TSTP Solution File: NUM394+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM394+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 : n002.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 11:47:34 EDT 2023
% Result : Theorem 7.57s 1.82s
% Output : Proof 10.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM394+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 16:56:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.50/1.08 Prover 1: Preprocessing ...
% 2.50/1.08 Prover 4: Preprocessing ...
% 3.14/1.12 Prover 0: Preprocessing ...
% 3.14/1.12 Prover 6: Preprocessing ...
% 3.14/1.12 Prover 2: Preprocessing ...
% 3.14/1.12 Prover 3: Preprocessing ...
% 3.14/1.12 Prover 5: Preprocessing ...
% 5.30/1.45 Prover 2: Proving ...
% 5.30/1.47 Prover 5: Proving ...
% 6.05/1.53 Prover 1: Warning: ignoring some quantifiers
% 6.05/1.57 Prover 3: Warning: ignoring some quantifiers
% 6.05/1.58 Prover 1: Constructing countermodel ...
% 6.05/1.59 Prover 3: Constructing countermodel ...
% 6.05/1.59 Prover 6: Proving ...
% 6.05/1.59 Prover 4: Warning: ignoring some quantifiers
% 6.66/1.62 Prover 4: Constructing countermodel ...
% 6.66/1.67 Prover 0: Proving ...
% 7.57/1.81 Prover 5: proved (1165ms)
% 7.57/1.82
% 7.57/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.57/1.82
% 7.57/1.82 Prover 2: proved (1172ms)
% 7.57/1.82
% 7.57/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.57/1.82
% 7.57/1.82 Prover 0: stopped
% 7.57/1.82 Prover 3: stopped
% 7.57/1.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.57/1.84 Prover 6: stopped
% 7.57/1.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.57/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.57/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.57/1.85 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.57/1.88 Prover 7: Preprocessing ...
% 7.57/1.88 Prover 10: Preprocessing ...
% 8.75/1.89 Prover 8: Preprocessing ...
% 8.75/1.89 Prover 11: Preprocessing ...
% 8.75/1.93 Prover 13: Preprocessing ...
% 8.75/1.95 Prover 10: Warning: ignoring some quantifiers
% 8.75/1.95 Prover 7: Warning: ignoring some quantifiers
% 8.75/1.96 Prover 10: Constructing countermodel ...
% 8.75/1.96 Prover 7: Constructing countermodel ...
% 9.38/1.98 Prover 13: Warning: ignoring some quantifiers
% 9.38/1.99 Prover 13: Constructing countermodel ...
% 10.02/2.05 Prover 1: gave up
% 10.02/2.06 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.02/2.06 Prover 8: Warning: ignoring some quantifiers
% 10.02/2.07 Prover 8: Constructing countermodel ...
% 10.23/2.09 Prover 16: Preprocessing ...
% 10.23/2.11 Prover 7: Found proof (size 15)
% 10.23/2.11 Prover 7: proved (295ms)
% 10.23/2.11 Prover 4: stopped
% 10.23/2.11 Prover 8: stopped
% 10.23/2.12 Prover 13: stopped
% 10.23/2.12 Prover 10: stopped
% 10.23/2.12 Prover 11: Warning: ignoring some quantifiers
% 10.59/2.13 Prover 16: Warning: ignoring some quantifiers
% 10.59/2.13 Prover 11: Constructing countermodel ...
% 10.59/2.13 Prover 16: Constructing countermodel ...
% 10.59/2.14 Prover 16: stopped
% 10.59/2.14 Prover 11: stopped
% 10.59/2.14
% 10.59/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.59/2.14
% 10.59/2.14 % SZS output start Proof for theBenchmark
% 10.70/2.15 Assumptions after simplification:
% 10.70/2.15 ---------------------------------
% 10.70/2.15
% 10.70/2.15 (cc1_ordinal1)
% 10.70/2.15 ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0:
% 10.70/2.15 $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v0))
% 10.70/2.15
% 10.70/2.15 (d2_ordinal1)
% 10.70/2.15 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ epsilon_transitive(v0)
% 10.70/2.15 | ~ in(v1, v0) | subset(v1, v0)) & ? [v0: $i] : ( ~ $i(v0) |
% 10.70/2.15 epsilon_transitive(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0) & ~ subset(v1,
% 10.70/2.15 v0)))
% 10.70/2.15
% 10.70/2.15 (redefinition_r1_ordinal1)
% 10.70/2.16 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | ~
% 10.70/2.16 ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) & ! [v0: $i] : !
% 10.70/2.16 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ordinal_subset(v0, v1) | ~ ordinal(v1)
% 10.70/2.16 | ~ ordinal(v0) | subset(v0, v1))
% 10.70/2.16
% 10.70/2.16 (reflexivity_r1_ordinal1)
% 10.70/2.16 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ordinal(v1) | ~
% 10.70/2.16 ordinal(v0) | ordinal_subset(v0, v0))
% 10.70/2.16
% 10.70/2.16 (t24_ordinal1)
% 10.70/2.16 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ordinal(v1)
% 10.70/2.16 | ~ ordinal(v0) | in(v1, v0) | in(v0, v1))
% 10.70/2.16
% 10.70/2.16 (t26_ordinal1)
% 10.70/2.16 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ordinal(v1) & ordinal(v0) & ~
% 10.70/2.16 ordinal_subset(v0, v1) & ~ in(v1, v0))
% 10.70/2.16
% 10.70/2.16 Further assumptions not needed in the proof:
% 10.70/2.16 --------------------------------------------
% 10.70/2.16 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, cc2_ordinal1,
% 10.70/2.16 connectedness_r1_ordinal1, existence_m1_subset_1, fc12_relat_1, fc1_xboole_0,
% 10.70/2.16 fc4_relat_1, rc1_funct_1, rc1_ordinal1, rc1_relat_1, rc1_xboole_0, rc2_funct_1,
% 10.70/2.16 rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1, rc5_funct_1,
% 10.70/2.16 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 10.70/2.16 t6_boole, t7_boole, t8_boole
% 10.70/2.16
% 10.70/2.16 Those formulas are unsatisfiable:
% 10.70/2.16 ---------------------------------
% 10.70/2.16
% 10.70/2.16 Begin of proof
% 10.70/2.16 |
% 10.70/2.16 | ALPHA: (cc1_ordinal1) implies:
% 10.70/2.16 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v0))
% 10.70/2.16 |
% 10.70/2.16 | ALPHA: (d2_ordinal1) implies:
% 10.70/2.16 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 10.70/2.16 | epsilon_transitive(v0) | ~ in(v1, v0) | subset(v1, v0))
% 10.70/2.16 |
% 10.70/2.16 | ALPHA: (redefinition_r1_ordinal1) implies:
% 10.70/2.17 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1)
% 10.70/2.17 | | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1))
% 10.70/2.17 |
% 10.70/2.17 | DELTA: instantiating (t26_ordinal1) with fresh symbols all_48_0, all_48_1
% 10.70/2.17 | gives:
% 10.70/2.17 | (4) $i(all_48_0) & $i(all_48_1) & ordinal(all_48_0) & ordinal(all_48_1) &
% 10.70/2.17 | ~ ordinal_subset(all_48_1, all_48_0) & ~ in(all_48_0, all_48_1)
% 10.70/2.17 |
% 10.70/2.17 | ALPHA: (4) implies:
% 10.70/2.17 | (5) ~ in(all_48_0, all_48_1)
% 10.70/2.17 | (6) ~ ordinal_subset(all_48_1, all_48_0)
% 10.70/2.17 | (7) ordinal(all_48_1)
% 10.70/2.17 | (8) ordinal(all_48_0)
% 10.70/2.17 | (9) $i(all_48_1)
% 10.70/2.17 | (10) $i(all_48_0)
% 10.70/2.17 |
% 10.70/2.17 | GROUND_INST: instantiating (t24_ordinal1) with all_48_1, all_48_0, simplifying
% 10.70/2.17 | with (5), (7), (8), (9), (10) gives:
% 10.70/2.17 | (11) all_48_0 = all_48_1 | in(all_48_1, all_48_0)
% 10.70/2.17 |
% 10.70/2.17 | GROUND_INST: instantiating (reflexivity_r1_ordinal1) with all_48_1, all_48_0,
% 10.70/2.17 | simplifying with (7), (8), (9), (10) gives:
% 10.70/2.17 | (12) ordinal_subset(all_48_1, all_48_1)
% 10.70/2.17 |
% 10.70/2.17 | GROUND_INST: instantiating (1) with all_48_0, simplifying with (8), (10)
% 10.70/2.17 | gives:
% 10.70/2.17 | (13) epsilon_transitive(all_48_0)
% 10.70/2.17 |
% 10.70/2.17 | PRED_UNIFY: (6), (12) imply:
% 10.70/2.17 | (14) ~ (all_48_0 = all_48_1)
% 10.70/2.17 |
% 10.70/2.17 | BETA: splitting (11) gives:
% 10.70/2.17 |
% 10.70/2.17 | Case 1:
% 10.70/2.17 | |
% 10.70/2.17 | | (15) in(all_48_1, all_48_0)
% 10.70/2.17 | |
% 10.70/2.17 | | GROUND_INST: instantiating (2) with all_48_0, all_48_1, simplifying with
% 10.70/2.17 | | (9), (10), (13), (15) gives:
% 10.70/2.17 | | (16) subset(all_48_1, all_48_0)
% 10.70/2.17 | |
% 10.70/2.17 | | GROUND_INST: instantiating (3) with all_48_1, all_48_0, simplifying with
% 10.70/2.17 | | (6), (7), (8), (9), (10), (16) gives:
% 10.70/2.17 | | (17) $false
% 10.70/2.17 | |
% 10.70/2.17 | | CLOSE: (17) is inconsistent.
% 10.70/2.17 | |
% 10.70/2.17 | Case 2:
% 10.70/2.17 | |
% 10.70/2.17 | | (18) all_48_0 = all_48_1
% 10.70/2.17 | |
% 10.70/2.17 | | REDUCE: (14), (18) imply:
% 10.70/2.17 | | (19) $false
% 10.70/2.17 | |
% 10.70/2.17 | | CLOSE: (19) is inconsistent.
% 10.70/2.17 | |
% 10.70/2.17 | End of split
% 10.70/2.17 |
% 10.70/2.17 End of proof
% 10.70/2.18 % SZS output end Proof for theBenchmark
% 10.70/2.18
% 10.70/2.18 1552ms
%------------------------------------------------------------------------------