TSTP Solution File: SEU149+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU149+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 17:42:48 EDT 2023
% Result : Theorem 4.88s 1.41s
% Output : Proof 6.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU149+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 21:55:52 EDT 2023
% 0.12/0.34 % 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
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 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 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 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 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 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 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
% 1.85/0.99 Prover 4: Preprocessing ...
% 1.85/0.99 Prover 1: Preprocessing ...
% 2.29/1.04 Prover 0: Preprocessing ...
% 2.29/1.04 Prover 6: Preprocessing ...
% 2.29/1.04 Prover 5: Preprocessing ...
% 2.29/1.04 Prover 3: Preprocessing ...
% 2.29/1.04 Prover 2: Preprocessing ...
% 3.55/1.21 Prover 1: Warning: ignoring some quantifiers
% 3.55/1.21 Prover 3: Warning: ignoring some quantifiers
% 3.55/1.21 Prover 4: Warning: ignoring some quantifiers
% 3.55/1.22 Prover 5: Proving ...
% 3.55/1.22 Prover 6: Proving ...
% 3.55/1.22 Prover 3: Constructing countermodel ...
% 3.55/1.23 Prover 4: Constructing countermodel ...
% 3.55/1.23 Prover 1: Constructing countermodel ...
% 4.00/1.26 Prover 2: Proving ...
% 4.00/1.26 Prover 0: Proving ...
% 4.88/1.41 Prover 2: proved (789ms)
% 4.88/1.41
% 4.88/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.88/1.42
% 4.88/1.42 Prover 3: stopped
% 4.88/1.42 Prover 0: stopped
% 4.88/1.42 Prover 5: stopped
% 4.88/1.43 Prover 6: stopped
% 4.88/1.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.88/1.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.88/1.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.88/1.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.88/1.43 Prover 7: Preprocessing ...
% 4.88/1.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.88/1.43 Prover 10: Preprocessing ...
% 4.88/1.44 Prover 8: Preprocessing ...
% 4.88/1.44 Prover 11: Preprocessing ...
% 4.88/1.45 Prover 13: Preprocessing ...
% 4.88/1.47 Prover 1: gave up
% 4.88/1.47 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.88/1.49 Prover 10: Warning: ignoring some quantifiers
% 4.88/1.49 Prover 8: Warning: ignoring some quantifiers
% 4.88/1.51 Prover 10: Constructing countermodel ...
% 4.88/1.52 Prover 7: Warning: ignoring some quantifiers
% 4.88/1.52 Prover 16: Preprocessing ...
% 4.88/1.53 Prover 7: Constructing countermodel ...
% 4.88/1.53 Prover 8: Constructing countermodel ...
% 4.88/1.54 Prover 13: Warning: ignoring some quantifiers
% 4.88/1.54 Prover 11: Warning: ignoring some quantifiers
% 4.88/1.55 Prover 13: Constructing countermodel ...
% 4.88/1.55 Prover 11: Constructing countermodel ...
% 4.88/1.56 Prover 16: Warning: ignoring some quantifiers
% 4.88/1.56 Prover 4: gave up
% 4.88/1.56 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.88/1.56 Prover 16: Constructing countermodel ...
% 4.88/1.57 Prover 19: Preprocessing ...
% 5.94/1.60 Prover 10: Found proof (size 10)
% 5.94/1.60 Prover 10: proved (179ms)
% 5.94/1.60 Prover 7: stopped
% 5.94/1.60 Prover 11: stopped
% 5.94/1.60 Prover 13: stopped
% 5.94/1.60 Prover 8: stopped
% 5.94/1.60 Prover 16: stopped
% 6.69/1.63 Prover 19: Warning: ignoring some quantifiers
% 6.69/1.64 Prover 19: Constructing countermodel ...
% 6.69/1.64 Prover 19: stopped
% 6.69/1.64
% 6.69/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.69/1.64
% 6.69/1.65 % SZS output start Proof for theBenchmark
% 6.69/1.65 Assumptions after simplification:
% 6.69/1.65 ---------------------------------
% 6.69/1.65
% 6.69/1.65 (commutativity_k2_tarski)
% 6.69/1.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) |
% 6.69/1.68 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 6.69/1.68
% 6.69/1.68 (d1_tarski)
% 6.69/1.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 6.92/1.68 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1:
% 6.92/1.68 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 6.92/1.68 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 |
% 6.92/1.68 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) |
% 6.92/1.68 ~ $i(v1) | ~ $i(v0) | in(v0, v1))
% 6.92/1.68
% 6.92/1.68 (d2_tarski)
% 6.92/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 |
% 6.92/1.69 ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 6.92/1.69 $i(v0) | ~ in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 6.92/1.69 $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 6.92/1.69 ~ $i(v0) | ? [v4: $i] : ($i(v4) & (v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~
% 6.92/1.69 in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0: $i] : ! [v1:
% 6.92/1.69 $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~
% 6.92/1.69 $i(v1) | ~ $i(v0) | in(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 6.92/1.69 ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0,
% 6.92/1.69 v2))
% 6.92/1.69
% 6.92/1.69 (t8_zfmisc_1)
% 6.92/1.69 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = v0) &
% 6.92/1.69 singleton(v0) = v3 & unordered_pair(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1)
% 6.92/1.69 & $i(v0))
% 6.92/1.69
% 6.92/1.69 Further assumptions not needed in the proof:
% 6.92/1.69 --------------------------------------------
% 6.92/1.69 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0
% 6.92/1.69
% 6.92/1.69 Those formulas are unsatisfiable:
% 6.92/1.69 ---------------------------------
% 6.92/1.69
% 6.92/1.69 Begin of proof
% 6.92/1.69 |
% 6.92/1.69 | ALPHA: (d1_tarski) implies:
% 6.92/1.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 6.92/1.69 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1))
% 6.92/1.69 |
% 6.92/1.69 | ALPHA: (d2_tarski) implies:
% 6.92/1.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 6.92/1.70 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, v2))
% 6.92/1.70 |
% 6.92/1.70 | DELTA: instantiating (t8_zfmisc_1) with fresh symbols all_11_0, all_11_1,
% 6.92/1.70 | all_11_2, all_11_3 gives:
% 6.92/1.70 | (3) ~ (all_11_2 = all_11_3) & singleton(all_11_3) = all_11_0 &
% 6.92/1.70 | unordered_pair(all_11_2, all_11_1) = all_11_0 & $i(all_11_0) &
% 6.92/1.70 | $i(all_11_1) & $i(all_11_2) & $i(all_11_3)
% 6.92/1.70 |
% 6.92/1.70 | ALPHA: (3) implies:
% 6.92/1.70 | (4) ~ (all_11_2 = all_11_3)
% 6.92/1.70 | (5) $i(all_11_3)
% 6.92/1.70 | (6) $i(all_11_2)
% 6.92/1.70 | (7) $i(all_11_1)
% 6.92/1.70 | (8) $i(all_11_0)
% 6.92/1.70 | (9) unordered_pair(all_11_2, all_11_1) = all_11_0
% 6.92/1.70 | (10) singleton(all_11_3) = all_11_0
% 6.92/1.70 |
% 6.92/1.70 | GROUND_INST: instantiating (2) with all_11_2, all_11_1, all_11_0, simplifying
% 6.92/1.70 | with (6), (7), (8), (9) gives:
% 6.92/1.70 | (11) in(all_11_2, all_11_0)
% 6.92/1.70 |
% 6.92/1.70 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_11_2, all_11_1,
% 6.92/1.70 | all_11_0, simplifying with (6), (7), (9) gives:
% 6.92/1.70 | (12) unordered_pair(all_11_1, all_11_2) = all_11_0 & $i(all_11_0)
% 6.92/1.70 |
% 6.92/1.70 | GROUND_INST: instantiating (1) with all_11_3, all_11_0, all_11_2, simplifying
% 6.92/1.70 | with (5), (6), (8), (10), (11) gives:
% 6.92/1.70 | (13) all_11_2 = all_11_3
% 6.92/1.70 |
% 6.92/1.70 | REDUCE: (4), (13) imply:
% 6.92/1.70 | (14) $false
% 6.92/1.71 |
% 6.92/1.71 | CLOSE: (14) is inconsistent.
% 6.92/1.71 |
% 6.92/1.71 End of proof
% 6.92/1.71 % SZS output end Proof for theBenchmark
% 6.92/1.71
% 6.92/1.71 1102ms
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