TSTP Solution File: SET987+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET987+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 : n021.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 15:27:18 EDT 2023
% Result : Theorem 4.75s 1.38s
% Output : Proof 5.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET987+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:10:11 EDT 2023
% 0.13/0.34 % 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 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 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
% 2.03/0.99 Prover 1: Preprocessing ...
% 2.03/0.99 Prover 4: Preprocessing ...
% 2.03/1.04 Prover 3: Preprocessing ...
% 2.03/1.04 Prover 2: Preprocessing ...
% 2.03/1.04 Prover 0: Preprocessing ...
% 2.03/1.04 Prover 6: Preprocessing ...
% 2.03/1.04 Prover 5: Preprocessing ...
% 3.62/1.22 Prover 1: Warning: ignoring some quantifiers
% 3.62/1.23 Prover 3: Warning: ignoring some quantifiers
% 3.62/1.24 Prover 1: Constructing countermodel ...
% 3.62/1.24 Prover 3: Constructing countermodel ...
% 3.62/1.24 Prover 6: Proving ...
% 3.62/1.24 Prover 5: Proving ...
% 3.62/1.24 Prover 4: Constructing countermodel ...
% 3.62/1.26 Prover 0: Proving ...
% 3.62/1.26 Prover 2: Proving ...
% 4.75/1.38 Prover 0: proved (757ms)
% 4.75/1.38
% 4.75/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.75/1.38
% 4.75/1.39 Prover 6: stopped
% 4.75/1.40 Prover 5: stopped
% 4.75/1.40 Prover 3: stopped
% 4.75/1.41 Prover 2: stopped
% 4.75/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.75/1.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.75/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.75/1.41 Prover 7: Preprocessing ...
% 4.75/1.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.75/1.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.75/1.42 Prover 10: Preprocessing ...
% 4.75/1.43 Prover 8: Preprocessing ...
% 4.75/1.44 Prover 11: Preprocessing ...
% 4.75/1.45 Prover 13: Preprocessing ...
% 4.75/1.47 Prover 10: Constructing countermodel ...
% 4.75/1.47 Prover 7: Constructing countermodel ...
% 4.75/1.47 Prover 1: Found proof (size 13)
% 4.75/1.47 Prover 4: Found proof (size 21)
% 4.75/1.47 Prover 1: proved (849ms)
% 4.75/1.47 Prover 4: proved (844ms)
% 4.75/1.47 Prover 10: stopped
% 4.75/1.48 Prover 7: stopped
% 4.75/1.48 Prover 13: stopped
% 4.75/1.50 Prover 8: Warning: ignoring some quantifiers
% 4.75/1.51 Prover 8: Constructing countermodel ...
% 4.75/1.51 Prover 11: Constructing countermodel ...
% 4.75/1.51 Prover 8: stopped
% 5.05/1.51 Prover 11: stopped
% 5.05/1.51
% 5.05/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.05/1.51
% 5.05/1.52 % SZS output start Proof for theBenchmark
% 5.05/1.52 Assumptions after simplification:
% 5.05/1.52 ---------------------------------
% 5.05/1.52
% 5.05/1.52 (t141_zfmisc_1)
% 5.88/1.55 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 5.88/1.55 $i] : ( ~ (v5 = v1) & ~ (v2 = 0) & singleton(v0) = v3 & set_difference(v4,
% 5.88/1.55 v3) = v5 & set_union2(v1, v3) = v4 & in(v0, v1) = v2 & $i(v5) & $i(v4) &
% 5.88/1.55 $i(v3) & $i(v1) & $i(v0))
% 5.88/1.55
% 5.88/1.55 (t40_xboole_1)
% 5.91/1.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 5.91/1.55 (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | ~ $i(v1) |
% 5.91/1.55 ~ $i(v0) | (set_difference(v0, v1) = v3 & $i(v3)))
% 5.91/1.55
% 5.91/1.55 (t65_zfmisc_1)
% 5.91/1.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 5.91/1.56 (singleton(v1) = v2) | ~ (set_difference(v0, v2) = v3) | ~ $i(v1) | ~
% 5.91/1.56 $i(v0) | in(v1, v0) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 5.91/1.56 (singleton(v1) = v2) | ~ (set_difference(v0, v2) = v0) | ~ $i(v1) | ~
% 5.91/1.56 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 5.91/1.56
% 5.91/1.56 (function-axioms)
% 5.91/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.91/1.56 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 5.91/1.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.91/1.56 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0:
% 5.91/1.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 5.91/1.56 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 5.91/1.56 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 5.91/1.56 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 5.91/1.56 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 5.91/1.56 (empty(v2) = v0))
% 5.91/1.56
% 5.91/1.56 Further assumptions not needed in the proof:
% 5.91/1.56 --------------------------------------------
% 5.91/1.56 antisymmetry_r2_hidden, commutativity_k2_xboole_0, fc2_xboole_0, fc3_xboole_0,
% 5.91/1.56 idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0
% 5.91/1.56
% 5.91/1.56 Those formulas are unsatisfiable:
% 5.91/1.56 ---------------------------------
% 5.91/1.56
% 5.91/1.56 Begin of proof
% 5.91/1.56 |
% 5.91/1.56 | ALPHA: (t65_zfmisc_1) implies:
% 5.91/1.56 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 5.91/1.56 | (singleton(v1) = v2) | ~ (set_difference(v0, v2) = v3) | ~ $i(v1) |
% 5.91/1.56 | ~ $i(v0) | in(v1, v0) = 0)
% 5.91/1.56 |
% 5.91/1.56 | ALPHA: (function-axioms) implies:
% 5.91/1.57 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.91/1.57 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 5.91/1.57 |
% 5.91/1.57 | DELTA: instantiating (t141_zfmisc_1) with fresh symbols all_15_0, all_15_1,
% 5.91/1.57 | all_15_2, all_15_3, all_15_4, all_15_5 gives:
% 5.91/1.57 | (3) ~ (all_15_0 = all_15_4) & ~ (all_15_3 = 0) & singleton(all_15_5) =
% 5.91/1.57 | all_15_2 & set_difference(all_15_1, all_15_2) = all_15_0 &
% 5.91/1.57 | set_union2(all_15_4, all_15_2) = all_15_1 & in(all_15_5, all_15_4) =
% 5.91/1.57 | all_15_3 & $i(all_15_0) & $i(all_15_1) & $i(all_15_2) & $i(all_15_4) &
% 5.91/1.57 | $i(all_15_5)
% 5.91/1.57 |
% 5.91/1.57 | ALPHA: (3) implies:
% 5.91/1.57 | (4) ~ (all_15_3 = 0)
% 5.91/1.57 | (5) ~ (all_15_0 = all_15_4)
% 5.91/1.57 | (6) $i(all_15_5)
% 5.91/1.57 | (7) $i(all_15_4)
% 5.91/1.57 | (8) $i(all_15_2)
% 5.91/1.57 | (9) in(all_15_5, all_15_4) = all_15_3
% 5.91/1.57 | (10) set_union2(all_15_4, all_15_2) = all_15_1
% 5.91/1.57 | (11) set_difference(all_15_1, all_15_2) = all_15_0
% 5.91/1.57 | (12) singleton(all_15_5) = all_15_2
% 5.91/1.57 |
% 5.91/1.57 | GROUND_INST: instantiating (t40_xboole_1) with all_15_4, all_15_2, all_15_1,
% 5.91/1.57 | all_15_0, simplifying with (7), (8), (10), (11) gives:
% 5.91/1.57 | (13) set_difference(all_15_4, all_15_2) = all_15_0 & $i(all_15_0)
% 5.91/1.57 |
% 5.91/1.57 | ALPHA: (13) implies:
% 5.91/1.57 | (14) set_difference(all_15_4, all_15_2) = all_15_0
% 5.91/1.57 |
% 5.91/1.57 | GROUND_INST: instantiating (1) with all_15_4, all_15_5, all_15_2, all_15_0,
% 5.91/1.57 | simplifying with (6), (7), (12), (14) gives:
% 5.91/1.57 | (15) all_15_0 = all_15_4 | in(all_15_5, all_15_4) = 0
% 5.91/1.57 |
% 5.91/1.58 | BETA: splitting (15) gives:
% 5.91/1.58 |
% 5.91/1.58 | Case 1:
% 5.91/1.58 | |
% 5.91/1.58 | | (16) in(all_15_5, all_15_4) = 0
% 5.91/1.58 | |
% 5.91/1.58 | | GROUND_INST: instantiating (2) with all_15_3, 0, all_15_4, all_15_5,
% 5.91/1.58 | | simplifying with (9), (16) gives:
% 5.91/1.58 | | (17) all_15_3 = 0
% 5.91/1.58 | |
% 5.91/1.58 | | REDUCE: (4), (17) imply:
% 5.91/1.58 | | (18) $false
% 5.91/1.58 | |
% 5.91/1.58 | | CLOSE: (18) is inconsistent.
% 5.91/1.58 | |
% 5.91/1.58 | Case 2:
% 5.91/1.58 | |
% 5.91/1.58 | | (19) all_15_0 = all_15_4
% 5.91/1.58 | |
% 5.91/1.58 | | REDUCE: (5), (19) imply:
% 5.91/1.58 | | (20) $false
% 5.91/1.58 | |
% 5.91/1.58 | | CLOSE: (20) is inconsistent.
% 5.91/1.58 | |
% 5.91/1.58 | End of split
% 5.91/1.58 |
% 5.91/1.58 End of proof
% 5.91/1.58 % SZS output end Proof for theBenchmark
% 5.91/1.58
% 5.91/1.58 973ms
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