TSTP Solution File: SEU303+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU303+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 : n019.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 4.02s 1.40s
% Output : Proof 6.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.17 % Problem : SEU303+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.18 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.39 % Computer : n019.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8042.1875MB
% 0.14/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Wed Aug 23 12:13:46 EDT 2023
% 0.14/0.39 % CPUTime :
% 0.21/0.66 ________ _____
% 0.21/0.66 ___ __ \_________(_)________________________________
% 0.21/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.66
% 0.21/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.66 (2023-06-19)
% 0.21/0.66
% 0.21/0.66 (c) Philipp Rümmer, 2009-2023
% 0.21/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.66 Amanda Stjerna.
% 0.21/0.66 Free software under BSD-3-Clause.
% 0.21/0.66
% 0.21/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.66
% 0.21/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.68 Running up to 7 provers in parallel.
% 0.21/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.98/1.06 Prover 4: Preprocessing ...
% 1.98/1.06 Prover 1: Preprocessing ...
% 2.32/1.11 Prover 6: Preprocessing ...
% 2.32/1.11 Prover 3: Preprocessing ...
% 2.32/1.11 Prover 5: Preprocessing ...
% 2.32/1.11 Prover 2: Preprocessing ...
% 2.32/1.11 Prover 0: Preprocessing ...
% 3.37/1.23 Prover 5: Constructing countermodel ...
% 3.37/1.23 Prover 1: Constructing countermodel ...
% 3.37/1.24 Prover 6: Constructing countermodel ...
% 3.53/1.25 Prover 3: Constructing countermodel ...
% 3.53/1.25 Prover 4: Constructing countermodel ...
% 3.53/1.28 Prover 2: Proving ...
% 3.53/1.29 Prover 0: Proving ...
% 4.02/1.34 Prover 3: gave up
% 4.02/1.35 Prover 1: gave up
% 4.02/1.36 Prover 6: gave up
% 4.02/1.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.02/1.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.02/1.36 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 4.02/1.38 Prover 8: Preprocessing ...
% 4.02/1.38 Prover 7: Preprocessing ...
% 4.02/1.39 Prover 9: Preprocessing ...
% 4.02/1.40 Prover 5: proved (711ms)
% 4.02/1.40
% 4.02/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.02/1.40
% 4.02/1.41 Prover 2: stopped
% 4.02/1.42 Prover 0: stopped
% 4.02/1.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.02/1.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.02/1.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.02/1.43 Prover 8: Warning: ignoring some quantifiers
% 4.02/1.44 Prover 8: Constructing countermodel ...
% 4.02/1.44 Prover 11: Preprocessing ...
% 4.02/1.44 Prover 10: Preprocessing ...
% 4.02/1.44 Prover 7: Constructing countermodel ...
% 4.02/1.45 Prover 13: Preprocessing ...
% 4.02/1.48 Prover 10: Constructing countermodel ...
% 4.02/1.52 Prover 13: Constructing countermodel ...
% 4.02/1.52 Prover 9: Constructing countermodel ...
% 4.02/1.53 Prover 9: stopped
% 4.02/1.53 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.02/1.53 Prover 8: gave up
% 4.86/1.53 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.86/1.54 Prover 10: gave up
% 4.86/1.54 Prover 16: Preprocessing ...
% 4.86/1.54 Prover 19: Preprocessing ...
% 4.86/1.55 Prover 11: Constructing countermodel ...
% 4.86/1.56 Prover 7: Found proof (size 16)
% 4.86/1.56 Prover 7: proved (212ms)
% 4.86/1.56 Prover 11: stopped
% 4.86/1.56 Prover 13: stopped
% 4.86/1.56 Prover 4: stopped
% 4.86/1.57 Prover 16: Constructing countermodel ...
% 4.86/1.58 Prover 16: stopped
% 4.86/1.59 Prover 19: Warning: ignoring some quantifiers
% 4.86/1.60 Prover 19: Constructing countermodel ...
% 4.86/1.60 Prover 19: stopped
% 4.86/1.60
% 4.86/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.86/1.60
% 4.86/1.61 % SZS output start Proof for theBenchmark
% 5.88/1.61 Assumptions after simplification:
% 5.88/1.61 ---------------------------------
% 5.88/1.62
% 5.88/1.62 (t146_relat_1)
% 6.02/1.67 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 6.02/1.67 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & relation_image(v0, v2)
% 6.02/1.67 = v1 & $i(v2) & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 6.02/1.67 (relation_dom(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ? [v2: $i] :
% 6.02/1.67 (relation_rng(v0) = v2 & relation_image(v0, v1) = v2 & $i(v2)))
% 6.02/1.67
% 6.02/1.67 (t17_finset_1)
% 6.02/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_image(v1, v0) = v2) |
% 6.02/1.67 ~ $i(v1) | ~ $i(v0) | ~ finite(v0) | ~ function(v1) | ~ relation(v1) |
% 6.02/1.67 finite(v2))
% 6.02/1.67
% 6.02/1.67 (t26_finset_1)
% 6.02/1.67 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng(v0) = v2 &
% 6.02/1.67 relation_dom(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & finite(v1) & function(v0)
% 6.02/1.67 & relation(v0) & ~ finite(v2))
% 6.02/1.67
% 6.02/1.67 (function-axioms)
% 6.02/1.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.02/1.68 (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0:
% 6.02/1.68 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~
% 6.02/1.68 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 6.02/1.68 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 6.02/1.68
% 6.02/1.68 Further assumptions not needed in the proof:
% 6.02/1.68 --------------------------------------------
% 6.02/1.68 dt_k1_relat_1, dt_k2_relat_1, dt_k9_relat_1, fc13_finset_1, rc1_funct_1
% 6.02/1.68
% 6.02/1.68 Those formulas are unsatisfiable:
% 6.02/1.68 ---------------------------------
% 6.02/1.68
% 6.02/1.68 Begin of proof
% 6.02/1.68 |
% 6.02/1.68 | ALPHA: (t146_relat_1) implies:
% 6.02/1.69 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 6.02/1.69 | ~ relation(v0) | ? [v2: $i] : (relation_rng(v0) = v2 &
% 6.02/1.69 | relation_image(v0, v1) = v2 & $i(v2)))
% 6.02/1.69 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 6.02/1.69 | ~ relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 &
% 6.02/1.69 | relation_image(v0, v2) = v1 & $i(v2) & $i(v1)))
% 6.02/1.69 |
% 6.02/1.69 | ALPHA: (function-axioms) implies:
% 6.02/1.69 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 6.02/1.69 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 6.02/1.69 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 6.02/1.69 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 6.02/1.69 |
% 6.02/1.70 | DELTA: instantiating (t26_finset_1) with fresh symbols all_8_0, all_8_1,
% 6.02/1.70 | all_8_2 gives:
% 6.02/1.70 | (5) relation_rng(all_8_2) = all_8_0 & relation_dom(all_8_2) = all_8_1 &
% 6.02/1.70 | $i(all_8_0) & $i(all_8_1) & $i(all_8_2) & finite(all_8_1) &
% 6.02/1.70 | function(all_8_2) & relation(all_8_2) & ~ finite(all_8_0)
% 6.02/1.70 |
% 6.02/1.70 | ALPHA: (5) implies:
% 6.02/1.70 | (6) ~ finite(all_8_0)
% 6.02/1.70 | (7) relation(all_8_2)
% 6.02/1.70 | (8) function(all_8_2)
% 6.02/1.70 | (9) finite(all_8_1)
% 6.02/1.70 | (10) $i(all_8_2)
% 6.02/1.70 | (11) relation_dom(all_8_2) = all_8_1
% 6.02/1.70 | (12) relation_rng(all_8_2) = all_8_0
% 6.02/1.70 |
% 6.02/1.70 | GROUND_INST: instantiating (1) with all_8_2, all_8_1, simplifying with (7),
% 6.02/1.70 | (10), (11) gives:
% 6.02/1.71 | (13) ? [v0: $i] : (relation_rng(all_8_2) = v0 & relation_image(all_8_2,
% 6.02/1.71 | all_8_1) = v0 & $i(v0))
% 6.02/1.71 |
% 6.02/1.71 | GROUND_INST: instantiating (2) with all_8_2, all_8_0, simplifying with (7),
% 6.02/1.71 | (10), (12) gives:
% 6.02/1.71 | (14) ? [v0: $i] : (relation_dom(all_8_2) = v0 & relation_image(all_8_2,
% 6.02/1.71 | v0) = all_8_0 & $i(v0) & $i(all_8_0))
% 6.02/1.71 |
% 6.02/1.71 | DELTA: instantiating (13) with fresh symbol all_19_0 gives:
% 6.02/1.71 | (15) relation_rng(all_8_2) = all_19_0 & relation_image(all_8_2, all_8_1) =
% 6.02/1.71 | all_19_0 & $i(all_19_0)
% 6.02/1.71 |
% 6.02/1.71 | ALPHA: (15) implies:
% 6.02/1.71 | (16) relation_image(all_8_2, all_8_1) = all_19_0
% 6.02/1.71 | (17) relation_rng(all_8_2) = all_19_0
% 6.02/1.71 |
% 6.02/1.71 | DELTA: instantiating (14) with fresh symbol all_21_0 gives:
% 6.02/1.71 | (18) relation_dom(all_8_2) = all_21_0 & relation_image(all_8_2, all_21_0) =
% 6.02/1.71 | all_8_0 & $i(all_21_0) & $i(all_8_0)
% 6.02/1.71 |
% 6.02/1.71 | ALPHA: (18) implies:
% 6.02/1.71 | (19) $i(all_21_0)
% 6.02/1.71 | (20) relation_dom(all_8_2) = all_21_0
% 6.02/1.71 |
% 6.02/1.71 | GROUND_INST: instantiating (3) with all_8_1, all_21_0, all_8_2, simplifying
% 6.02/1.71 | with (11), (20) gives:
% 6.02/1.71 | (21) all_21_0 = all_8_1
% 6.02/1.72 |
% 6.02/1.72 | GROUND_INST: instantiating (4) with all_8_0, all_19_0, all_8_2, simplifying
% 6.02/1.72 | with (12), (17) gives:
% 6.02/1.72 | (22) all_19_0 = all_8_0
% 6.02/1.72 |
% 6.02/1.72 | REDUCE: (16), (22) imply:
% 6.02/1.72 | (23) relation_image(all_8_2, all_8_1) = all_8_0
% 6.02/1.72 |
% 6.02/1.72 | REDUCE: (19), (21) imply:
% 6.02/1.72 | (24) $i(all_8_1)
% 6.02/1.72 |
% 6.02/1.72 | GROUND_INST: instantiating (t17_finset_1) with all_8_1, all_8_2, all_8_0,
% 6.02/1.72 | simplifying with (6), (7), (8), (9), (10), (23), (24) gives:
% 6.02/1.72 | (25) $false
% 6.02/1.72 |
% 6.02/1.72 | CLOSE: (25) is inconsistent.
% 6.02/1.72 |
% 6.02/1.72 End of proof
% 6.02/1.72 % SZS output end Proof for theBenchmark
% 6.02/1.72
% 6.02/1.72 1059ms
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