TSTP Solution File: SEU158+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU158+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n020.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 17:42:52 EDT 2023
% Result : Theorem 3.32s 1.25s
% Output : Proof 4.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU158+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Wed Aug 23 14:34:30 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.63 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 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 1.92/0.97 Prover 1: Preprocessing ...
% 1.92/0.97 Prover 4: Preprocessing ...
% 2.07/1.02 Prover 6: Preprocessing ...
% 2.07/1.02 Prover 5: Preprocessing ...
% 2.07/1.02 Prover 2: Preprocessing ...
% 2.07/1.02 Prover 0: Preprocessing ...
% 2.07/1.02 Prover 3: Preprocessing ...
% 2.98/1.12 Prover 1: Warning: ignoring some quantifiers
% 2.98/1.13 Prover 3: Warning: ignoring some quantifiers
% 2.98/1.13 Prover 1: Constructing countermodel ...
% 2.98/1.14 Prover 5: Proving ...
% 2.98/1.14 Prover 4: Constructing countermodel ...
% 2.98/1.14 Prover 6: Proving ...
% 2.98/1.14 Prover 2: Proving ...
% 2.98/1.14 Prover 0: Proving ...
% 2.98/1.14 Prover 3: Constructing countermodel ...
% 3.32/1.24 Prover 3: proved (607ms)
% 3.32/1.24
% 3.32/1.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.32/1.25
% 3.32/1.25 Prover 0: stopped
% 3.32/1.25 Prover 6: stopped
% 3.32/1.25 Prover 2: stopped
% 3.32/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.32/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.32/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.32/1.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.32/1.25 Prover 5: proved (622ms)
% 3.32/1.25
% 3.32/1.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.32/1.25
% 3.89/1.26 Prover 7: Preprocessing ...
% 3.89/1.26 Prover 8: Preprocessing ...
% 3.89/1.27 Prover 10: Preprocessing ...
% 3.89/1.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.89/1.27 Prover 11: Preprocessing ...
% 4.04/1.30 Prover 13: Preprocessing ...
% 4.04/1.30 Prover 7: Warning: ignoring some quantifiers
% 4.04/1.30 Prover 7: Constructing countermodel ...
% 4.04/1.31 Prover 10: Warning: ignoring some quantifiers
% 4.04/1.31 Prover 10: Constructing countermodel ...
% 4.04/1.31 Prover 8: Warning: ignoring some quantifiers
% 4.32/1.32 Prover 1: Found proof (size 22)
% 4.32/1.32 Prover 1: proved (694ms)
% 4.32/1.32 Prover 10: stopped
% 4.32/1.32 Prover 4: stopped
% 4.32/1.32 Prover 7: stopped
% 4.32/1.33 Prover 8: Constructing countermodel ...
% 4.32/1.33 Prover 8: stopped
% 4.32/1.34 Prover 13: Warning: ignoring some quantifiers
% 4.44/1.34 Prover 13: Constructing countermodel ...
% 4.44/1.34 Prover 11: Constructing countermodel ...
% 4.44/1.34 Prover 13: stopped
% 4.44/1.34 Prover 11: stopped
% 4.44/1.34
% 4.44/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.44/1.35
% 4.44/1.35 % SZS output start Proof for theBenchmark
% 4.44/1.35 Assumptions after simplification:
% 4.44/1.35 ---------------------------------
% 4.44/1.35
% 4.44/1.35 (l2_zfmisc_1)
% 4.44/1.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.44/1.39 (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 4.44/1.39 [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] :
% 4.44/1.39 ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | ~ $i(v1) |
% 4.44/1.39 ~ $i(v0) | in(v0, v1) = 0)
% 4.44/1.39
% 4.44/1.39 (t37_zfmisc_1)
% 4.44/1.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 4.44/1.39 (singleton(v0) = v2 & in(v0, v1) = v4 & subset(v2, v1) = v3 & $i(v2) & $i(v1)
% 4.44/1.39 & $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))
% 4.44/1.39
% 4.44/1.39 (function-axioms)
% 4.44/1.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.44/1.39 [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 4.44/1.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 4.44/1.39 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 4.44/1.39 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 4.44/1.39 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 4.44/1.39 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 4.44/1.39 (empty(v2) = v0))
% 4.44/1.39
% 4.44/1.39 Further assumptions not needed in the proof:
% 4.44/1.39 --------------------------------------------
% 4.44/1.39 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 4.44/1.39
% 4.44/1.39 Those formulas are unsatisfiable:
% 4.44/1.39 ---------------------------------
% 4.44/1.39
% 4.44/1.39 Begin of proof
% 4.44/1.39 |
% 4.44/1.40 | ALPHA: (l2_zfmisc_1) implies:
% 4.44/1.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~
% 4.44/1.40 | (subset(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0) | in(v0, v1) = 0)
% 4.44/1.40 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.44/1.40 | (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~
% 4.44/1.40 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 4.44/1.40 |
% 4.44/1.40 | ALPHA: (function-axioms) implies:
% 4.44/1.40 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.44/1.40 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.44/1.40 |
% 4.44/1.40 | DELTA: instantiating (t37_zfmisc_1) with fresh symbols all_11_0, all_11_1,
% 4.44/1.40 | all_11_2, all_11_3, all_11_4 gives:
% 4.44/1.40 | (4) singleton(all_11_4) = all_11_2 & in(all_11_4, all_11_3) = all_11_0 &
% 4.44/1.40 | subset(all_11_2, all_11_3) = all_11_1 & $i(all_11_2) & $i(all_11_3) &
% 4.44/1.40 | $i(all_11_4) & ((all_11_0 = 0 & ~ (all_11_1 = 0)) | (all_11_1 = 0 & ~
% 4.44/1.40 | (all_11_0 = 0)))
% 4.44/1.40 |
% 4.44/1.40 | ALPHA: (4) implies:
% 4.44/1.40 | (5) $i(all_11_4)
% 4.44/1.40 | (6) $i(all_11_3)
% 4.44/1.40 | (7) subset(all_11_2, all_11_3) = all_11_1
% 4.44/1.41 | (8) in(all_11_4, all_11_3) = all_11_0
% 4.44/1.41 | (9) singleton(all_11_4) = all_11_2
% 4.44/1.41 | (10) (all_11_0 = 0 & ~ (all_11_1 = 0)) | (all_11_1 = 0 & ~ (all_11_0 =
% 4.44/1.41 | 0))
% 4.44/1.41 |
% 4.44/1.41 | GROUND_INST: instantiating (2) with all_11_4, all_11_3, all_11_2, all_11_1,
% 4.44/1.41 | simplifying with (5), (6), (7), (9) gives:
% 4.44/1.41 | (11) all_11_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_11_4, all_11_3) =
% 4.44/1.41 | v0)
% 4.44/1.41 |
% 4.44/1.41 | BETA: splitting (10) gives:
% 4.44/1.41 |
% 4.44/1.41 | Case 1:
% 4.44/1.41 | |
% 4.44/1.41 | | (12) all_11_0 = 0 & ~ (all_11_1 = 0)
% 4.44/1.41 | |
% 4.44/1.41 | | ALPHA: (12) implies:
% 4.44/1.41 | | (13) all_11_0 = 0
% 4.44/1.41 | | (14) ~ (all_11_1 = 0)
% 4.44/1.41 | |
% 4.44/1.41 | | REDUCE: (8), (13) imply:
% 4.44/1.41 | | (15) in(all_11_4, all_11_3) = 0
% 4.44/1.41 | |
% 4.44/1.41 | | BETA: splitting (11) gives:
% 4.44/1.41 | |
% 4.44/1.41 | | Case 1:
% 4.44/1.41 | | |
% 4.44/1.41 | | | (16) all_11_1 = 0
% 4.44/1.41 | | |
% 4.44/1.41 | | | REDUCE: (14), (16) imply:
% 4.44/1.41 | | | (17) $false
% 4.44/1.41 | | |
% 4.44/1.41 | | | CLOSE: (17) is inconsistent.
% 4.44/1.41 | | |
% 4.44/1.41 | | Case 2:
% 4.44/1.41 | | |
% 4.44/1.41 | | | (18) ? [v0: int] : ( ~ (v0 = 0) & in(all_11_4, all_11_3) = v0)
% 4.44/1.41 | | |
% 4.44/1.41 | | | DELTA: instantiating (18) with fresh symbol all_24_0 gives:
% 4.44/1.41 | | | (19) ~ (all_24_0 = 0) & in(all_11_4, all_11_3) = all_24_0
% 4.44/1.41 | | |
% 4.44/1.41 | | | ALPHA: (19) implies:
% 4.44/1.41 | | | (20) ~ (all_24_0 = 0)
% 4.44/1.41 | | | (21) in(all_11_4, all_11_3) = all_24_0
% 4.44/1.41 | | |
% 4.44/1.41 | | | GROUND_INST: instantiating (3) with 0, all_24_0, all_11_3, all_11_4,
% 4.44/1.41 | | | simplifying with (15), (21) gives:
% 4.44/1.41 | | | (22) all_24_0 = 0
% 4.44/1.41 | | |
% 4.44/1.41 | | | REDUCE: (20), (22) imply:
% 4.44/1.41 | | | (23) $false
% 4.44/1.41 | | |
% 4.44/1.41 | | | CLOSE: (23) is inconsistent.
% 4.44/1.41 | | |
% 4.44/1.41 | | End of split
% 4.44/1.41 | |
% 4.44/1.41 | Case 2:
% 4.44/1.41 | |
% 4.44/1.42 | | (24) all_11_1 = 0 & ~ (all_11_0 = 0)
% 4.44/1.42 | |
% 4.44/1.42 | | ALPHA: (24) implies:
% 4.44/1.42 | | (25) all_11_1 = 0
% 4.44/1.42 | | (26) ~ (all_11_0 = 0)
% 4.44/1.42 | |
% 4.44/1.42 | | REDUCE: (7), (25) imply:
% 4.44/1.42 | | (27) subset(all_11_2, all_11_3) = 0
% 4.44/1.42 | |
% 4.44/1.42 | | GROUND_INST: instantiating (1) with all_11_4, all_11_3, all_11_2,
% 4.44/1.42 | | simplifying with (5), (6), (9), (27) gives:
% 4.44/1.42 | | (28) in(all_11_4, all_11_3) = 0
% 4.44/1.42 | |
% 4.44/1.42 | | GROUND_INST: instantiating (3) with all_11_0, 0, all_11_3, all_11_4,
% 4.44/1.42 | | simplifying with (8), (28) gives:
% 4.44/1.42 | | (29) all_11_0 = 0
% 4.44/1.42 | |
% 4.44/1.42 | | REDUCE: (26), (29) imply:
% 4.44/1.42 | | (30) $false
% 4.44/1.42 | |
% 4.44/1.42 | | CLOSE: (30) is inconsistent.
% 4.44/1.42 | |
% 4.44/1.42 | End of split
% 4.44/1.42 |
% 4.44/1.42 End of proof
% 4.44/1.42 % SZS output end Proof for theBenchmark
% 4.44/1.42
% 4.44/1.42 813ms
%------------------------------------------------------------------------------