TSTP Solution File: SET908+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET908+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 15:26:59 EDT 2023
% Result : Theorem 6.12s 1.67s
% Output : Proof 8.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET908+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 : n022.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 13:32:40 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.10/1.02 Prover 1: Preprocessing ...
% 2.10/1.02 Prover 4: Preprocessing ...
% 2.10/1.07 Prover 3: Preprocessing ...
% 2.10/1.07 Prover 0: Preprocessing ...
% 2.10/1.07 Prover 6: Preprocessing ...
% 2.10/1.07 Prover 2: Preprocessing ...
% 2.10/1.07 Prover 5: Preprocessing ...
% 4.13/1.38 Prover 4: Warning: ignoring some quantifiers
% 4.13/1.38 Prover 1: Warning: ignoring some quantifiers
% 4.13/1.39 Prover 3: Warning: ignoring some quantifiers
% 4.13/1.41 Prover 2: Proving ...
% 4.13/1.41 Prover 6: Proving ...
% 4.13/1.41 Prover 3: Constructing countermodel ...
% 4.13/1.41 Prover 1: Constructing countermodel ...
% 4.13/1.41 Prover 4: Constructing countermodel ...
% 4.13/1.42 Prover 5: Proving ...
% 4.13/1.43 Prover 0: Proving ...
% 6.12/1.67 Prover 2: proved (1034ms)
% 6.12/1.67
% 6.12/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.12/1.67
% 6.12/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.12/1.67 Prover 0: stopped
% 6.12/1.67 Prover 5: stopped
% 6.12/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.12/1.68 Prover 6: stopped
% 6.12/1.70 Prover 3: stopped
% 6.85/1.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.85/1.71 Prover 8: Preprocessing ...
% 6.85/1.71 Prover 7: Preprocessing ...
% 6.85/1.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.85/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.85/1.71 Prover 10: Preprocessing ...
% 6.85/1.72 Prover 11: Preprocessing ...
% 6.85/1.74 Prover 13: Preprocessing ...
% 6.85/1.75 Prover 7: Warning: ignoring some quantifiers
% 6.85/1.75 Prover 10: Warning: ignoring some quantifiers
% 6.85/1.76 Prover 7: Constructing countermodel ...
% 6.85/1.77 Prover 10: Constructing countermodel ...
% 6.85/1.77 Prover 4: gave up
% 6.85/1.77 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.85/1.78 Prover 8: Warning: ignoring some quantifiers
% 6.85/1.79 Prover 8: Constructing countermodel ...
% 6.85/1.79 Prover 16: Preprocessing ...
% 7.55/1.84 Prover 13: Warning: ignoring some quantifiers
% 7.55/1.84 Prover 13: Constructing countermodel ...
% 7.55/1.85 Prover 10: Found proof (size 12)
% 7.55/1.85 Prover 10: proved (164ms)
% 7.55/1.85 Prover 8: stopped
% 7.55/1.85 Prover 1: stopped
% 7.55/1.85 Prover 7: stopped
% 7.55/1.85 Prover 13: stopped
% 7.55/1.86 Prover 16: Warning: ignoring some quantifiers
% 7.55/1.87 Prover 16: Constructing countermodel ...
% 7.55/1.87 Prover 11: Warning: ignoring some quantifiers
% 7.55/1.87 Prover 16: stopped
% 7.55/1.88 Prover 11: Constructing countermodel ...
% 7.55/1.88 Prover 11: stopped
% 7.55/1.89
% 7.55/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.55/1.89
% 8.16/1.89 % SZS output start Proof for theBenchmark
% 8.16/1.89 Assumptions after simplification:
% 8.16/1.89 ---------------------------------
% 8.16/1.89
% 8.16/1.89 (commutativity_k2_xboole_0)
% 8.24/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 8.24/1.92 $i(v1) | ~ $i(v0) | (set_union2(v1, v0) = v2 & $i(v2)))
% 8.24/1.92
% 8.24/1.92 (d1_tarski)
% 8.24/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 8.24/1.92 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1:
% 8.24/1.92 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 8.24/1.92 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 |
% 8.24/1.92 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) |
% 8.24/1.92 ~ $i(v1) | ~ $i(v0) | in(v0, v1))
% 8.24/1.92
% 8.24/1.92 (d1_xboole_0)
% 8.24/1.92 $i(empty_set) & ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) & ? [v0: $i]
% 8.24/1.92 : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0)))
% 8.24/1.92
% 8.24/1.92 (d2_xboole_0)
% 8.24/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0,
% 8.24/1.93 v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3,
% 8.24/1.93 v2) | in(v3, v1) | in(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 8.24/1.93 ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 8.24/1.93 $i(v1) | ~ $i(v0) | ~ in(v3, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i]
% 8.24/1.93 : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~
% 8.24/1.93 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2)) & ? [v0: $i] :
% 8.24/1.93 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_union2(v1, v2) =
% 8.24/1.93 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ($i(v4) & ( ~
% 8.24/1.93 in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1)
% 8.24/1.93 | in(v4, v0))))
% 8.24/1.93
% 8.24/1.93 (t49_zfmisc_1)
% 8.24/1.93 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(v0) = v2
% 8.24/1.93 & set_union2(v2, v1) = empty_set & $i(v2) & $i(v1) & $i(v0))
% 8.24/1.93
% 8.24/1.93 Further assumptions not needed in the proof:
% 8.24/1.93 --------------------------------------------
% 8.24/1.93 antisymmetry_r2_hidden, fc1_xboole_0, fc2_xboole_0, fc3_xboole_0,
% 8.24/1.93 idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0
% 8.24/1.93
% 8.24/1.93 Those formulas are unsatisfiable:
% 8.24/1.93 ---------------------------------
% 8.24/1.93
% 8.24/1.93 Begin of proof
% 8.24/1.93 |
% 8.24/1.93 | ALPHA: (d1_tarski) implies:
% 8.24/1.94 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~
% 8.24/1.94 | $i(v0) | in(v0, v1))
% 8.24/1.94 |
% 8.24/1.94 | ALPHA: (d1_xboole_0) implies:
% 8.24/1.94 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set))
% 8.24/1.94 |
% 8.24/1.94 | ALPHA: (d2_xboole_0) implies:
% 8.24/1.94 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.24/1.94 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 8.24/1.94 | $i(v0) | ~ in(v3, v1) | in(v3, v2))
% 8.24/1.94 |
% 8.24/1.94 | ALPHA: (t49_zfmisc_1) implies:
% 8.24/1.94 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(v0) = v2 &
% 8.24/1.94 | set_union2(v2, v1) = empty_set & $i(v2) & $i(v1) & $i(v0))
% 8.24/1.94 |
% 8.24/1.94 | DELTA: instantiating (4) with fresh symbols all_17_0, all_17_1, all_17_2
% 8.24/1.94 | gives:
% 8.24/1.94 | (5) singleton(all_17_2) = all_17_0 & set_union2(all_17_0, all_17_1) =
% 8.24/1.94 | empty_set & $i(all_17_0) & $i(all_17_1) & $i(all_17_2)
% 8.24/1.94 |
% 8.24/1.94 | ALPHA: (5) implies:
% 8.24/1.94 | (6) $i(all_17_2)
% 8.24/1.94 | (7) $i(all_17_1)
% 8.24/1.94 | (8) $i(all_17_0)
% 8.24/1.94 | (9) set_union2(all_17_0, all_17_1) = empty_set
% 8.24/1.94 | (10) singleton(all_17_2) = all_17_0
% 8.24/1.94 |
% 8.24/1.94 | GROUND_INST: instantiating (commutativity_k2_xboole_0) with all_17_0,
% 8.24/1.94 | all_17_1, empty_set, simplifying with (7), (8), (9) gives:
% 8.24/1.94 | (11) set_union2(all_17_1, all_17_0) = empty_set & $i(empty_set)
% 8.24/1.94 |
% 8.24/1.94 | ALPHA: (11) implies:
% 8.24/1.94 | (12) $i(empty_set)
% 8.24/1.95 | (13) set_union2(all_17_1, all_17_0) = empty_set
% 8.24/1.95 |
% 8.24/1.95 | GROUND_INST: instantiating (1) with all_17_2, all_17_0, simplifying with (6),
% 8.24/1.95 | (8), (10) gives:
% 8.24/1.95 | (14) in(all_17_2, all_17_0)
% 8.24/1.95 |
% 8.24/1.95 | GROUND_INST: instantiating (3) with all_17_1, all_17_0, empty_set, all_17_2,
% 8.24/1.95 | simplifying with (6), (7), (8), (12), (13), (14) gives:
% 8.24/1.95 | (15) in(all_17_2, empty_set)
% 8.24/1.95 |
% 8.24/1.95 | GROUND_INST: instantiating (2) with all_17_2, simplifying with (6), (15)
% 8.24/1.95 | gives:
% 8.24/1.95 | (16) $false
% 8.24/1.95 |
% 8.24/1.95 | CLOSE: (16) is inconsistent.
% 8.24/1.95 |
% 8.24/1.95 End of proof
% 8.24/1.95 % SZS output end Proof for theBenchmark
% 8.24/1.95
% 8.24/1.95 1338ms
%------------------------------------------------------------------------------