TSTP Solution File: SEU117+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU117+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 17:42:34 EDT 2023
% Result : Theorem 9.38s 2.08s
% Output : Proof 11.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU117+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n002.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 : Wed Aug 23 14:55:16 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 ...
% 0.21/0.64 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 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 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 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
% 2.52/1.11 Prover 1: Preprocessing ...
% 2.52/1.11 Prover 4: Preprocessing ...
% 3.11/1.15 Prover 2: Preprocessing ...
% 3.11/1.15 Prover 5: Preprocessing ...
% 3.11/1.15 Prover 0: Preprocessing ...
% 3.11/1.15 Prover 6: Preprocessing ...
% 3.11/1.15 Prover 3: Preprocessing ...
% 5.38/1.57 Prover 1: Warning: ignoring some quantifiers
% 5.96/1.58 Prover 2: Proving ...
% 6.04/1.59 Prover 1: Constructing countermodel ...
% 6.04/1.59 Prover 5: Proving ...
% 6.04/1.60 Prover 6: Proving ...
% 6.04/1.60 Prover 4: Warning: ignoring some quantifiers
% 6.04/1.60 Prover 3: Warning: ignoring some quantifiers
% 6.22/1.62 Prover 3: Constructing countermodel ...
% 6.32/1.65 Prover 4: Constructing countermodel ...
% 6.93/1.77 Prover 0: Proving ...
% 9.38/2.08 Prover 3: proved (1428ms)
% 9.38/2.08
% 9.38/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.38/2.08
% 9.38/2.08 Prover 6: stopped
% 9.38/2.08 Prover 5: stopped
% 9.38/2.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.38/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.38/2.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.38/2.09 Prover 2: stopped
% 9.38/2.09 Prover 0: stopped
% 9.38/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.38/2.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.07/2.17 Prover 10: Preprocessing ...
% 10.07/2.17 Prover 8: Preprocessing ...
% 10.07/2.18 Prover 13: Preprocessing ...
% 10.07/2.18 Prover 7: Preprocessing ...
% 10.07/2.18 Prover 11: Preprocessing ...
% 10.67/2.25 Prover 1: Found proof (size 39)
% 10.67/2.26 Prover 1: proved (1609ms)
% 10.67/2.26 Prover 13: Warning: ignoring some quantifiers
% 10.67/2.26 Prover 10: Warning: ignoring some quantifiers
% 10.67/2.26 Prover 4: stopped
% 10.67/2.26 Prover 7: Warning: ignoring some quantifiers
% 10.67/2.27 Prover 11: stopped
% 10.67/2.27 Prover 10: Constructing countermodel ...
% 10.97/2.27 Prover 13: Constructing countermodel ...
% 10.97/2.27 Prover 7: Constructing countermodel ...
% 10.97/2.28 Prover 10: stopped
% 10.97/2.28 Prover 7: stopped
% 10.97/2.28 Prover 13: stopped
% 10.97/2.30 Prover 8: Warning: ignoring some quantifiers
% 10.97/2.31 Prover 8: Constructing countermodel ...
% 10.97/2.31 Prover 8: stopped
% 10.97/2.31
% 10.97/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.97/2.31
% 10.97/2.32 % SZS output start Proof for theBenchmark
% 10.97/2.32 Assumptions after simplification:
% 10.97/2.32 ---------------------------------
% 10.97/2.32
% 10.97/2.33 (d5_finsub_1)
% 11.31/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = v2) | ~
% 11.31/2.35 (preboolean(v1) = 0) | ~ $i(v1) | ~ $i(v0) | (( ~ (v2 = v1) | ( ! [v3: $i]
% 11.31/2.35 : ! [v4: any] : ( ~ (subset(v3, v0) = v4) | ~ $i(v3) | ? [v5: any]
% 11.31/2.35 : ? [v6: any] : (in(v3, v1) = v5 & finite(v3) = v6 & ( ~ (v5 = 0) |
% 11.31/2.35 (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (subset(v3, v0) = 0) |
% 11.31/2.35 ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 &
% 11.31/2.35 finite(v3) = v4 & ( ~ (v4 = 0) | v5 = 0))))) & (v2 = v1 | ? [v3:
% 11.31/2.35 $i] : ? [v4: any] : ? [v5: any] : ? [v6: any] : (subset(v3, v0) =
% 11.31/2.35 v5 & in(v3, v1) = v4 & finite(v3) = v6 & $i(v3) & ( ~ (v6 = 0) | ~
% 11.31/2.35 (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v6 = 0 & v5 = 0))))))
% 11.31/2.35
% 11.31/2.35 (fc2_finsub_1)
% 11.31/2.36 ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) |
% 11.31/2.36 diff_closed(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) =
% 11.31/2.36 v1) | ~ $i(v0) | cup_closed(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.31/2.36 (finite_subsets(v0) = v1) | ~ $i(v0) | preboolean(v1) = 0) & ! [v0: $i] :
% 11.31/2.36 ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~
% 11.31/2.36 (v2 = 0) & empty(v1) = v2))
% 11.31/2.36
% 11.31/2.36 (t2_subset)
% 11.31/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 11.31/2.36 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 &
% 11.31/2.36 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 11.31/2.36
% 11.31/2.36 (t32_finsub_1)
% 11.31/2.36 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 11.31/2.36 = 0) & finite_subsets(v0) = v2 & powerset(v0) = v3 & element(v1, v3) = v4
% 11.31/2.36 & element(v1, v2) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.31/2.36
% 11.31/2.36 (t3_subset)
% 11.31/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 11.31/2.36 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 11.31/2.36 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i]
% 11.31/2.36 : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1)
% 11.31/2.36 | ~ $i(v0) | subset(v0, v1) = 0)
% 11.31/2.36
% 11.31/2.36 (function-axioms)
% 11.43/2.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.43/2.37 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 11.43/2.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 11.43/2.37 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 11.43/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.43/2.37 : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0:
% 11.43/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.43/2.37 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 11.43/2.37 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1)
% 11.43/2.37 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.43/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~
% 11.43/2.37 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.43/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) =
% 11.43/2.37 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.43/2.37 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) =
% 11.43/2.37 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.43/2.37 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~
% 11.43/2.37 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.43/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (natural(v2) = v1) | ~
% 11.43/2.37 (natural(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.43/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cap_closed(v2) = v1) | ~
% 11.43/2.37 (cap_closed(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 11.43/2.37 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) & ! [v0: $i]
% 11.43/2.37 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 11.43/2.37 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.43/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (finite(v2) = v1) | ~
% 11.43/2.37 (finite(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 11.43/2.37 : ! [v2: $i] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) =
% 11.43/2.37 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.43/2.37 $i] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0)) & !
% 11.43/2.37 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 11.43/2.37 | ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0)) & ! [v0:
% 11.43/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.43/2.37 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 11.43/2.37
% 11.43/2.37 Further assumptions not needed in the proof:
% 11.43/2.37 --------------------------------------------
% 11.43/2.37 antisymmetry_r2_hidden, cc1_finset_1, cc1_finsub_1, cc2_finset_1, cc2_finsub_1,
% 11.43/2.37 cc3_finsub_1, dt_k5_finsub_1, existence_m1_subset_1, fc1_finsub_1, fc1_subset_1,
% 11.43/2.37 fc1_xboole_0, rc1_finset_1, rc1_finsub_1, rc1_subset_1, rc1_xboole_0,
% 11.43/2.37 rc2_finset_1, rc2_subset_1, rc2_xboole_0, rc3_finset_1, rc4_finset_1,
% 11.43/2.37 reflexivity_r1_tarski, t1_subset, t4_subset, t5_subset, t6_boole, t7_boole,
% 11.43/2.37 t8_boole
% 11.43/2.37
% 11.43/2.37 Those formulas are unsatisfiable:
% 11.43/2.37 ---------------------------------
% 11.43/2.37
% 11.43/2.37 Begin of proof
% 11.43/2.37 |
% 11.43/2.37 | ALPHA: (fc2_finsub_1) implies:
% 11.43/2.37 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) |
% 11.43/2.37 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 11.43/2.37 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) |
% 11.43/2.37 | preboolean(v1) = 0)
% 11.43/2.38 |
% 11.43/2.38 | ALPHA: (t3_subset) implies:
% 11.43/2.38 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 11.43/2.38 | (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~
% 11.43/2.38 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 11.43/2.38 |
% 11.43/2.38 | ALPHA: (function-axioms) implies:
% 11.43/2.38 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.43/2.38 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 11.43/2.38 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.43/2.38 | ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 11.43/2.38 | v2) = v0))
% 11.43/2.38 |
% 11.43/2.38 | DELTA: instantiating (t32_finsub_1) with fresh symbols all_39_0, all_39_1,
% 11.43/2.38 | all_39_2, all_39_3, all_39_4 gives:
% 11.43/2.38 | (6) ~ (all_39_0 = 0) & finite_subsets(all_39_4) = all_39_2 &
% 11.43/2.38 | powerset(all_39_4) = all_39_1 & element(all_39_3, all_39_1) = all_39_0
% 11.43/2.38 | & element(all_39_3, all_39_2) = 0 & $i(all_39_1) & $i(all_39_2) &
% 11.43/2.38 | $i(all_39_3) & $i(all_39_4)
% 11.43/2.38 |
% 11.43/2.38 | ALPHA: (6) implies:
% 11.43/2.38 | (7) ~ (all_39_0 = 0)
% 11.43/2.38 | (8) $i(all_39_4)
% 11.43/2.38 | (9) $i(all_39_3)
% 11.43/2.38 | (10) $i(all_39_2)
% 11.43/2.38 | (11) element(all_39_3, all_39_2) = 0
% 11.43/2.38 | (12) element(all_39_3, all_39_1) = all_39_0
% 11.43/2.38 | (13) powerset(all_39_4) = all_39_1
% 11.43/2.38 | (14) finite_subsets(all_39_4) = all_39_2
% 11.43/2.38 |
% 11.43/2.38 | GROUND_INST: instantiating (3) with all_39_3, all_39_4, all_39_1, all_39_0,
% 11.43/2.38 | simplifying with (8), (9), (12), (13) gives:
% 11.43/2.38 | (15) all_39_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_39_3,
% 11.43/2.38 | all_39_4) = v0)
% 11.43/2.38 |
% 11.43/2.38 | GROUND_INST: instantiating (2) with all_39_4, all_39_2, simplifying with (8),
% 11.43/2.38 | (14) gives:
% 11.43/2.38 | (16) preboolean(all_39_2) = 0
% 11.43/2.38 |
% 11.43/2.38 | GROUND_INST: instantiating (1) with all_39_4, all_39_2, simplifying with (8),
% 11.43/2.38 | (14) gives:
% 11.43/2.38 | (17) ? [v0: int] : ( ~ (v0 = 0) & empty(all_39_2) = v0)
% 11.43/2.38 |
% 11.43/2.38 | DELTA: instantiating (17) with fresh symbol all_49_0 gives:
% 11.43/2.38 | (18) ~ (all_49_0 = 0) & empty(all_39_2) = all_49_0
% 11.43/2.38 |
% 11.43/2.38 | ALPHA: (18) implies:
% 11.43/2.38 | (19) ~ (all_49_0 = 0)
% 11.43/2.38 | (20) empty(all_39_2) = all_49_0
% 11.43/2.38 |
% 11.43/2.38 | BETA: splitting (15) gives:
% 11.43/2.38 |
% 11.43/2.38 | Case 1:
% 11.43/2.38 | |
% 11.43/2.38 | | (21) all_39_0 = 0
% 11.43/2.38 | |
% 11.43/2.38 | | REDUCE: (7), (21) imply:
% 11.43/2.38 | | (22) $false
% 11.43/2.38 | |
% 11.43/2.38 | | CLOSE: (22) is inconsistent.
% 11.43/2.38 | |
% 11.43/2.38 | Case 2:
% 11.43/2.38 | |
% 11.43/2.39 | | (23) ? [v0: int] : ( ~ (v0 = 0) & subset(all_39_3, all_39_4) = v0)
% 11.43/2.39 | |
% 11.43/2.39 | | DELTA: instantiating (23) with fresh symbol all_62_0 gives:
% 11.43/2.39 | | (24) ~ (all_62_0 = 0) & subset(all_39_3, all_39_4) = all_62_0
% 11.43/2.39 | |
% 11.43/2.39 | | ALPHA: (24) implies:
% 11.43/2.39 | | (25) ~ (all_62_0 = 0)
% 11.43/2.39 | | (26) subset(all_39_3, all_39_4) = all_62_0
% 11.43/2.39 | |
% 11.43/2.39 | | GROUND_INST: instantiating (d5_finsub_1) with all_39_4, all_39_2, all_39_2,
% 11.43/2.39 | | simplifying with (8), (10), (14), (16) gives:
% 11.43/2.39 | | (27) ! [v0: $i] : ! [v1: any] : ( ~ (subset(v0, all_39_4) = v1) | ~
% 11.43/2.39 | | $i(v0) | ? [v2: any] : ? [v3: any] : (in(v0, all_39_2) = v2 &
% 11.43/2.39 | | finite(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0:
% 11.43/2.39 | | $i] : ( ~ (subset(v0, all_39_4) = 0) | ~ $i(v0) | ? [v1: any] :
% 11.43/2.39 | | ? [v2: any] : (in(v0, all_39_2) = v2 & finite(v0) = v1 & ( ~ (v1 =
% 11.43/2.39 | | 0) | v2 = 0)))
% 11.43/2.39 | |
% 11.43/2.39 | | ALPHA: (27) implies:
% 11.43/2.39 | | (28) ! [v0: $i] : ! [v1: any] : ( ~ (subset(v0, all_39_4) = v1) | ~
% 11.43/2.39 | | $i(v0) | ? [v2: any] : ? [v3: any] : (in(v0, all_39_2) = v2 &
% 11.43/2.39 | | finite(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 11.43/2.39 | |
% 11.43/2.39 | | GROUND_INST: instantiating (28) with all_39_3, all_62_0, simplifying with
% 11.43/2.39 | | (9), (26) gives:
% 11.43/2.39 | | (29) ? [v0: any] : ? [v1: any] : (in(all_39_3, all_39_2) = v0 &
% 11.43/2.39 | | finite(all_39_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_62_0 = 0)))
% 11.43/2.39 | |
% 11.43/2.39 | | DELTA: instantiating (29) with fresh symbols all_81_0, all_81_1 gives:
% 11.43/2.39 | | (30) in(all_39_3, all_39_2) = all_81_1 & finite(all_39_3) = all_81_0 & (
% 11.43/2.39 | | ~ (all_81_1 = 0) | (all_81_0 = 0 & all_62_0 = 0))
% 11.43/2.39 | |
% 11.43/2.39 | | ALPHA: (30) implies:
% 11.43/2.39 | | (31) in(all_39_3, all_39_2) = all_81_1
% 11.43/2.39 | | (32) ~ (all_81_1 = 0) | (all_81_0 = 0 & all_62_0 = 0)
% 11.43/2.39 | |
% 11.43/2.39 | | BETA: splitting (32) gives:
% 11.43/2.39 | |
% 11.43/2.39 | | Case 1:
% 11.43/2.39 | | |
% 11.43/2.39 | | | (33) ~ (all_81_1 = 0)
% 11.43/2.39 | | |
% 11.43/2.39 | | | GROUND_INST: instantiating (t2_subset) with all_39_3, all_39_2, all_81_1,
% 11.43/2.39 | | | simplifying with (9), (10), (31) gives:
% 11.43/2.39 | | | (34) all_81_1 = 0 | ? [v0: any] : ? [v1: any] : (element(all_39_3,
% 11.43/2.39 | | | all_39_2) = v0 & empty(all_39_2) = v1 & ( ~ (v0 = 0) | v1 =
% 11.43/2.39 | | | 0))
% 11.43/2.39 | | |
% 11.43/2.39 | | | BETA: splitting (34) gives:
% 11.43/2.39 | | |
% 11.43/2.39 | | | Case 1:
% 11.43/2.39 | | | |
% 11.43/2.39 | | | | (35) all_81_1 = 0
% 11.43/2.39 | | | |
% 11.43/2.39 | | | | REDUCE: (33), (35) imply:
% 11.43/2.39 | | | | (36) $false
% 11.43/2.39 | | | |
% 11.43/2.39 | | | | CLOSE: (36) is inconsistent.
% 11.43/2.39 | | | |
% 11.43/2.39 | | | Case 2:
% 11.43/2.39 | | | |
% 11.43/2.39 | | | | (37) ? [v0: any] : ? [v1: any] : (element(all_39_3, all_39_2) = v0
% 11.43/2.39 | | | | & empty(all_39_2) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 11.43/2.39 | | | |
% 11.43/2.39 | | | | DELTA: instantiating (37) with fresh symbols all_138_0, all_138_1 gives:
% 11.43/2.39 | | | | (38) element(all_39_3, all_39_2) = all_138_1 & empty(all_39_2) =
% 11.43/2.39 | | | | all_138_0 & ( ~ (all_138_1 = 0) | all_138_0 = 0)
% 11.43/2.39 | | | |
% 11.43/2.39 | | | | ALPHA: (38) implies:
% 11.43/2.39 | | | | (39) empty(all_39_2) = all_138_0
% 11.43/2.39 | | | | (40) element(all_39_3, all_39_2) = all_138_1
% 11.43/2.39 | | | | (41) ~ (all_138_1 = 0) | all_138_0 = 0
% 11.43/2.39 | | | |
% 11.43/2.39 | | | | GROUND_INST: instantiating (4) with all_49_0, all_138_0, all_39_2,
% 11.43/2.39 | | | | simplifying with (20), (39) gives:
% 11.43/2.39 | | | | (42) all_138_0 = all_49_0
% 11.43/2.39 | | | |
% 11.43/2.39 | | | | GROUND_INST: instantiating (5) with 0, all_138_1, all_39_2, all_39_3,
% 11.43/2.39 | | | | simplifying with (11), (40) gives:
% 11.43/2.39 | | | | (43) all_138_1 = 0
% 11.43/2.39 | | | |
% 11.43/2.39 | | | | BETA: splitting (41) gives:
% 11.43/2.39 | | | |
% 11.43/2.39 | | | | Case 1:
% 11.43/2.40 | | | | |
% 11.43/2.40 | | | | | (44) ~ (all_138_1 = 0)
% 11.43/2.40 | | | | |
% 11.43/2.40 | | | | | REDUCE: (43), (44) imply:
% 11.43/2.40 | | | | | (45) $false
% 11.43/2.40 | | | | |
% 11.43/2.40 | | | | | CLOSE: (45) is inconsistent.
% 11.43/2.40 | | | | |
% 11.43/2.40 | | | | Case 2:
% 11.43/2.40 | | | | |
% 11.43/2.40 | | | | | (46) all_138_0 = 0
% 11.43/2.40 | | | | |
% 11.43/2.40 | | | | | COMBINE_EQS: (42), (46) imply:
% 11.43/2.40 | | | | | (47) all_49_0 = 0
% 11.43/2.40 | | | | |
% 11.43/2.40 | | | | | REDUCE: (19), (47) imply:
% 11.43/2.40 | | | | | (48) $false
% 11.43/2.40 | | | | |
% 11.43/2.40 | | | | | CLOSE: (48) is inconsistent.
% 11.43/2.40 | | | | |
% 11.43/2.40 | | | | End of split
% 11.43/2.40 | | | |
% 11.43/2.40 | | | End of split
% 11.43/2.40 | | |
% 11.43/2.40 | | Case 2:
% 11.43/2.40 | | |
% 11.43/2.40 | | | (49) all_81_0 = 0 & all_62_0 = 0
% 11.43/2.40 | | |
% 11.43/2.40 | | | ALPHA: (49) implies:
% 11.43/2.40 | | | (50) all_62_0 = 0
% 11.43/2.40 | | |
% 11.43/2.40 | | | REDUCE: (25), (50) imply:
% 11.43/2.40 | | | (51) $false
% 11.43/2.40 | | |
% 11.43/2.40 | | | CLOSE: (51) is inconsistent.
% 11.43/2.40 | | |
% 11.43/2.40 | | End of split
% 11.43/2.40 | |
% 11.43/2.40 | End of split
% 11.43/2.40 |
% 11.43/2.40 End of proof
% 11.43/2.40 % SZS output end Proof for theBenchmark
% 11.43/2.40
% 11.43/2.40 1776ms
%------------------------------------------------------------------------------