TSTP Solution File: SEU303+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU303+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 : n007.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 17:43:57 EDT 2023
% Result : Theorem 14.64s 2.90s
% Output : Proof 18.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU303+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.34 % Computer : n007.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Wed Aug 23 14:52:54 EDT 2023
% 0.15/0.35 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.29/1.21 Prover 1: Preprocessing ...
% 3.29/1.22 Prover 4: Preprocessing ...
% 3.90/1.25 Prover 5: Preprocessing ...
% 3.90/1.25 Prover 0: Preprocessing ...
% 3.90/1.25 Prover 6: Preprocessing ...
% 3.90/1.25 Prover 3: Preprocessing ...
% 3.90/1.25 Prover 2: Preprocessing ...
% 7.74/1.79 Prover 2: Proving ...
% 7.74/1.79 Prover 5: Proving ...
% 7.74/1.80 Prover 1: Warning: ignoring some quantifiers
% 7.74/1.85 Prover 1: Constructing countermodel ...
% 8.33/1.88 Prover 3: Warning: ignoring some quantifiers
% 8.57/1.93 Prover 3: Constructing countermodel ...
% 8.57/1.94 Prover 6: Proving ...
% 8.57/1.98 Prover 4: Warning: ignoring some quantifiers
% 9.23/2.04 Prover 4: Constructing countermodel ...
% 9.23/2.10 Prover 0: Proving ...
% 13.63/2.76 Prover 3: gave up
% 13.63/2.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.64/2.87 Prover 7: Preprocessing ...
% 14.64/2.90 Prover 5: proved (2266ms)
% 14.64/2.90
% 14.64/2.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.64/2.90
% 15.77/2.91 Prover 2: stopped
% 15.77/2.91 Prover 0: stopped
% 15.77/2.93 Prover 6: stopped
% 15.77/2.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.77/2.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.77/2.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.77/2.95 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.77/2.96 Prover 7: Warning: ignoring some quantifiers
% 15.77/2.98 Prover 7: Constructing countermodel ...
% 15.77/2.99 Prover 10: Preprocessing ...
% 16.44/3.02 Prover 8: Preprocessing ...
% 16.44/3.04 Prover 11: Preprocessing ...
% 16.44/3.05 Prover 13: Preprocessing ...
% 16.44/3.08 Prover 10: Warning: ignoring some quantifiers
% 16.44/3.08 Prover 10: Constructing countermodel ...
% 17.19/3.15 Prover 13: Warning: ignoring some quantifiers
% 17.19/3.16 Prover 8: Warning: ignoring some quantifiers
% 17.19/3.17 Prover 8: Constructing countermodel ...
% 17.19/3.18 Prover 13: Constructing countermodel ...
% 18.01/3.25 Prover 10: gave up
% 18.01/3.26 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 18.01/3.28 Prover 7: Found proof (size 16)
% 18.01/3.28 Prover 7: proved (511ms)
% 18.01/3.28 Prover 13: stopped
% 18.01/3.28 Prover 4: stopped
% 18.01/3.28 Prover 8: stopped
% 18.01/3.28 Prover 1: stopped
% 18.01/3.29 Prover 11: Warning: ignoring some quantifiers
% 18.73/3.31 Prover 11: Constructing countermodel ...
% 18.73/3.31 Prover 16: Preprocessing ...
% 18.73/3.32 Prover 11: stopped
% 18.73/3.33 Prover 16: stopped
% 18.73/3.33
% 18.73/3.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.73/3.33
% 18.73/3.34 % SZS output start Proof for theBenchmark
% 18.73/3.34 Assumptions after simplification:
% 18.73/3.34 ---------------------------------
% 18.73/3.34
% 18.73/3.34 (t146_relat_1)
% 18.73/3.36 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 18.73/3.36 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & relation_image(v0, v2)
% 18.73/3.36 = v1 & $i(v2) & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 18.73/3.36 (relation_dom(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ? [v2: $i] :
% 18.73/3.36 (relation_rng(v0) = v2 & relation_image(v0, v1) = v2 & $i(v2)))
% 18.73/3.36
% 18.73/3.36 (t17_finset_1)
% 18.73/3.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_image(v1, v0) = v2) |
% 18.73/3.36 ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ~ finite(v0) |
% 18.73/3.36 finite(v2))
% 18.73/3.36
% 18.73/3.36 (t26_finset_1)
% 18.73/3.37 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng(v0) = v2 &
% 18.73/3.37 relation_dom(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & relation(v0) &
% 18.73/3.37 function(v0) & finite(v1) & ~ finite(v2))
% 18.73/3.37
% 18.73/3.37 (function-axioms)
% 18.73/3.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.73/3.37 (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0:
% 18.73/3.37 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~
% 18.73/3.37 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 18.73/3.37 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i]
% 18.73/3.37 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 18.73/3.37 (powerset(v2) = v0))
% 18.73/3.37
% 18.73/3.37 Further assumptions not needed in the proof:
% 18.73/3.37 --------------------------------------------
% 18.73/3.37 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1,
% 18.73/3.37 cc1_relat_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1,
% 18.73/3.37 cc4_arytm_3, existence_m1_subset_1, fc12_relat_1, fc13_finset_1, fc1_subset_1,
% 18.73/3.37 fc1_xboole_0, fc2_ordinal1, fc4_relat_1, fc5_ordinal1, fc5_relat_1, fc6_funct_1,
% 18.73/3.37 fc6_relat_1, fc7_relat_1, fc8_arytm_3, fc8_relat_1, rc1_arytm_3, rc1_finset_1,
% 18.73/3.37 rc1_funcop_1, rc1_funct_1, rc1_ordinal1, rc1_ordinal2, rc1_relat_1,
% 18.73/3.37 rc1_subset_1, rc1_xboole_0, rc2_arytm_3, rc2_finset_1, rc2_funct_1,
% 18.73/3.37 rc2_ordinal1, rc2_ordinal2, rc2_relat_1, rc2_subset_1, rc2_xboole_0,
% 18.73/3.37 rc3_arytm_3, rc3_finset_1, rc3_funct_1, rc3_ordinal1, rc3_relat_1, rc4_funct_1,
% 18.73/3.37 rc4_ordinal1, rc5_funct_1, reflexivity_r1_tarski, t1_subset, t2_subset,
% 18.73/3.37 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 18.73/3.37
% 18.73/3.37 Those formulas are unsatisfiable:
% 18.73/3.37 ---------------------------------
% 18.73/3.37
% 18.73/3.37 Begin of proof
% 18.73/3.37 |
% 18.73/3.37 | ALPHA: (t146_relat_1) implies:
% 18.73/3.37 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 18.73/3.37 | ~ relation(v0) | ? [v2: $i] : (relation_rng(v0) = v2 &
% 18.73/3.37 | relation_image(v0, v1) = v2 & $i(v2)))
% 18.73/3.38 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 18.73/3.38 | ~ relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 &
% 18.73/3.38 | relation_image(v0, v2) = v1 & $i(v2) & $i(v1)))
% 18.73/3.38 |
% 18.73/3.38 | ALPHA: (function-axioms) implies:
% 18.73/3.38 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.73/3.38 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 18.73/3.38 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.73/3.38 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 18.73/3.38 |
% 18.73/3.38 | DELTA: instantiating (t26_finset_1) with fresh symbols all_82_0, all_82_1,
% 18.73/3.38 | all_82_2 gives:
% 18.73/3.38 | (5) relation_rng(all_82_2) = all_82_0 & relation_dom(all_82_2) = all_82_1 &
% 18.73/3.38 | $i(all_82_0) & $i(all_82_1) & $i(all_82_2) & relation(all_82_2) &
% 18.73/3.38 | function(all_82_2) & finite(all_82_1) & ~ finite(all_82_0)
% 18.73/3.38 |
% 18.73/3.38 | ALPHA: (5) implies:
% 18.73/3.38 | (6) ~ finite(all_82_0)
% 18.73/3.38 | (7) finite(all_82_1)
% 18.73/3.38 | (8) function(all_82_2)
% 18.73/3.38 | (9) relation(all_82_2)
% 18.73/3.38 | (10) $i(all_82_2)
% 18.73/3.38 | (11) relation_dom(all_82_2) = all_82_1
% 18.73/3.38 | (12) relation_rng(all_82_2) = all_82_0
% 18.73/3.38 |
% 18.73/3.38 | GROUND_INST: instantiating (1) with all_82_2, all_82_1, simplifying with (9),
% 18.73/3.38 | (10), (11) gives:
% 18.73/3.38 | (13) ? [v0: $i] : (relation_rng(all_82_2) = v0 & relation_image(all_82_2,
% 18.73/3.38 | all_82_1) = v0 & $i(v0))
% 18.73/3.38 |
% 18.73/3.38 | GROUND_INST: instantiating (2) with all_82_2, all_82_0, simplifying with (9),
% 18.73/3.38 | (10), (12) gives:
% 18.73/3.38 | (14) ? [v0: $i] : (relation_dom(all_82_2) = v0 & relation_image(all_82_2,
% 18.73/3.38 | v0) = all_82_0 & $i(v0) & $i(all_82_0))
% 18.73/3.38 |
% 18.73/3.38 | DELTA: instantiating (13) with fresh symbol all_94_0 gives:
% 18.73/3.38 | (15) relation_rng(all_82_2) = all_94_0 & relation_image(all_82_2, all_82_1)
% 18.73/3.38 | = all_94_0 & $i(all_94_0)
% 18.73/3.38 |
% 18.73/3.38 | ALPHA: (15) implies:
% 18.73/3.38 | (16) relation_image(all_82_2, all_82_1) = all_94_0
% 18.73/3.38 | (17) relation_rng(all_82_2) = all_94_0
% 18.73/3.38 |
% 18.73/3.38 | DELTA: instantiating (14) with fresh symbol all_96_0 gives:
% 18.73/3.39 | (18) relation_dom(all_82_2) = all_96_0 & relation_image(all_82_2, all_96_0)
% 18.73/3.39 | = all_82_0 & $i(all_96_0) & $i(all_82_0)
% 18.73/3.39 |
% 18.73/3.39 | ALPHA: (18) implies:
% 18.73/3.39 | (19) $i(all_96_0)
% 18.73/3.39 | (20) relation_dom(all_82_2) = all_96_0
% 18.73/3.39 |
% 18.73/3.39 | GROUND_INST: instantiating (3) with all_82_1, all_96_0, all_82_2, simplifying
% 18.73/3.39 | with (11), (20) gives:
% 18.73/3.39 | (21) all_96_0 = all_82_1
% 18.73/3.39 |
% 18.73/3.39 | GROUND_INST: instantiating (4) with all_82_0, all_94_0, all_82_2, simplifying
% 18.73/3.39 | with (12), (17) gives:
% 18.73/3.39 | (22) all_94_0 = all_82_0
% 18.73/3.39 |
% 18.73/3.39 | REDUCE: (16), (22) imply:
% 18.73/3.39 | (23) relation_image(all_82_2, all_82_1) = all_82_0
% 18.73/3.39 |
% 18.73/3.39 | REDUCE: (19), (21) imply:
% 18.73/3.39 | (24) $i(all_82_1)
% 18.73/3.39 |
% 18.73/3.39 | GROUND_INST: instantiating (t17_finset_1) with all_82_1, all_82_2, all_82_0,
% 18.73/3.39 | simplifying with (6), (7), (8), (9), (10), (23), (24) gives:
% 18.73/3.39 | (25) $false
% 18.73/3.39 |
% 18.73/3.39 | CLOSE: (25) is inconsistent.
% 18.73/3.39 |
% 18.73/3.39 End of proof
% 18.73/3.39 % SZS output end Proof for theBenchmark
% 18.73/3.39
% 18.73/3.39 2783ms
%------------------------------------------------------------------------------