, all_12_2) = v0)
% 6.03/1.56 | |
% 6.03/1.56 | | DELTA: instantiating (23) with fresh symbol all_30_0 gives:
% 6.03/1.56 | | (24) ~ (all_30_0 = 0) & in(all_12_4, all_12_2) = all_30_0
% 6.03/1.56 | |
% 6.03/1.56 | | ALPHA: (24) implies:
% 6.03/1.56 | | (25) ~ (all_30_0 = 0)
% 6.03/1.56 | | (26) in(all_12_4, all_12_2) = all_30_0
% 6.03/1.56 | |
% 6.03/1.56 | | GROUND_INST: instantiating (1) with all_12_4, all_12_2, all_30_0,
% 6.03/1.56 | | simplifying with (7), (10), (22), (26) gives:
% 6.03/1.56 | | (27) all_30_0 = 0
% 6.03/1.56 | |
% 6.03/1.56 | | REDUCE: (25), (27) imply:
% 6.03/1.56 | | (28) $false
% 6.03/1.56 | |
% 6.03/1.56 | | CLOSE: (28) is inconsistent.
% 6.03/1.56 | |
% 6.03/1.56 | Case 2:
% 6.03/1.56 | |
% 6.03/1.56 | | (29) ~ (all_12_0 = all_12_2) & ~ (all_12_3 = all_12_4)
% 6.03/1.56 | |
% 6.03/1.56 | | ALPHA: (29) implies:
% 6.03/1.56 | | (30) ~ (all_12_3 = all_12_4)
% 6.03/1.56 | | (31) ~ (all_12_0 = all_12_2)
% 6.03/1.56 | |
% 6.03/1.56 | | BETA: splitting (14) gives:
% 6.03/1.56 | |
% 6.03/1.56 | | Case 1:
% 6.03/1.56 | | |
% 6.03/1.56 | | | (32) in(all_12_4, all_12_1) = 0
% 6.03/1.56 | | |
% 6.03/1.56 | | | GROUND_INST: instantiating (2) with all_12_3, all_12_1, all_12_4,
% 6.03/1.56 | | | simplifying with (7), (8), (9), (11), (32) gives:
% 6.03/1.56 | | | (33) all_12_3 = all_12_4
% 6.03/1.56 | | |
% 6.03/1.56 | | | REDUCE: (30), (33) imply:
% 6.03/1.56 | | | (34) $false
% 6.03/1.56 | | |
% 6.03/1.56 | | | CLOSE: (34) is inconsistent.
% 6.03/1.56 | | |
% 6.03/1.56 | | Case 2:
% 6.03/1.56 | | |
% 6.03/1.56 | | | (35) all_12_0 = all_12_2
% 6.03/1.56 | | |
% 6.03/1.56 | | | REDUCE: (31), (35) imply:
% 6.03/1.56 | | | (36) $false
% 6.03/1.56 | | |
% 6.03/1.56 | | | CLOSE: (36) is inconsistent.
% 6.03/1.56 | | |
% 6.03/1.56 | | End of split
% 6.03/1.56 | |
% 6.03/1.57 | End of split
% 6.03/1.57 |
% 6.03/1.57 End of proof
% 6.03/1.57 % SZS output end Proof for theBenchmark
% 6.03/1.57
% 6.03/1.57 966ms
%------------------------------------------------------------------------------