TSTP Solution File: SET063+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET063+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n018.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 15:23:30 EDT 2023
% Result : Theorem 20.16s 3.60s
% Output : Proof 31.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET063+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.31 % Computer : n018.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Sat Aug 26 09:03:59 EDT 2023
% 0.12/0.31 % CPUTime :
% 0.16/0.60 ________ _____
% 0.16/0.60 ___ __ \_________(_)________________________________
% 0.16/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.60
% 0.16/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.60 (2023-06-19)
% 0.16/0.60
% 0.16/0.60 (c) Philipp Rümmer, 2009-2023
% 0.16/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.60 Amanda Stjerna.
% 0.16/0.60 Free software under BSD-3-Clause.
% 0.16/0.60
% 0.16/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.60
% 0.16/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.16/0.61 Running up to 7 provers in parallel.
% 0.16/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.16/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 3.38/1.27 Prover 4: Preprocessing ...
% 3.38/1.27 Prover 1: Preprocessing ...
% 3.87/1.32 Prover 2: Preprocessing ...
% 3.87/1.32 Prover 3: Preprocessing ...
% 3.87/1.32 Prover 5: Preprocessing ...
% 3.87/1.32 Prover 0: Preprocessing ...
% 3.87/1.32 Prover 6: Preprocessing ...
% 10.00/2.28 Prover 1: Warning: ignoring some quantifiers
% 12.23/2.48 Prover 5: Proving ...
% 12.23/2.48 Prover 3: Warning: ignoring some quantifiers
% 12.23/2.49 Prover 1: Constructing countermodel ...
% 12.23/2.50 Prover 6: Proving ...
% 12.23/2.51 Prover 3: Constructing countermodel ...
% 12.23/2.54 Prover 4: Warning: ignoring some quantifiers
% 12.96/2.61 Prover 4: Constructing countermodel ...
% 13.47/2.69 Prover 2: Proving ...
% 14.03/2.74 Prover 0: Proving ...
% 20.16/3.59 Prover 0: proved (2971ms)
% 20.16/3.60
% 20.16/3.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.16/3.60
% 20.16/3.60 Prover 3: stopped
% 20.16/3.60 Prover 5: stopped
% 20.16/3.60 Prover 2: stopped
% 20.61/3.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 20.61/3.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 20.61/3.62 Prover 6: stopped
% 20.61/3.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 20.61/3.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 20.61/3.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 20.61/3.73 Prover 8: Preprocessing ...
% 20.61/3.73 Prover 7: Preprocessing ...
% 20.61/3.82 Prover 11: Preprocessing ...
% 20.61/3.82 Prover 13: Preprocessing ...
% 20.61/3.82 Prover 10: Preprocessing ...
% 22.95/4.00 Prover 7: Warning: ignoring some quantifiers
% 22.95/4.01 Prover 8: Warning: ignoring some quantifiers
% 22.95/4.02 Prover 7: Constructing countermodel ...
% 23.77/4.06 Prover 8: Constructing countermodel ...
% 24.07/4.10 Prover 10: Warning: ignoring some quantifiers
% 24.45/4.15 Prover 10: Constructing countermodel ...
% 24.57/4.17 Prover 11: Warning: ignoring some quantifiers
% 24.57/4.18 Prover 13: Warning: ignoring some quantifiers
% 24.57/4.20 Prover 13: Constructing countermodel ...
% 25.06/4.24 Prover 11: Constructing countermodel ...
% 26.75/4.53 Prover 10: gave up
% 26.75/4.56 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 26.75/4.62 Prover 16: Preprocessing ...
% 28.86/4.82 Prover 16: Warning: ignoring some quantifiers
% 28.86/4.83 Prover 16: Constructing countermodel ...
% 31.25/5.08 Prover 4: Found proof (size 22)
% 31.25/5.08 Prover 4: proved (4444ms)
% 31.25/5.08 Prover 1: stopped
% 31.25/5.08 Prover 11: stopped
% 31.25/5.08 Prover 16: stopped
% 31.25/5.08 Prover 7: stopped
% 31.25/5.08 Prover 13: stopped
% 31.25/5.09 Prover 8: stopped
% 31.25/5.09
% 31.25/5.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.25/5.09
% 31.25/5.09 % SZS output start Proof for theBenchmark
% 31.25/5.10 Assumptions after simplification:
% 31.25/5.10 ---------------------------------
% 31.25/5.10
% 31.25/5.10 (corollary_of_null_class_is_subclass)
% 31.25/5.13 $i(null_class) & ? [v0: $i] : ( ~ (v0 = null_class) & subclass(v0,
% 31.25/5.13 null_class) = 0 & $i(v0))
% 31.25/5.13
% 31.25/5.13 (extensionality)
% 31.25/5.13 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subclass(v1, v0) = 0) | ~ $i(v1) |
% 31.25/5.13 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subclass(v0, v1) = v2)) & ! [v0:
% 31.25/5.13 $i] : ! [v1: $i] : (v1 = v0 | ~ (subclass(v0, v1) = 0) | ~ $i(v1) | ~
% 31.25/5.13 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subclass(v1, v0) = v2)) & ! [v0: $i]
% 31.25/5.13 : ! [v1: int] : (v1 = 0 | ~ (subclass(v0, v0) = v1) | ~ $i(v0))
% 31.25/5.13
% 31.25/5.13 (null_class_defn)
% 31.71/5.14 $i(null_class) & ! [v0: $i] : ( ~ (member(v0, null_class) = 0) | ~ $i(v0))
% 31.71/5.14
% 31.71/5.14 (subclass_defn)
% 31.71/5.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 31.71/5.14 (subclass(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 31.71/5.14 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i]
% 31.71/5.14 : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0, v1) = v2) | ~
% 31.71/5.14 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3,
% 31.71/5.14 v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] :
% 31.71/5.14 ! [v2: $i] : ( ~ (subclass(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2)
% 31.71/5.14 | ~ $i(v1) | ~ $i(v0) | member(v2, v1) = 0)
% 31.71/5.14
% 31.71/5.14 Further assumptions not needed in the proof:
% 31.71/5.14 --------------------------------------------
% 31.71/5.14 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 31.71/5.14 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 31.71/5.14 element_relation, element_relation_defn, first_second, flip, flip_defn,
% 31.71/5.14 function_defn, identity_relation, image_defn, inductive_defn, infinity,
% 31.71/5.14 intersection, inverse_defn, ordered_pair_defn, power_class, power_class_defn,
% 31.71/5.14 range_of_defn, regularity, replacement, restrict_defn, rotate, rotate_defn,
% 31.71/5.14 singleton_set_defn, successor_defn, successor_relation_defn1,
% 31.71/5.14 successor_relation_defn2, sum_class, sum_class_defn, union_defn, unordered_pair,
% 31.71/5.14 unordered_pair_defn
% 31.71/5.14
% 31.71/5.14 Those formulas are unsatisfiable:
% 31.71/5.14 ---------------------------------
% 31.71/5.14
% 31.71/5.14 Begin of proof
% 31.71/5.14 |
% 31.71/5.14 | ALPHA: (subclass_defn) implies:
% 31.71/5.15 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0,
% 31.71/5.15 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 31.71/5.15 | ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 31.71/5.15 |
% 31.71/5.15 | ALPHA: (extensionality) implies:
% 31.71/5.15 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subclass(v1, v0) = 0) | ~
% 31.71/5.15 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subclass(v0, v1) =
% 31.71/5.15 | v2))
% 31.71/5.15 |
% 31.71/5.15 | ALPHA: (null_class_defn) implies:
% 31.71/5.15 | (3) ! [v0: $i] : ( ~ (member(v0, null_class) = 0) | ~ $i(v0))
% 31.71/5.15 |
% 31.71/5.15 | ALPHA: (corollary_of_null_class_is_subclass) implies:
% 31.71/5.15 | (4) $i(null_class)
% 31.71/5.15 | (5) ? [v0: $i] : ( ~ (v0 = null_class) & subclass(v0, null_class) = 0 &
% 31.71/5.15 | $i(v0))
% 31.71/5.15 |
% 31.71/5.15 | DELTA: instantiating (5) with fresh symbol all_38_0 gives:
% 31.71/5.15 | (6) ~ (all_38_0 = null_class) & subclass(all_38_0, null_class) = 0 &
% 31.71/5.15 | $i(all_38_0)
% 31.71/5.15 |
% 31.71/5.15 | ALPHA: (6) implies:
% 31.71/5.15 | (7) ~ (all_38_0 = null_class)
% 31.71/5.15 | (8) $i(all_38_0)
% 31.71/5.15 | (9) subclass(all_38_0, null_class) = 0
% 31.71/5.15 |
% 31.71/5.15 | GROUND_INST: instantiating (2) with null_class, all_38_0, simplifying with
% 31.71/5.15 | (4), (8), (9) gives:
% 31.71/5.15 | (10) all_38_0 = null_class | ? [v0: int] : ( ~ (v0 = 0) &
% 31.71/5.15 | subclass(null_class, all_38_0) = v0)
% 31.71/5.15 |
% 31.71/5.15 | BETA: splitting (10) gives:
% 31.71/5.15 |
% 31.71/5.15 | Case 1:
% 31.71/5.15 | |
% 31.71/5.15 | | (11) all_38_0 = null_class
% 31.71/5.15 | |
% 31.71/5.15 | | REDUCE: (7), (11) imply:
% 31.71/5.15 | | (12) $false
% 31.71/5.16 | |
% 31.71/5.16 | | CLOSE: (12) is inconsistent.
% 31.71/5.16 | |
% 31.71/5.16 | Case 2:
% 31.71/5.16 | |
% 31.71/5.16 | | (13) ? [v0: int] : ( ~ (v0 = 0) & subclass(null_class, all_38_0) = v0)
% 31.71/5.16 | |
% 31.71/5.16 | | DELTA: instantiating (13) with fresh symbol all_115_0 gives:
% 31.71/5.16 | | (14) ~ (all_115_0 = 0) & subclass(null_class, all_38_0) = all_115_0
% 31.71/5.16 | |
% 31.71/5.16 | | ALPHA: (14) implies:
% 31.71/5.16 | | (15) ~ (all_115_0 = 0)
% 31.71/5.16 | | (16) subclass(null_class, all_38_0) = all_115_0
% 31.71/5.16 | |
% 31.71/5.16 | | GROUND_INST: instantiating (1) with null_class, all_38_0, all_115_0,
% 31.71/5.16 | | simplifying with (4), (8), (16) gives:
% 31.71/5.16 | | (17) all_115_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 31.71/5.16 | | member(v0, all_38_0) = v1 & member(v0, null_class) = 0 & $i(v0))
% 31.71/5.16 | |
% 31.71/5.16 | | BETA: splitting (17) gives:
% 31.71/5.16 | |
% 31.71/5.16 | | Case 1:
% 31.71/5.16 | | |
% 31.71/5.16 | | | (18) all_115_0 = 0
% 31.71/5.16 | | |
% 31.71/5.16 | | | REDUCE: (15), (18) imply:
% 31.71/5.16 | | | (19) $false
% 31.71/5.16 | | |
% 31.71/5.16 | | | CLOSE: (19) is inconsistent.
% 31.71/5.16 | | |
% 31.71/5.16 | | Case 2:
% 31.71/5.16 | | |
% 31.71/5.16 | | | (20) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_38_0) =
% 31.71/5.16 | | | v1 & member(v0, null_class) = 0 & $i(v0))
% 31.71/5.16 | | |
% 31.71/5.16 | | | DELTA: instantiating (20) with fresh symbols all_254_0, all_254_1 gives:
% 31.71/5.16 | | | (21) ~ (all_254_0 = 0) & member(all_254_1, all_38_0) = all_254_0 &
% 31.71/5.16 | | | member(all_254_1, null_class) = 0 & $i(all_254_1)
% 31.71/5.16 | | |
% 31.71/5.16 | | | ALPHA: (21) implies:
% 31.71/5.16 | | | (22) $i(all_254_1)
% 31.71/5.16 | | | (23) member(all_254_1, null_class) = 0
% 31.71/5.16 | | |
% 31.71/5.16 | | | GROUND_INST: instantiating (3) with all_254_1, simplifying with (22), (23)
% 31.71/5.16 | | | gives:
% 31.71/5.16 | | | (24) $false
% 31.71/5.16 | | |
% 31.71/5.16 | | | CLOSE: (24) is inconsistent.
% 31.71/5.16 | | |
% 31.71/5.16 | | End of split
% 31.71/5.16 | |
% 31.71/5.16 | End of split
% 31.71/5.16 |
% 31.71/5.16 End of proof
% 31.71/5.16 % SZS output end Proof for theBenchmark
% 31.71/5.16
% 31.71/5.16 4563ms
%------------------------------------------------------------------------------