TSTP Solution File: SET923+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET923+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 : n022.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 3.64s 1.28s
% Output : Proof 4.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET923+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 16:18:25 EDT 2023
% 0.13/0.35 % 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.61/0.95 Prover 4: Preprocessing ...
% 1.61/0.95 Prover 1: Preprocessing ...
% 2.32/1.01 Prover 6: Preprocessing ...
% 2.32/1.01 Prover 2: Preprocessing ...
% 2.32/1.01 Prover 5: Preprocessing ...
% 2.32/1.01 Prover 0: Preprocessing ...
% 2.32/1.01 Prover 3: Preprocessing ...
% 3.00/1.13 Prover 3: Warning: ignoring some quantifiers
% 3.00/1.13 Prover 1: Warning: ignoring some quantifiers
% 3.00/1.16 Prover 3: Constructing countermodel ...
% 3.00/1.16 Prover 1: Constructing countermodel ...
% 3.00/1.16 Prover 4: Constructing countermodel ...
% 3.00/1.16 Prover 6: Proving ...
% 3.00/1.17 Prover 2: Proving ...
% 3.00/1.17 Prover 0: Proving ...
% 3.00/1.18 Prover 5: Proving ...
% 3.64/1.28 Prover 3: proved (637ms)
% 3.64/1.28
% 3.64/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.64/1.28
% 3.64/1.28 Prover 2: proved (647ms)
% 3.64/1.28 Prover 6: proved (640ms)
% 3.64/1.28
% 3.64/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.64/1.28
% 3.64/1.28
% 3.64/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.64/1.28
% 4.29/1.29 Prover 5: proved (640ms)
% 4.29/1.29 Prover 0: proved (648ms)
% 4.29/1.29
% 4.29/1.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.29/1.29
% 4.33/1.30
% 4.33/1.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.33/1.30
% 4.33/1.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.33/1.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.33/1.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.33/1.30 Prover 7: Preprocessing ...
% 4.33/1.30 Prover 8: Preprocessing ...
% 4.33/1.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.33/1.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.33/1.30 Prover 10: Preprocessing ...
% 4.33/1.31 Prover 4: Found proof (size 12)
% 4.33/1.31 Prover 1: Found proof (size 12)
% 4.33/1.31 Prover 1: proved (676ms)
% 4.33/1.31 Prover 4: proved (675ms)
% 4.33/1.32 Prover 13: Preprocessing ...
% 4.33/1.33 Prover 11: Preprocessing ...
% 4.33/1.35 Prover 7: Warning: ignoring some quantifiers
% 4.33/1.35 Prover 7: Constructing countermodel ...
% 4.33/1.35 Prover 13: stopped
% 4.33/1.35 Prover 11: stopped
% 4.33/1.36 Prover 7: stopped
% 4.33/1.36 Prover 10: Warning: ignoring some quantifiers
% 4.33/1.36 Prover 8: Warning: ignoring some quantifiers
% 4.33/1.36 Prover 10: Constructing countermodel ...
% 4.33/1.37 Prover 10: stopped
% 4.33/1.37 Prover 8: Constructing countermodel ...
% 4.33/1.37 Prover 8: stopped
% 4.33/1.37
% 4.33/1.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.33/1.37
% 4.33/1.38 % SZS output start Proof for theBenchmark
% 4.33/1.38 Assumptions after simplification:
% 4.33/1.38 ---------------------------------
% 4.33/1.38
% 4.33/1.38 (l4_zfmisc_1)
% 4.33/1.41 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 4.33/1.41 0 | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = v3) | ~ $i(v1) | ~
% 4.33/1.41 $i(v0) | ( ~ (v2 = v0) & ~ (v0 = empty_set))) & ! [v0: $i] : ! [v1: $i] :
% 4.33/1.41 ! [v2: $i] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~
% 4.33/1.41 (subset(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0))
% 4.33/1.41
% 4.33/1.41 (t37_xboole_1)
% 4.74/1.41 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 4.74/1.41 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~
% 4.74/1.41 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 4.74/1.41 (set_difference(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | subset(v0,
% 4.74/1.41 v1) = 0)
% 4.74/1.41
% 4.74/1.41 (t66_zfmisc_1)
% 4.96/1.42 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v0) & ~
% 4.96/1.42 (v0 = empty_set) & set_difference(v0, v2) = empty_set & singleton(v1) = v2 &
% 4.96/1.42 $i(v2) & $i(v1) & $i(v0))
% 4.96/1.42
% 4.96/1.42 Further assumptions not needed in the proof:
% 4.96/1.42 --------------------------------------------
% 4.96/1.42 fc1_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 4.96/1.42
% 4.96/1.42 Those formulas are unsatisfiable:
% 4.96/1.42 ---------------------------------
% 4.96/1.42
% 4.96/1.42 Begin of proof
% 4.96/1.42 |
% 4.96/1.42 | ALPHA: (l4_zfmisc_1) implies:
% 4.96/1.42 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | v0 = empty_set |
% 4.96/1.42 | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0) | ~ $i(v1) | ~
% 4.96/1.42 | $i(v0))
% 4.96/1.42 |
% 4.96/1.42 | ALPHA: (t37_xboole_1) implies:
% 4.96/1.42 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) |
% 4.96/1.42 | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = 0)
% 4.96/1.42 |
% 4.96/1.42 | ALPHA: (t66_zfmisc_1) implies:
% 4.96/1.42 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v0) & ~ (v0 =
% 4.96/1.42 | empty_set) & set_difference(v0, v2) = empty_set & singleton(v1) =
% 4.96/1.42 | v2 & $i(v2) & $i(v1) & $i(v0))
% 4.96/1.42 |
% 4.96/1.43 | DELTA: instantiating (3) with fresh symbols all_12_0, all_12_1, all_12_2
% 4.96/1.43 | gives:
% 4.96/1.43 | (4) ~ (all_12_0 = all_12_2) & ~ (all_12_2 = empty_set) &
% 4.96/1.43 | set_difference(all_12_2, all_12_0) = empty_set & singleton(all_12_1) =
% 4.96/1.43 | all_12_0 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2)
% 4.96/1.43 |
% 4.96/1.43 | ALPHA: (4) implies:
% 4.96/1.43 | (5) ~ (all_12_2 = empty_set)
% 4.96/1.43 | (6) ~ (all_12_0 = all_12_2)
% 4.96/1.43 | (7) $i(all_12_2)
% 4.96/1.43 | (8) $i(all_12_1)
% 4.96/1.43 | (9) $i(all_12_0)
% 4.96/1.43 | (10) singleton(all_12_1) = all_12_0
% 4.96/1.43 | (11) set_difference(all_12_2, all_12_0) = empty_set
% 4.96/1.43 |
% 4.96/1.43 | GROUND_INST: instantiating (2) with all_12_2, all_12_0, simplifying with (7),
% 4.96/1.43 | (9), (11) gives:
% 4.96/1.43 | (12) subset(all_12_2, all_12_0) = 0
% 4.96/1.43 |
% 4.96/1.43 | GROUND_INST: instantiating (1) with all_12_2, all_12_1, all_12_0, simplifying
% 4.96/1.43 | with (7), (8), (10), (12) gives:
% 4.96/1.43 | (13) all_12_0 = all_12_2 | all_12_2 = empty_set
% 4.96/1.43 |
% 4.96/1.43 | BETA: splitting (13) gives:
% 4.96/1.43 |
% 4.96/1.43 | Case 1:
% 4.96/1.43 | |
% 4.96/1.43 | | (14) all_12_2 = empty_set
% 4.96/1.43 | |
% 4.96/1.43 | | REDUCE: (5), (14) imply:
% 4.96/1.43 | | (15) $false
% 4.96/1.44 | |
% 4.96/1.44 | | CLOSE: (15) is inconsistent.
% 4.96/1.44 | |
% 4.96/1.44 | Case 2:
% 4.96/1.44 | |
% 4.96/1.44 | | (16) all_12_0 = all_12_2
% 4.96/1.44 | |
% 4.96/1.44 | | REDUCE: (6), (16) imply:
% 4.96/1.44 | | (17) $false
% 4.96/1.44 | |
% 4.96/1.44 | | CLOSE: (17) is inconsistent.
% 4.96/1.44 | |
% 4.96/1.44 | End of split
% 4.96/1.44 |
% 4.96/1.44 End of proof
% 4.96/1.44 % SZS output end Proof for theBenchmark
% 4.96/1.44
% 4.96/1.44 825ms
%------------------------------------------------------------------------------