TSTP Solution File: SEU158+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU158+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n028.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 3.23s 1.20s
% Output : Proof 4.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU158+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n028.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Wed Aug 23 15:59:04 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.77/0.95 Prover 1: Preprocessing ...
% 1.77/0.95 Prover 4: Preprocessing ...
% 2.19/1.00 Prover 3: Preprocessing ...
% 2.19/1.00 Prover 5: Preprocessing ...
% 2.19/1.00 Prover 2: Preprocessing ...
% 2.19/1.00 Prover 6: Preprocessing ...
% 2.19/1.00 Prover 0: Preprocessing ...
% 2.89/1.08 Prover 1: Warning: ignoring some quantifiers
% 2.89/1.08 Prover 3: Warning: ignoring some quantifiers
% 2.89/1.09 Prover 2: Proving ...
% 2.89/1.09 Prover 6: Proving ...
% 2.89/1.09 Prover 5: Proving ...
% 2.89/1.10 Prover 3: Constructing countermodel ...
% 2.89/1.10 Prover 4: Constructing countermodel ...
% 2.89/1.10 Prover 1: Constructing countermodel ...
% 3.12/1.13 Prover 0: Proving ...
% 3.23/1.20 Prover 0: proved (566ms)
% 3.23/1.20
% 3.23/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.23/1.20
% 3.23/1.20 Prover 2: proved (565ms)
% 3.23/1.20
% 3.23/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.23/1.20
% 3.23/1.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.23/1.20 Prover 5: stopped
% 3.23/1.20 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.23/1.20 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.23/1.20 Prover 6: stopped
% 3.23/1.21 Prover 7: Preprocessing ...
% 3.23/1.21 Prover 8: Preprocessing ...
% 3.79/1.21 Prover 10: Preprocessing ...
% 3.79/1.21 Prover 3: stopped
% 3.79/1.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.79/1.23 Prover 7: Warning: ignoring some quantifiers
% 3.79/1.23 Prover 10: Warning: ignoring some quantifiers
% 3.79/1.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.79/1.23 Prover 10: Constructing countermodel ...
% 3.79/1.23 Prover 11: Preprocessing ...
% 3.79/1.24 Prover 7: Constructing countermodel ...
% 3.79/1.25 Prover 1: Found proof (size 22)
% 3.79/1.25 Prover 1: proved (623ms)
% 3.79/1.25 Prover 7: stopped
% 3.79/1.26 Prover 10: stopped
% 3.79/1.26 Prover 13: Preprocessing ...
% 3.79/1.26 Prover 8: Warning: ignoring some quantifiers
% 3.79/1.26 Prover 4: stopped
% 3.79/1.26 Prover 8: Constructing countermodel ...
% 3.79/1.27 Prover 8: stopped
% 4.25/1.28 Prover 13: Warning: ignoring some quantifiers
% 4.25/1.28 Prover 11: Constructing countermodel ...
% 4.25/1.28 Prover 13: Constructing countermodel ...
% 4.25/1.29 Prover 11: stopped
% 4.25/1.29 Prover 13: stopped
% 4.25/1.29
% 4.25/1.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.25/1.29
% 4.25/1.29 % SZS output start Proof for theBenchmark
% 4.25/1.30 Assumptions after simplification:
% 4.25/1.30 ---------------------------------
% 4.25/1.30
% 4.25/1.30 (l2_zfmisc_1)
% 4.25/1.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.25/1.32 (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 4.25/1.32 [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] :
% 4.25/1.33 ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | ~ $i(v1) |
% 4.25/1.33 ~ $i(v0) | in(v0, v1) = 0)
% 4.25/1.33
% 4.25/1.33 (t37_zfmisc_1)
% 4.25/1.33 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 4.25/1.33 (singleton(v0) = v2 & in(v0, v1) = v4 & subset(v2, v1) = v3 & $i(v2) & $i(v1)
% 4.25/1.33 & $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))
% 4.25/1.33
% 4.25/1.33 (function-axioms)
% 4.25/1.33 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.25/1.33 [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 4.25/1.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 4.25/1.33 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 4.25/1.33 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 4.25/1.33 (singleton(v2) = v0))
% 4.25/1.33
% 4.25/1.33 Further assumptions not needed in the proof:
% 4.25/1.33 --------------------------------------------
% 4.25/1.33 antisymmetry_r2_hidden, dt_k1_tarski, reflexivity_r1_tarski
% 4.25/1.33
% 4.25/1.33 Those formulas are unsatisfiable:
% 4.25/1.33 ---------------------------------
% 4.25/1.33
% 4.25/1.33 Begin of proof
% 4.25/1.33 |
% 4.25/1.33 | ALPHA: (l2_zfmisc_1) implies:
% 4.25/1.33 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~
% 4.25/1.33 | (subset(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0) | in(v0, v1) = 0)
% 4.25/1.34 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.25/1.34 | (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~
% 4.25/1.34 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 4.25/1.34 |
% 4.25/1.34 | ALPHA: (function-axioms) implies:
% 4.25/1.34 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.25/1.34 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.25/1.34 |
% 4.25/1.34 | DELTA: instantiating (t37_zfmisc_1) with fresh symbols all_7_0, all_7_1,
% 4.25/1.34 | all_7_2, all_7_3, all_7_4 gives:
% 4.25/1.34 | (4) singleton(all_7_4) = all_7_2 & in(all_7_4, all_7_3) = all_7_0 &
% 4.25/1.34 | subset(all_7_2, all_7_3) = all_7_1 & $i(all_7_2) & $i(all_7_3) &
% 4.25/1.34 | $i(all_7_4) & ((all_7_0 = 0 & ~ (all_7_1 = 0)) | (all_7_1 = 0 & ~
% 4.25/1.34 | (all_7_0 = 0)))
% 4.25/1.34 |
% 4.25/1.34 | ALPHA: (4) implies:
% 4.25/1.34 | (5) $i(all_7_4)
% 4.25/1.34 | (6) $i(all_7_3)
% 4.25/1.34 | (7) subset(all_7_2, all_7_3) = all_7_1
% 4.25/1.34 | (8) in(all_7_4, all_7_3) = all_7_0
% 4.25/1.34 | (9) singleton(all_7_4) = all_7_2
% 4.25/1.34 | (10) (all_7_0 = 0 & ~ (all_7_1 = 0)) | (all_7_1 = 0 & ~ (all_7_0 = 0))
% 4.25/1.34 |
% 4.25/1.34 | GROUND_INST: instantiating (2) with all_7_4, all_7_3, all_7_2, all_7_1,
% 4.25/1.34 | simplifying with (5), (6), (7), (9) gives:
% 4.25/1.34 | (11) all_7_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_7_4, all_7_3) = v0)
% 4.25/1.34 |
% 4.25/1.34 | BETA: splitting (10) gives:
% 4.25/1.34 |
% 4.25/1.35 | Case 1:
% 4.25/1.35 | |
% 4.25/1.35 | | (12) all_7_0 = 0 & ~ (all_7_1 = 0)
% 4.25/1.35 | |
% 4.25/1.35 | | ALPHA: (12) implies:
% 4.25/1.35 | | (13) all_7_0 = 0
% 4.25/1.35 | | (14) ~ (all_7_1 = 0)
% 4.25/1.35 | |
% 4.25/1.35 | | REDUCE: (8), (13) imply:
% 4.25/1.35 | | (15) in(all_7_4, all_7_3) = 0
% 4.25/1.35 | |
% 4.25/1.35 | | BETA: splitting (11) gives:
% 4.25/1.35 | |
% 4.25/1.35 | | Case 1:
% 4.25/1.35 | | |
% 4.25/1.35 | | | (16) all_7_1 = 0
% 4.25/1.35 | | |
% 4.25/1.35 | | | REDUCE: (14), (16) imply:
% 4.25/1.35 | | | (17) $false
% 4.25/1.35 | | |
% 4.25/1.35 | | | CLOSE: (17) is inconsistent.
% 4.25/1.35 | | |
% 4.25/1.35 | | Case 2:
% 4.25/1.35 | | |
% 4.25/1.35 | | | (18) ? [v0: int] : ( ~ (v0 = 0) & in(all_7_4, all_7_3) = v0)
% 4.25/1.35 | | |
% 4.25/1.35 | | | DELTA: instantiating (18) with fresh symbol all_20_0 gives:
% 4.25/1.35 | | | (19) ~ (all_20_0 = 0) & in(all_7_4, all_7_3) = all_20_0
% 4.25/1.35 | | |
% 4.25/1.35 | | | ALPHA: (19) implies:
% 4.25/1.35 | | | (20) ~ (all_20_0 = 0)
% 4.25/1.35 | | | (21) in(all_7_4, all_7_3) = all_20_0
% 4.25/1.35 | | |
% 4.25/1.35 | | | GROUND_INST: instantiating (3) with 0, all_20_0, all_7_3, all_7_4,
% 4.25/1.35 | | | simplifying with (15), (21) gives:
% 4.25/1.35 | | | (22) all_20_0 = 0
% 4.25/1.35 | | |
% 4.25/1.35 | | | REDUCE: (20), (22) imply:
% 4.25/1.35 | | | (23) $false
% 4.25/1.35 | | |
% 4.25/1.35 | | | CLOSE: (23) is inconsistent.
% 4.25/1.35 | | |
% 4.25/1.35 | | End of split
% 4.25/1.35 | |
% 4.25/1.35 | Case 2:
% 4.25/1.35 | |
% 4.25/1.35 | | (24) all_7_1 = 0 & ~ (all_7_0 = 0)
% 4.25/1.35 | |
% 4.25/1.35 | | ALPHA: (24) implies:
% 4.25/1.35 | | (25) all_7_1 = 0
% 4.25/1.35 | | (26) ~ (all_7_0 = 0)
% 4.25/1.35 | |
% 4.25/1.35 | | REDUCE: (7), (25) imply:
% 4.25/1.35 | | (27) subset(all_7_2, all_7_3) = 0
% 4.25/1.35 | |
% 4.25/1.35 | | GROUND_INST: instantiating (1) with all_7_4, all_7_3, all_7_2, simplifying
% 4.25/1.35 | | with (5), (6), (9), (27) gives:
% 4.25/1.35 | | (28) in(all_7_4, all_7_3) = 0
% 4.25/1.35 | |
% 4.25/1.35 | | GROUND_INST: instantiating (3) with all_7_0, 0, all_7_3, all_7_4,
% 4.25/1.35 | | simplifying with (8), (28) gives:
% 4.25/1.35 | | (29) all_7_0 = 0
% 4.25/1.35 | |
% 4.25/1.35 | | REDUCE: (26), (29) imply:
% 4.25/1.35 | | (30) $false
% 4.25/1.35 | |
% 4.25/1.35 | | CLOSE: (30) is inconsistent.
% 4.25/1.35 | |
% 4.25/1.35 | End of split
% 4.25/1.35 |
% 4.25/1.35 End of proof
% 4.25/1.35 % SZS output end Proof for theBenchmark
% 4.25/1.35
% 4.25/1.35 743ms
%------------------------------------------------------------------------------