TSTP Solution File: NUM414+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM414+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 : n025.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 11:47:37 EDT 2023
% Result : Theorem 11.29s 2.33s
% Output : Proof 14.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n025.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 10:18:22 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.60 ________ _____
% 0.18/0.60 ___ __ \_________(_)________________________________
% 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.60
% 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.60 (2023-06-19)
% 0.18/0.60
% 0.18/0.60 (c) Philipp Rümmer, 2009-2023
% 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.60 Amanda Stjerna.
% 0.18/0.60 Free software under BSD-3-Clause.
% 0.18/0.60
% 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.60
% 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.75/1.11 Prover 1: Preprocessing ...
% 2.75/1.11 Prover 4: Preprocessing ...
% 3.18/1.15 Prover 6: Preprocessing ...
% 3.18/1.15 Prover 5: Preprocessing ...
% 3.18/1.15 Prover 3: Preprocessing ...
% 3.18/1.15 Prover 0: Preprocessing ...
% 3.18/1.15 Prover 2: Preprocessing ...
% 5.22/1.51 Prover 2: Proving ...
% 5.22/1.51 Prover 5: Proving ...
% 6.12/1.58 Prover 1: Warning: ignoring some quantifiers
% 6.48/1.63 Prover 6: Proving ...
% 6.48/1.63 Prover 1: Constructing countermodel ...
% 6.48/1.64 Prover 3: Warning: ignoring some quantifiers
% 6.48/1.65 Prover 3: Constructing countermodel ...
% 6.66/1.65 Prover 4: Warning: ignoring some quantifiers
% 6.66/1.67 Prover 4: Constructing countermodel ...
% 7.17/1.76 Prover 0: Proving ...
% 8.27/1.91 Prover 1: gave up
% 8.27/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.27/1.92 Prover 3: gave up
% 8.27/1.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.85/2.00 Prover 8: Preprocessing ...
% 8.85/2.01 Prover 7: Preprocessing ...
% 8.85/2.14 Prover 7: Warning: ignoring some quantifiers
% 8.85/2.15 Prover 7: Constructing countermodel ...
% 10.05/2.19 Prover 8: Warning: ignoring some quantifiers
% 10.71/2.21 Prover 8: Constructing countermodel ...
% 11.29/2.33 Prover 0: proved (1713ms)
% 11.29/2.33
% 11.29/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.29/2.33
% 11.29/2.33 Prover 5: stopped
% 11.29/2.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.29/2.35 Prover 2: stopped
% 11.29/2.36 Prover 6: stopped
% 11.29/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.29/2.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.29/2.37 Prover 10: Preprocessing ...
% 11.92/2.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.24/2.41 Prover 11: Preprocessing ...
% 12.24/2.42 Prover 10: Warning: ignoring some quantifiers
% 12.33/2.42 Prover 13: Preprocessing ...
% 12.33/2.44 Prover 16: Preprocessing ...
% 12.33/2.45 Prover 10: Constructing countermodel ...
% 12.33/2.45 Prover 8: gave up
% 12.33/2.46 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.33/2.50 Prover 19: Preprocessing ...
% 12.97/2.53 Prover 13: Warning: ignoring some quantifiers
% 12.97/2.54 Prover 16: Warning: ignoring some quantifiers
% 12.97/2.55 Prover 16: Constructing countermodel ...
% 12.97/2.55 Prover 13: Constructing countermodel ...
% 13.53/2.66 Prover 11: Warning: ignoring some quantifiers
% 13.53/2.66 Prover 11: Constructing countermodel ...
% 14.30/2.70 Prover 19: Warning: ignoring some quantifiers
% 14.30/2.74 Prover 19: Constructing countermodel ...
% 14.30/2.76 Prover 10: Found proof (size 17)
% 14.30/2.76 Prover 10: proved (425ms)
% 14.30/2.76 Prover 16: stopped
% 14.30/2.76 Prover 19: stopped
% 14.30/2.76 Prover 13: stopped
% 14.30/2.76 Prover 7: stopped
% 14.30/2.76 Prover 4: stopped
% 14.30/2.76 Prover 11: stopped
% 14.30/2.76
% 14.30/2.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.30/2.76
% 14.30/2.76 % SZS output start Proof for theBenchmark
% 14.30/2.77 Assumptions after simplification:
% 14.30/2.77 ---------------------------------
% 14.30/2.77
% 14.30/2.77 (connectedness_r1_ordinal1)
% 14.30/2.77 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ordinal(v1) | ~
% 14.30/2.77 ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1))
% 14.30/2.77
% 14.30/2.77 (d8_xboole_0)
% 14.30/2.78 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ subset(v0,
% 14.30/2.78 v1) | proper_subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 14.30/2.78 $i(v0) | ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0: $i] : ( ~
% 14.30/2.78 $i(v0) | ~ proper_subset(v0, v0))
% 14.30/2.78
% 14.30/2.78 (redefinition_r1_ordinal1)
% 14.30/2.78 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | ~
% 14.30/2.78 ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) & ! [v0: $i] : !
% 14.30/2.78 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ordinal_subset(v0, v1) | ~ ordinal(v1)
% 14.30/2.78 | ~ ordinal(v0) | subset(v0, v1))
% 14.30/2.78
% 14.30/2.78 (t50_ordinal1)
% 14.30/2.78 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ordinal(v1) &
% 14.30/2.78 ordinal(v0) & ~ proper_subset(v1, v0) & ~ proper_subset(v0, v1))
% 14.30/2.78
% 14.30/2.78 Further assumptions not needed in the proof:
% 14.30/2.78 --------------------------------------------
% 14.30/2.78 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_ordinal1,
% 14.30/2.78 cc1_relat_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1, existence_m1_subset_1,
% 14.30/2.78 fc12_relat_1, fc1_xboole_0, fc2_ordinal1, fc4_relat_1,
% 14.30/2.78 irreflexivity_r2_xboole_0, rc1_funct_1, rc1_ordinal1, rc1_relat_1, rc1_xboole_0,
% 14.30/2.78 rc2_funct_1, rc2_ordinal1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_ordinal1,
% 14.30/2.78 rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc5_funct_1, reflexivity_r1_ordinal1,
% 14.30/2.78 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 14.30/2.78 t6_boole, t7_boole, t8_boole
% 14.30/2.78
% 14.30/2.78 Those formulas are unsatisfiable:
% 14.30/2.78 ---------------------------------
% 14.30/2.78
% 14.30/2.78 Begin of proof
% 14.30/2.78 |
% 14.30/2.78 | ALPHA: (d8_xboole_0) implies:
% 14.30/2.78 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 14.30/2.78 | subset(v0, v1) | proper_subset(v0, v1))
% 14.30/2.78 |
% 14.30/2.78 | ALPHA: (redefinition_r1_ordinal1) implies:
% 14.30/2.79 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 14.30/2.79 | ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0,
% 14.30/2.79 | v1))
% 14.30/2.79 |
% 14.30/2.79 | DELTA: instantiating (t50_ordinal1) with fresh symbols all_53_0, all_53_1
% 14.30/2.79 | gives:
% 14.30/2.79 | (3) ~ (all_53_0 = all_53_1) & $i(all_53_0) & $i(all_53_1) &
% 14.30/2.79 | ordinal(all_53_0) & ordinal(all_53_1) & ~ proper_subset(all_53_0,
% 14.30/2.79 | all_53_1) & ~ proper_subset(all_53_1, all_53_0)
% 14.30/2.79 |
% 14.30/2.79 | ALPHA: (3) implies:
% 14.30/2.79 | (4) ~ (all_53_0 = all_53_1)
% 14.30/2.79 | (5) ~ proper_subset(all_53_1, all_53_0)
% 14.30/2.79 | (6) ~ proper_subset(all_53_0, all_53_1)
% 14.30/2.79 | (7) ordinal(all_53_1)
% 14.30/2.79 | (8) ordinal(all_53_0)
% 14.30/2.79 | (9) $i(all_53_1)
% 14.30/2.79 | (10) $i(all_53_0)
% 14.30/2.79 |
% 14.30/2.79 | GROUND_INST: instantiating (connectedness_r1_ordinal1) with all_53_1,
% 14.30/2.79 | all_53_0, simplifying with (7), (8), (9), (10) gives:
% 14.30/2.79 | (11) ordinal_subset(all_53_0, all_53_1) | ordinal_subset(all_53_1,
% 14.30/2.79 | all_53_0)
% 14.30/2.79 |
% 14.30/2.79 | BETA: splitting (11) gives:
% 14.30/2.79 |
% 14.30/2.79 | Case 1:
% 14.30/2.79 | |
% 14.30/2.79 | | (12) ordinal_subset(all_53_0, all_53_1)
% 14.30/2.79 | |
% 14.30/2.79 | | GROUND_INST: instantiating (2) with all_53_0, all_53_1, simplifying with
% 14.30/2.79 | | (7), (8), (9), (10), (12) gives:
% 14.30/2.79 | | (13) subset(all_53_0, all_53_1)
% 14.30/2.79 | |
% 14.30/2.79 | | GROUND_INST: instantiating (1) with all_53_0, all_53_1, simplifying with
% 14.30/2.79 | | (6), (9), (10), (13) gives:
% 14.30/2.79 | | (14) all_53_0 = all_53_1
% 14.30/2.79 | |
% 14.30/2.79 | | REDUCE: (4), (14) imply:
% 14.30/2.79 | | (15) $false
% 14.30/2.79 | |
% 14.30/2.79 | | CLOSE: (15) is inconsistent.
% 14.30/2.79 | |
% 14.30/2.79 | Case 2:
% 14.30/2.79 | |
% 14.30/2.79 | | (16) ordinal_subset(all_53_1, all_53_0)
% 14.30/2.79 | |
% 14.30/2.79 | | GROUND_INST: instantiating (2) with all_53_1, all_53_0, simplifying with
% 14.30/2.79 | | (7), (8), (9), (10), (16) gives:
% 14.30/2.80 | | (17) subset(all_53_1, all_53_0)
% 14.30/2.80 | |
% 14.30/2.80 | | GROUND_INST: instantiating (1) with all_53_1, all_53_0, simplifying with
% 14.30/2.80 | | (5), (9), (10), (17) gives:
% 14.30/2.80 | | (18) all_53_0 = all_53_1
% 14.30/2.80 | |
% 14.30/2.80 | | REDUCE: (4), (18) imply:
% 14.30/2.80 | | (19) $false
% 14.30/2.80 | |
% 14.30/2.80 | | CLOSE: (19) is inconsistent.
% 14.30/2.80 | |
% 14.30/2.80 | End of split
% 14.30/2.80 |
% 14.30/2.80 End of proof
% 14.30/2.80 % SZS output end Proof for theBenchmark
% 14.30/2.80
% 14.30/2.80 2200ms
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