TSTP Solution File: SEU149+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU149+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 : n032.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 17:42:47 EDT 2023
% Result : Theorem 4.27s 1.30s
% Output : Proof 6.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU149+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Wed Aug 23 20:05:56 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.17/0.51 ________ _____
% 0.17/0.51 ___ __ \_________(_)________________________________
% 0.17/0.51 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.51 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.51 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.51
% 0.17/0.51 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.51 (2023-06-19)
% 0.17/0.51
% 0.17/0.51 (c) Philipp Rümmer, 2009-2023
% 0.17/0.51 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.51 Amanda Stjerna.
% 0.17/0.51 Free software under BSD-3-Clause.
% 0.17/0.51
% 0.17/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.51
% 0.17/0.51 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.17/0.52 Running up to 7 provers in parallel.
% 0.17/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.14/0.84 Prover 4: Preprocessing ...
% 1.14/0.84 Prover 1: Preprocessing ...
% 1.85/0.88 Prover 2: Preprocessing ...
% 1.85/0.88 Prover 5: Preprocessing ...
% 1.85/0.88 Prover 3: Preprocessing ...
% 1.85/0.89 Prover 0: Preprocessing ...
% 1.85/0.89 Prover 6: Preprocessing ...
% 2.71/1.04 Prover 1: Warning: ignoring some quantifiers
% 2.71/1.05 Prover 3: Warning: ignoring some quantifiers
% 2.71/1.05 Prover 4: Warning: ignoring some quantifiers
% 2.71/1.06 Prover 3: Constructing countermodel ...
% 2.71/1.06 Prover 1: Constructing countermodel ...
% 2.71/1.06 Prover 4: Constructing countermodel ...
% 2.71/1.08 Prover 6: Proving ...
% 3.28/1.08 Prover 5: Proving ...
% 3.28/1.09 Prover 0: Proving ...
% 3.28/1.11 Prover 2: Proving ...
% 4.27/1.29 Prover 2: proved (767ms)
% 4.27/1.30
% 4.27/1.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.27/1.30
% 4.27/1.30 Prover 0: stopped
% 4.27/1.30 Prover 6: stopped
% 4.27/1.30 Prover 3: stopped
% 4.27/1.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.27/1.30 Prover 5: stopped
% 4.27/1.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.27/1.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.27/1.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.27/1.32 Prover 7: Preprocessing ...
% 4.27/1.32 Prover 8: Preprocessing ...
% 4.27/1.32 Prover 10: Preprocessing ...
% 4.27/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.27/1.33 Prover 11: Preprocessing ...
% 4.27/1.34 Prover 13: Preprocessing ...
% 4.27/1.38 Prover 10: Warning: ignoring some quantifiers
% 4.27/1.38 Prover 7: Warning: ignoring some quantifiers
% 4.27/1.39 Prover 8: Warning: ignoring some quantifiers
% 4.27/1.39 Prover 10: Constructing countermodel ...
% 4.27/1.39 Prover 11: Warning: ignoring some quantifiers
% 4.27/1.39 Prover 7: Constructing countermodel ...
% 4.27/1.40 Prover 11: Constructing countermodel ...
% 4.27/1.40 Prover 1: gave up
% 4.27/1.40 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.27/1.40 Prover 8: Constructing countermodel ...
% 5.11/1.43 Prover 16: Preprocessing ...
% 5.11/1.44 Prover 13: Warning: ignoring some quantifiers
% 5.11/1.44 Prover 13: Constructing countermodel ...
% 5.11/1.45 Prover 11: gave up
% 5.11/1.45 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.11/1.46 Prover 19: Preprocessing ...
% 5.11/1.47 Prover 7: Found proof (size 11)
% 5.11/1.47 Prover 7: proved (169ms)
% 5.11/1.47 Prover 8: stopped
% 5.11/1.47 Prover 13: stopped
% 5.11/1.47 Prover 10: stopped
% 5.11/1.47 Prover 4: stopped
% 5.11/1.47 Prover 16: Warning: ignoring some quantifiers
% 5.11/1.48 Prover 16: Constructing countermodel ...
% 5.11/1.48 Prover 16: stopped
% 6.04/1.51 Prover 19: Warning: ignoring some quantifiers
% 6.04/1.52 Prover 19: Constructing countermodel ...
% 6.04/1.52 Prover 19: stopped
% 6.04/1.52
% 6.04/1.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.04/1.52
% 6.04/1.52 % SZS output start Proof for theBenchmark
% 6.04/1.53 Assumptions after simplification:
% 6.04/1.53 ---------------------------------
% 6.04/1.53
% 6.04/1.53 (commutativity_k2_tarski)
% 6.04/1.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) |
% 6.04/1.57 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i]
% 6.04/1.57 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) |
% 6.04/1.57 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 6.04/1.57
% 6.04/1.57 (d1_tarski)
% 6.04/1.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 6.04/1.58 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1:
% 6.04/1.58 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 6.04/1.58 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 |
% 6.04/1.58 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) |
% 6.04/1.58 ~ $i(v1) | ~ $i(v0) | in(v0, v1))
% 6.04/1.58
% 6.04/1.58 (d2_tarski)
% 6.04/1.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 |
% 6.04/1.59 ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 6.04/1.59 $i(v0) | ~ in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 6.04/1.59 $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 6.04/1.59 ~ $i(v0) | ? [v4: $i] : ($i(v4) & (v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~
% 6.04/1.59 in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0: $i] : ! [v1:
% 6.04/1.59 $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~
% 6.04/1.59 $i(v1) | ~ $i(v0) | in(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 6.04/1.59 ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0,
% 6.04/1.59 v2))
% 6.04/1.59
% 6.04/1.59 (t8_zfmisc_1)
% 6.04/1.59 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = v0) &
% 6.04/1.59 singleton(v0) = v3 & unordered_pair(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1)
% 6.04/1.59 & $i(v0))
% 6.04/1.59
% 6.04/1.59 Further assumptions not needed in the proof:
% 6.04/1.59 --------------------------------------------
% 6.04/1.59 antisymmetry_r2_hidden, dt_k1_tarski, dt_k2_tarski
% 6.04/1.59
% 6.04/1.59 Those formulas are unsatisfiable:
% 6.04/1.59 ---------------------------------
% 6.04/1.59
% 6.04/1.59 Begin of proof
% 6.04/1.59 |
% 6.04/1.59 | ALPHA: (commutativity_k2_tarski) implies:
% 6.04/1.59 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 6.04/1.60 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 &
% 6.51/1.60 | $i(v2)))
% 6.51/1.60 |
% 6.51/1.60 | ALPHA: (d1_tarski) implies:
% 6.51/1.60 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 6.51/1.60 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1))
% 6.51/1.60 |
% 6.51/1.60 | ALPHA: (d2_tarski) implies:
% 6.51/1.60 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 6.51/1.60 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, v2))
% 6.51/1.60 |
% 6.51/1.60 | DELTA: instantiating (t8_zfmisc_1) with fresh symbols all_7_0, all_7_1,
% 6.51/1.60 | all_7_2, all_7_3 gives:
% 6.51/1.60 | (4) ~ (all_7_2 = all_7_3) & singleton(all_7_3) = all_7_0 &
% 6.51/1.60 | unordered_pair(all_7_2, all_7_1) = all_7_0 & $i(all_7_0) & $i(all_7_1)
% 6.51/1.60 | & $i(all_7_2) & $i(all_7_3)
% 6.51/1.60 |
% 6.51/1.60 | ALPHA: (4) implies:
% 6.51/1.60 | (5) ~ (all_7_2 = all_7_3)
% 6.51/1.60 | (6) $i(all_7_3)
% 6.51/1.60 | (7) $i(all_7_2)
% 6.51/1.60 | (8) $i(all_7_1)
% 6.51/1.60 | (9) unordered_pair(all_7_2, all_7_1) = all_7_0
% 6.51/1.61 | (10) singleton(all_7_3) = all_7_0
% 6.51/1.61 |
% 6.51/1.61 | GROUND_INST: instantiating (1) with all_7_1, all_7_2, all_7_0, simplifying
% 6.51/1.61 | with (7), (8), (9) gives:
% 6.51/1.61 | (11) unordered_pair(all_7_1, all_7_2) = all_7_0 & $i(all_7_0)
% 6.51/1.61 |
% 6.51/1.61 | ALPHA: (11) implies:
% 6.51/1.61 | (12) $i(all_7_0)
% 6.51/1.61 |
% 6.51/1.61 | GROUND_INST: instantiating (3) with all_7_2, all_7_1, all_7_0, simplifying
% 6.51/1.61 | with (7), (8), (9), (12) gives:
% 6.51/1.61 | (13) in(all_7_2, all_7_0)
% 6.51/1.61 |
% 6.51/1.61 | GROUND_INST: instantiating (2) with all_7_3, all_7_0, all_7_2, simplifying
% 6.51/1.61 | with (6), (7), (10), (12), (13) gives:
% 6.51/1.61 | (14) all_7_2 = all_7_3
% 6.51/1.61 |
% 6.51/1.61 | REDUCE: (5), (14) imply:
% 6.51/1.61 | (15) $false
% 6.51/1.61 |
% 6.51/1.61 | CLOSE: (15) is inconsistent.
% 6.51/1.61 |
% 6.51/1.61 End of proof
% 6.51/1.61 % SZS output end Proof for theBenchmark
% 6.51/1.61
% 6.51/1.61 1101ms
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