TSTP Solution File: NUM390+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM390+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 : n022.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 11:47:33 EDT 2023
% Result : Theorem 8.15s 1.90s
% Output : Proof 11.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM390+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 11:47:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.31/1.07 Prover 1: Preprocessing ...
% 2.31/1.07 Prover 4: Preprocessing ...
% 3.06/1.11 Prover 3: Preprocessing ...
% 3.06/1.11 Prover 5: Preprocessing ...
% 3.06/1.12 Prover 2: Preprocessing ...
% 3.06/1.12 Prover 0: Preprocessing ...
% 3.06/1.12 Prover 6: Preprocessing ...
% 5.00/1.44 Prover 5: Proving ...
% 5.00/1.45 Prover 2: Proving ...
% 5.93/1.56 Prover 1: Warning: ignoring some quantifiers
% 5.93/1.58 Prover 1: Constructing countermodel ...
% 5.93/1.59 Prover 6: Proving ...
% 5.93/1.60 Prover 3: Warning: ignoring some quantifiers
% 5.93/1.62 Prover 3: Constructing countermodel ...
% 5.93/1.63 Prover 4: Warning: ignoring some quantifiers
% 6.64/1.67 Prover 4: Constructing countermodel ...
% 7.44/1.76 Prover 0: Proving ...
% 8.15/1.90 Prover 2: proved (1254ms)
% 8.15/1.90
% 8.15/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.15/1.90
% 8.15/1.91 Prover 5: stopped
% 8.15/1.91 Prover 3: stopped
% 8.15/1.91 Prover 6: stopped
% 8.15/1.91 Prover 0: stopped
% 8.15/1.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.15/1.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.15/1.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.15/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.15/1.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.87/1.99 Prover 11: Preprocessing ...
% 9.19/2.00 Prover 7: Preprocessing ...
% 9.19/2.01 Prover 1: gave up
% 9.19/2.01 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.19/2.01 Prover 8: Preprocessing ...
% 9.19/2.01 Prover 13: Preprocessing ...
% 9.19/2.02 Prover 10: Preprocessing ...
% 9.19/2.04 Prover 16: Preprocessing ...
% 9.61/2.10 Prover 7: Warning: ignoring some quantifiers
% 9.61/2.10 Prover 10: Warning: ignoring some quantifiers
% 9.61/2.11 Prover 10: Constructing countermodel ...
% 9.61/2.11 Prover 13: Warning: ignoring some quantifiers
% 9.61/2.12 Prover 16: Warning: ignoring some quantifiers
% 9.61/2.12 Prover 7: Constructing countermodel ...
% 9.61/2.13 Prover 13: Constructing countermodel ...
% 9.61/2.13 Prover 16: Constructing countermodel ...
% 9.61/2.14 Prover 8: Warning: ignoring some quantifiers
% 9.73/2.16 Prover 8: Constructing countermodel ...
% 11.12/2.29 Prover 11: Warning: ignoring some quantifiers
% 11.12/2.31 Prover 11: Constructing countermodel ...
% 11.12/2.32 Prover 7: Found proof (size 17)
% 11.12/2.32 Prover 7: proved (410ms)
% 11.12/2.32 Prover 10: Found proof (size 24)
% 11.12/2.32 Prover 10: proved (410ms)
% 11.12/2.32 Prover 4: stopped
% 11.12/2.32 Prover 16: stopped
% 11.12/2.32 Prover 13: stopped
% 11.12/2.32 Prover 8: stopped
% 11.12/2.33 Prover 11: stopped
% 11.12/2.33
% 11.12/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.12/2.33
% 11.12/2.33 % SZS output start Proof for theBenchmark
% 11.12/2.33 Assumptions after simplification:
% 11.12/2.33 ---------------------------------
% 11.12/2.34
% 11.12/2.34 (cc1_ordinal1)
% 11.12/2.34 ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0:
% 11.12/2.34 $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v0))
% 11.12/2.34
% 11.12/2.34 (d2_ordinal1)
% 11.12/2.34 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ epsilon_transitive(v0)
% 11.12/2.34 | ~ in(v1, v0) | subset(v1, v0)) & ? [v0: $i] : ( ~ $i(v0) |
% 11.12/2.34 epsilon_transitive(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0) & ~ subset(v1,
% 11.12/2.34 v0)))
% 11.12/2.34
% 11.12/2.34 (d8_xboole_0)
% 11.12/2.34 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ subset(v0,
% 11.12/2.34 v1) | proper_subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 11.12/2.34 $i(v0) | ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0: $i] : ( ~
% 11.71/2.34 $i(v0) | ~ proper_subset(v0, v0))
% 11.71/2.34
% 11.71/2.34 (t1_xboole_1)
% 11.71/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 11.71/2.35 ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2))
% 11.71/2.35
% 11.71/2.35 (t21_ordinal1)
% 11.71/2.35 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ epsilon_transitive(v0)
% 11.71/2.35 | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1))
% 11.71/2.35
% 11.71/2.35 (t22_ordinal1)
% 11.71/2.35 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) &
% 11.71/2.35 subset(v0, v1) & epsilon_transitive(v0) & ordinal(v2) & ordinal(v1) & in(v1,
% 11.71/2.35 v2) & ~ in(v0, v2))
% 11.71/2.35
% 11.71/2.35 (t7_ordinal1)
% 11.71/2.35 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v1, v0) | ~
% 11.71/2.35 in(v0, v1))
% 11.71/2.35
% 11.71/2.35 Further assumptions not needed in the proof:
% 11.71/2.35 --------------------------------------------
% 11.71/2.35 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_relat_1,
% 11.71/2.35 cc2_funct_1, cc2_ordinal1, existence_m1_subset_1, fc12_relat_1, fc1_xboole_0,
% 11.71/2.35 fc4_relat_1, irreflexivity_r2_xboole_0, rc1_funct_1, rc1_ordinal1, rc1_relat_1,
% 11.71/2.35 rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1,
% 11.71/2.35 rc4_funct_1, rc5_funct_1, reflexivity_r1_tarski, t1_subset, t2_subset,
% 11.71/2.35 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 11.71/2.35
% 11.71/2.35 Those formulas are unsatisfiable:
% 11.71/2.35 ---------------------------------
% 11.71/2.35
% 11.71/2.35 Begin of proof
% 11.71/2.35 |
% 11.71/2.35 | ALPHA: (cc1_ordinal1) implies:
% 11.71/2.35 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v0))
% 11.71/2.35 |
% 11.71/2.35 | ALPHA: (d2_ordinal1) implies:
% 11.71/2.35 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 11.71/2.35 | epsilon_transitive(v0) | ~ in(v1, v0) | subset(v1, v0))
% 11.71/2.35 |
% 11.71/2.35 | ALPHA: (d8_xboole_0) implies:
% 11.71/2.35 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 11.71/2.35 | subset(v0, v1) | proper_subset(v0, v1))
% 11.71/2.35 |
% 11.71/2.35 | DELTA: instantiating (t22_ordinal1) with fresh symbols all_50_0, all_50_1,
% 11.71/2.35 | all_50_2 gives:
% 11.71/2.35 | (4) $i(all_50_0) & $i(all_50_1) & $i(all_50_2) & subset(all_50_2, all_50_1)
% 11.71/2.35 | & epsilon_transitive(all_50_2) & ordinal(all_50_0) & ordinal(all_50_1)
% 11.71/2.35 | & in(all_50_1, all_50_0) & ~ in(all_50_2, all_50_0)
% 11.71/2.35 |
% 11.71/2.35 | ALPHA: (4) implies:
% 11.71/2.36 | (5) ~ in(all_50_2, all_50_0)
% 11.71/2.36 | (6) in(all_50_1, all_50_0)
% 11.71/2.36 | (7) ordinal(all_50_0)
% 11.71/2.36 | (8) epsilon_transitive(all_50_2)
% 11.71/2.36 | (9) subset(all_50_2, all_50_1)
% 11.71/2.36 | (10) $i(all_50_2)
% 11.71/2.36 | (11) $i(all_50_1)
% 11.71/2.36 | (12) $i(all_50_0)
% 11.71/2.36 |
% 11.71/2.36 | GROUND_INST: instantiating (1) with all_50_0, simplifying with (7), (12)
% 11.71/2.36 | gives:
% 11.71/2.36 | (13) epsilon_transitive(all_50_0)
% 11.71/2.36 |
% 11.71/2.36 | GROUND_INST: instantiating (t7_ordinal1) with all_50_1, all_50_2, simplifying
% 11.71/2.36 | with (9), (10), (11) gives:
% 11.71/2.36 | (14) ~ in(all_50_1, all_50_2)
% 11.71/2.36 |
% 11.71/2.36 | PRED_UNIFY: (6), (14) imply:
% 11.71/2.36 | (15) ~ (all_50_0 = all_50_2)
% 11.71/2.36 |
% 11.71/2.36 | GROUND_INST: instantiating (2) with all_50_0, all_50_1, simplifying with (6),
% 11.71/2.36 | (11), (12), (13) gives:
% 11.71/2.36 | (16) subset(all_50_1, all_50_0)
% 11.71/2.36 |
% 11.71/2.36 | GROUND_INST: instantiating (t1_xboole_1) with all_50_2, all_50_1, all_50_0,
% 11.71/2.36 | simplifying with (9), (10), (11), (12), (16) gives:
% 11.71/2.36 | (17) subset(all_50_2, all_50_0)
% 11.71/2.36 |
% 11.71/2.36 | GROUND_INST: instantiating (3) with all_50_2, all_50_0, simplifying with (10),
% 11.71/2.36 | (12), (17) gives:
% 11.71/2.36 | (18) all_50_0 = all_50_2 | proper_subset(all_50_2, all_50_0)
% 11.71/2.36 |
% 11.71/2.36 | BETA: splitting (18) gives:
% 11.71/2.36 |
% 11.71/2.36 | Case 1:
% 11.71/2.36 | |
% 11.71/2.36 | | (19) proper_subset(all_50_2, all_50_0)
% 11.71/2.36 | |
% 11.71/2.36 | | GROUND_INST: instantiating (t21_ordinal1) with all_50_2, all_50_0,
% 11.71/2.36 | | simplifying with (5), (7), (8), (10), (12), (19) gives:
% 11.71/2.36 | | (20) $false
% 11.71/2.36 | |
% 11.71/2.36 | | CLOSE: (20) is inconsistent.
% 11.71/2.36 | |
% 11.71/2.36 | Case 2:
% 11.71/2.36 | |
% 11.71/2.36 | | (21) all_50_0 = all_50_2
% 11.71/2.36 | |
% 11.71/2.36 | | REDUCE: (15), (21) imply:
% 11.71/2.36 | | (22) $false
% 11.71/2.36 | |
% 11.71/2.36 | | CLOSE: (22) is inconsistent.
% 11.71/2.36 | |
% 11.71/2.36 | End of split
% 11.71/2.36 |
% 11.71/2.36 End of proof
% 11.71/2.36 % SZS output end Proof for theBenchmark
% 11.71/2.36
% 11.71/2.36 1744ms
%------------------------------------------------------------------------------