TSTP Solution File: SEU178+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU178+1 : TPTP v8.1.2. Released v3.3.0.
% 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 17:43:04 EDT 2023
% Result : Theorem 10.49s 2.25s
% Output : Proof 13.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU178+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 21:01:57 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.57/1.04 Prover 4: Preprocessing ...
% 2.57/1.04 Prover 1: Preprocessing ...
% 2.87/1.08 Prover 3: Preprocessing ...
% 2.87/1.08 Prover 0: Preprocessing ...
% 2.87/1.08 Prover 6: Preprocessing ...
% 2.87/1.08 Prover 5: Preprocessing ...
% 2.87/1.08 Prover 2: Preprocessing ...
% 6.25/1.59 Prover 1: Warning: ignoring some quantifiers
% 6.55/1.64 Prover 3: Warning: ignoring some quantifiers
% 6.55/1.65 Prover 1: Constructing countermodel ...
% 6.55/1.66 Prover 6: Proving ...
% 6.55/1.67 Prover 2: Proving ...
% 6.55/1.67 Prover 5: Proving ...
% 6.55/1.68 Prover 3: Constructing countermodel ...
% 6.55/1.69 Prover 4: Warning: ignoring some quantifiers
% 7.16/1.74 Prover 4: Constructing countermodel ...
% 7.64/1.84 Prover 0: Proving ...
% 10.49/2.25 Prover 3: proved (1610ms)
% 10.49/2.25
% 10.49/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.49/2.25
% 10.49/2.25 Prover 6: stopped
% 10.49/2.25 Prover 2: stopped
% 10.49/2.25 Prover 0: stopped
% 10.49/2.25 Prover 5: stopped
% 10.49/2.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.49/2.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.49/2.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.49/2.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.49/2.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.39/2.36 Prover 1: Found proof (size 66)
% 11.39/2.36 Prover 1: proved (1737ms)
% 11.39/2.36 Prover 4: stopped
% 11.39/2.39 Prover 11: Preprocessing ...
% 11.39/2.40 Prover 10: Preprocessing ...
% 11.39/2.40 Prover 7: Preprocessing ...
% 12.13/2.41 Prover 13: Preprocessing ...
% 12.13/2.42 Prover 8: Preprocessing ...
% 12.13/2.43 Prover 10: stopped
% 12.13/2.44 Prover 7: stopped
% 12.13/2.45 Prover 13: stopped
% 12.13/2.45 Prover 11: stopped
% 12.65/2.52 Prover 8: Warning: ignoring some quantifiers
% 12.65/2.53 Prover 8: Constructing countermodel ...
% 12.65/2.54 Prover 8: stopped
% 12.65/2.54
% 12.65/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.65/2.54
% 12.65/2.55 % SZS output start Proof for theBenchmark
% 12.65/2.56 Assumptions after simplification:
% 12.65/2.56 ---------------------------------
% 12.65/2.56
% 12.65/2.56 (d1_relat_1)
% 13.06/2.58 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (relation(v0) = v1) | ~ $i(v0) | ?
% 13.06/2.58 [v2: $i] : (in(v2, v0) = 0 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~
% 13.06/2.58 (ordered_pair(v3, v4) = v2) | ~ $i(v4) | ~ $i(v3)))) & ! [v0: $i] : (
% 13.06/2.58 ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~
% 13.06/2.58 $i(v1) | ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) = v1 & $i(v3) &
% 13.06/2.58 $i(v2))))
% 13.06/2.58
% 13.06/2.58 (d3_tarski)
% 13.06/2.59 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 13.06/2.59 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 13.06/2.59 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 13.06/2.59 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 13.06/2.59 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 13.06/2.59
% 13.06/2.59 (d4_relat_1)
% 13.06/2.59 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 13.06/2.59 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 13.06/2.59 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 13.06/2.59 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) =
% 13.06/2.59 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 13.06/2.59 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6)
% 13.06/2.59 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 13.06/2.59 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 13.06/2.59 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 13.06/2.59 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 13.06/2.59 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) &
% 13.06/2.59 $i(v3)))))))
% 13.06/2.59
% 13.06/2.59 (d5_relat_1)
% 13.06/2.60 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 13.06/2.60 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 13.06/2.60 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 13.06/2.60 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) =
% 13.06/2.60 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 13.06/2.60 : ? [v6: $i] : (ordered_pair(v5, v3) = v6 & in(v6, v0) = 0 & $i(v6)
% 13.06/2.60 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 13.06/2.60 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 13.06/2.60 (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 13.06/2.60 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 13.06/2.60 $i] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) &
% 13.06/2.60 $i(v3)))))))
% 13.06/2.60
% 13.06/2.60 (t106_zfmisc_1)
% 13.06/2.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.06/2.60 $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~
% 13.06/2.60 (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) |
% 13.06/2.60 ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (in(v1, v3) = v8 &
% 13.06/2.60 in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1:
% 13.06/2.60 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 13.06/2.60 (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~
% 13.06/2.60 (in(v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1,
% 13.06/2.60 v3) = 0 & in(v0, v2) = 0))
% 13.06/2.60
% 13.06/2.60 (t21_relat_1)
% 13.06/2.60 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 13.06/2.60 = 0) & cartesian_product2(v1, v2) = v3 & relation_rng(v0) = v2 &
% 13.06/2.60 relation_dom(v0) = v1 & subset(v0, v3) = v4 & relation(v0) = 0 & $i(v3) &
% 13.06/2.60 $i(v2) & $i(v1) & $i(v0))
% 13.06/2.60
% 13.06/2.60 (function-axioms)
% 13.06/2.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.06/2.61 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 13.06/2.61 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.06/2.61 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & !
% 13.06/2.61 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.06/2.61 $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & !
% 13.06/2.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.06/2.61 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 13.06/2.61 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3,
% 13.06/2.61 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 13.06/2.61 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.06/2.61 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 13.06/2.61 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 13.06/2.61 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.06/2.61 $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] :
% 13.06/2.61 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 13.06/2.61 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 13.06/2.61 ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : !
% 13.06/2.61 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 13.06/2.61 (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.06/2.61 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 13.06/2.61 (relation(v2) = v0))
% 13.06/2.61
% 13.06/2.61 Further assumptions not needed in the proof:
% 13.06/2.61 --------------------------------------------
% 13.06/2.61 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, dt_k1_relat_1,
% 13.06/2.61 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_tarski,
% 13.06/2.61 dt_k2_zfmisc_1, dt_k4_tarski, dt_m1_subset_1, existence_m1_subset_1,
% 13.06/2.61 fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_subset_1, fc3_subset_1,
% 13.06/2.61 fc4_subset_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_subset_1,
% 13.06/2.61 rc2_xboole_0, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset,
% 13.06/2.61 t5_subset, t6_boole, t7_boole, t8_boole
% 13.06/2.61
% 13.06/2.61 Those formulas are unsatisfiable:
% 13.06/2.61 ---------------------------------
% 13.06/2.61
% 13.06/2.61 Begin of proof
% 13.06/2.61 |
% 13.06/2.61 | ALPHA: (d1_relat_1) implies:
% 13.06/2.61 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~
% 13.06/2.61 | (in(v1, v0) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] :
% 13.06/2.61 | (ordered_pair(v2, v3) = v1 & $i(v3) & $i(v2))))
% 13.06/2.61 |
% 13.06/2.61 | ALPHA: (d3_tarski) implies:
% 13.06/2.61 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 13.06/2.61 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 13.06/2.61 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 13.06/2.61 |
% 13.06/2.61 | ALPHA: (t106_zfmisc_1) implies:
% 13.06/2.61 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 13.06/2.61 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) =
% 13.06/2.61 | v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~
% 13.06/2.61 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8:
% 13.06/2.61 | any] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 =
% 13.06/2.61 | 0))))
% 13.06/2.61 |
% 13.06/2.62 | ALPHA: (function-axioms) implies:
% 13.06/2.62 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.06/2.62 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 13.06/2.62 |
% 13.06/2.62 | DELTA: instantiating (t21_relat_1) with fresh symbols all_36_0, all_36_1,
% 13.06/2.62 | all_36_2, all_36_3, all_36_4 gives:
% 13.06/2.62 | (5) ~ (all_36_0 = 0) & cartesian_product2(all_36_3, all_36_2) = all_36_1 &
% 13.06/2.62 | relation_rng(all_36_4) = all_36_2 & relation_dom(all_36_4) = all_36_3 &
% 13.06/2.62 | subset(all_36_4, all_36_1) = all_36_0 & relation(all_36_4) = 0 &
% 13.06/2.62 | $i(all_36_1) & $i(all_36_2) & $i(all_36_3) & $i(all_36_4)
% 13.06/2.62 |
% 13.06/2.62 | ALPHA: (5) implies:
% 13.06/2.62 | (6) ~ (all_36_0 = 0)
% 13.06/2.62 | (7) $i(all_36_4)
% 13.06/2.62 | (8) $i(all_36_3)
% 13.06/2.62 | (9) $i(all_36_2)
% 13.06/2.62 | (10) $i(all_36_1)
% 13.06/2.62 | (11) relation(all_36_4) = 0
% 13.06/2.62 | (12) subset(all_36_4, all_36_1) = all_36_0
% 13.06/2.62 | (13) relation_dom(all_36_4) = all_36_3
% 13.06/2.62 | (14) relation_rng(all_36_4) = all_36_2
% 13.06/2.62 | (15) cartesian_product2(all_36_3, all_36_2) = all_36_1
% 13.06/2.62 |
% 13.06/2.62 | GROUND_INST: instantiating (1) with all_36_4, simplifying with (7), (11)
% 13.06/2.62 | gives:
% 13.06/2.62 | (16) ! [v0: $i] : ( ~ (in(v0, all_36_4) = 0) | ~ $i(v0) | ? [v1: $i] :
% 13.06/2.62 | ? [v2: $i] : (ordered_pair(v1, v2) = v0 & $i(v2) & $i(v1)))
% 13.06/2.62 |
% 13.06/2.62 | GROUND_INST: instantiating (2) with all_36_4, all_36_1, all_36_0, simplifying
% 13.06/2.62 | with (7), (10), (12) gives:
% 13.06/2.62 | (17) all_36_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 13.06/2.62 | all_36_1) = v1 & in(v0, all_36_4) = 0 & $i(v0))
% 13.06/2.62 |
% 13.06/2.62 | GROUND_INST: instantiating (d4_relat_1) with all_36_4, all_36_3, simplifying
% 13.06/2.62 | with (7), (13) gives:
% 13.06/2.63 | (18) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_4) = v0) | ( ? [v0: any]
% 13.06/2.63 | : (v0 = all_36_3 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1,
% 13.06/2.63 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] :
% 13.06/2.63 | ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, all_36_4) = 0) |
% 13.06/2.63 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 13.06/2.63 | (ordered_pair(v1, v3) = v4 & in(v4, all_36_4) = 0 & $i(v4) &
% 13.06/2.63 | $i(v3))))) & ( ~ $i(all_36_3) | ( ! [v0: $i] : ! [v1: int]
% 13.06/2.63 | : (v1 = 0 | ~ (in(v0, all_36_3) = v1) | ~ $i(v0) | ! [v2: $i]
% 13.06/2.63 | : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 13.06/2.63 | all_36_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0,
% 13.06/2.63 | all_36_3) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 13.06/2.63 | (ordered_pair(v0, v1) = v2 & in(v2, all_36_4) = 0 & $i(v2) &
% 13.06/2.63 | $i(v1))))))
% 13.06/2.63 |
% 13.06/2.63 | GROUND_INST: instantiating (d5_relat_1) with all_36_4, all_36_2, simplifying
% 13.06/2.63 | with (7), (14) gives:
% 13.06/2.63 | (19) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_4) = v0) | ( ? [v0: any]
% 13.06/2.63 | : (v0 = all_36_2 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1,
% 13.06/2.63 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] :
% 13.06/2.63 | ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, all_36_4) = 0) |
% 13.06/2.63 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 13.06/2.63 | (ordered_pair(v3, v1) = v4 & in(v4, all_36_4) = 0 & $i(v4) &
% 13.06/2.63 | $i(v3))))) & ( ~ $i(all_36_2) | ( ! [v0: $i] : ! [v1: int]
% 13.06/2.63 | : (v1 = 0 | ~ (in(v0, all_36_2) = v1) | ~ $i(v0) | ! [v2: $i]
% 13.06/2.63 | : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3,
% 13.06/2.63 | all_36_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0,
% 13.06/2.63 | all_36_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 13.06/2.63 | (ordered_pair(v1, v0) = v2 & in(v2, all_36_4) = 0 & $i(v2) &
% 13.06/2.63 | $i(v1))))))
% 13.06/2.63 |
% 13.06/2.63 | BETA: splitting (19) gives:
% 13.06/2.63 |
% 13.06/2.63 | Case 1:
% 13.06/2.63 | |
% 13.06/2.63 | | (20) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_4) = v0)
% 13.06/2.63 | |
% 13.06/2.63 | | DELTA: instantiating (20) with fresh symbol all_52_0 gives:
% 13.06/2.63 | | (21) ~ (all_52_0 = 0) & relation(all_36_4) = all_52_0
% 13.06/2.63 | |
% 13.06/2.63 | | ALPHA: (21) implies:
% 13.06/2.63 | | (22) ~ (all_52_0 = 0)
% 13.06/2.63 | | (23) relation(all_36_4) = all_52_0
% 13.06/2.63 | |
% 13.06/2.63 | | DELTA: instantiating (20) with fresh symbol all_54_0 gives:
% 13.06/2.63 | | (24) ~ (all_54_0 = 0) & relation(all_36_4) = all_54_0
% 13.06/2.63 | |
% 13.06/2.63 | | ALPHA: (24) implies:
% 13.06/2.63 | | (25) relation(all_36_4) = all_54_0
% 13.06/2.63 | |
% 13.06/2.63 | | GROUND_INST: instantiating (4) with 0, all_54_0, all_36_4, simplifying with
% 13.06/2.63 | | (11), (25) gives:
% 13.06/2.63 | | (26) all_54_0 = 0
% 13.06/2.63 | |
% 13.06/2.63 | | GROUND_INST: instantiating (4) with all_52_0, all_54_0, all_36_4,
% 13.06/2.63 | | simplifying with (23), (25) gives:
% 13.06/2.63 | | (27) all_54_0 = all_52_0
% 13.06/2.63 | |
% 13.06/2.63 | | COMBINE_EQS: (26), (27) imply:
% 13.06/2.63 | | (28) all_52_0 = 0
% 13.06/2.63 | |
% 13.06/2.63 | | REDUCE: (22), (28) imply:
% 13.06/2.63 | | (29) $false
% 13.06/2.64 | |
% 13.06/2.64 | | CLOSE: (29) is inconsistent.
% 13.06/2.64 | |
% 13.06/2.64 | Case 2:
% 13.06/2.64 | |
% 13.06/2.64 | | (30) ? [v0: any] : (v0 = all_36_2 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 13.06/2.64 | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] :
% 13.06/2.64 | | ! [v4: $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4,
% 13.06/2.64 | | all_36_4) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] :
% 13.06/2.64 | | ? [v4: $i] : (ordered_pair(v3, v1) = v4 & in(v4, all_36_4) = 0
% 13.06/2.64 | | & $i(v4) & $i(v3))))) & ( ~ $i(all_36_2) | ( ! [v0: $i] : !
% 13.06/2.64 | | [v1: int] : (v1 = 0 | ~ (in(v0, all_36_2) = v1) | ~ $i(v0) |
% 13.06/2.64 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) |
% 13.06/2.64 | | ~ (in(v3, all_36_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~
% 13.06/2.64 | | (in(v0, all_36_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i]
% 13.06/2.64 | | : (ordered_pair(v1, v0) = v2 & in(v2, all_36_4) = 0 & $i(v2) &
% 13.06/2.64 | | $i(v1)))))
% 13.06/2.64 | |
% 13.06/2.64 | | ALPHA: (30) implies:
% 13.06/2.64 | | (31) ~ $i(all_36_2) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 13.06/2.64 | | all_36_2) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : (
% 13.06/2.64 | | ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_36_4) = 0) | ~
% 13.06/2.64 | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_36_2) = 0) | ~
% 13.06/2.64 | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) = v2
% 13.06/2.64 | | & in(v2, all_36_4) = 0 & $i(v2) & $i(v1))))
% 13.06/2.64 | |
% 13.06/2.64 | | BETA: splitting (18) gives:
% 13.06/2.64 | |
% 13.06/2.64 | | Case 1:
% 13.06/2.64 | | |
% 13.06/2.64 | | | (32) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_4) = v0)
% 13.06/2.64 | | |
% 13.06/2.64 | | | DELTA: instantiating (32) with fresh symbol all_52_0 gives:
% 13.06/2.64 | | | (33) ~ (all_52_0 = 0) & relation(all_36_4) = all_52_0
% 13.06/2.64 | | |
% 13.06/2.64 | | | ALPHA: (33) implies:
% 13.06/2.64 | | | (34) ~ (all_52_0 = 0)
% 13.06/2.64 | | | (35) relation(all_36_4) = all_52_0
% 13.06/2.64 | | |
% 13.06/2.64 | | | GROUND_INST: instantiating (4) with 0, all_52_0, all_36_4, simplifying
% 13.06/2.64 | | | with (11), (35) gives:
% 13.06/2.64 | | | (36) all_52_0 = 0
% 13.06/2.64 | | |
% 13.06/2.64 | | | REDUCE: (34), (36) imply:
% 13.06/2.64 | | | (37) $false
% 13.06/2.64 | | |
% 13.06/2.64 | | | CLOSE: (37) is inconsistent.
% 13.06/2.64 | | |
% 13.06/2.64 | | Case 2:
% 13.06/2.64 | | |
% 13.06/2.65 | | | (38) ? [v0: any] : (v0 = all_36_3 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 13.06/2.65 | | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i]
% 13.06/2.65 | | | : ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4,
% 13.06/2.65 | | | all_36_4) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] :
% 13.06/2.65 | | | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_36_4)
% 13.06/2.65 | | | = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_36_3) | ( ! [v0:
% 13.06/2.65 | | | $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_36_3) = v1) |
% 13.06/2.65 | | | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0,
% 13.06/2.65 | | | v2) = v3) | ~ (in(v3, all_36_4) = 0) | ~ $i(v2))) &
% 13.06/2.65 | | | ! [v0: $i] : ( ~ (in(v0, all_36_3) = 0) | ~ $i(v0) | ? [v1:
% 13.06/2.65 | | | $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 13.06/2.65 | | | all_36_4) = 0 & $i(v2) & $i(v1)))))
% 13.06/2.65 | | |
% 13.06/2.65 | | | ALPHA: (38) implies:
% 13.06/2.65 | | | (39) ~ $i(all_36_3) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 13.06/2.65 | | | (in(v0, all_36_3) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3:
% 13.06/2.65 | | | $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_36_4)
% 13.06/2.65 | | | = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_36_3) =
% 13.06/2.65 | | | 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 13.06/2.65 | | | (ordered_pair(v0, v1) = v2 & in(v2, all_36_4) = 0 & $i(v2) &
% 13.06/2.65 | | | $i(v1))))
% 13.06/2.65 | | |
% 13.06/2.65 | | | BETA: splitting (17) gives:
% 13.06/2.65 | | |
% 13.06/2.65 | | | Case 1:
% 13.06/2.65 | | | |
% 13.06/2.65 | | | | (40) all_36_0 = 0
% 13.06/2.65 | | | |
% 13.06/2.65 | | | | REDUCE: (6), (40) imply:
% 13.06/2.65 | | | | (41) $false
% 13.06/2.65 | | | |
% 13.06/2.65 | | | | CLOSE: (41) is inconsistent.
% 13.06/2.65 | | | |
% 13.06/2.65 | | | Case 2:
% 13.06/2.65 | | | |
% 13.06/2.65 | | | | (42) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_36_1) =
% 13.06/2.65 | | | | v1 & in(v0, all_36_4) = 0 & $i(v0))
% 13.06/2.65 | | | |
% 13.06/2.65 | | | | DELTA: instantiating (42) with fresh symbols all_56_0, all_56_1 gives:
% 13.06/2.65 | | | | (43) ~ (all_56_0 = 0) & in(all_56_1, all_36_1) = all_56_0 &
% 13.06/2.65 | | | | in(all_56_1, all_36_4) = 0 & $i(all_56_1)
% 13.06/2.65 | | | |
% 13.06/2.65 | | | | ALPHA: (43) implies:
% 13.06/2.65 | | | | (44) ~ (all_56_0 = 0)
% 13.06/2.65 | | | | (45) $i(all_56_1)
% 13.06/2.65 | | | | (46) in(all_56_1, all_36_4) = 0
% 13.06/2.65 | | | | (47) in(all_56_1, all_36_1) = all_56_0
% 13.06/2.65 | | | |
% 13.06/2.65 | | | | BETA: splitting (39) gives:
% 13.06/2.65 | | | |
% 13.06/2.65 | | | | Case 1:
% 13.06/2.65 | | | | |
% 13.06/2.65 | | | | | (48) ~ $i(all_36_3)
% 13.06/2.65 | | | | |
% 13.06/2.65 | | | | | PRED_UNIFY: (8), (48) imply:
% 13.06/2.65 | | | | | (49) $false
% 13.06/2.65 | | | | |
% 13.06/2.65 | | | | | CLOSE: (49) is inconsistent.
% 13.06/2.65 | | | | |
% 13.06/2.65 | | | | Case 2:
% 13.06/2.65 | | | | |
% 13.06/2.65 | | | | | (50) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_36_3) =
% 13.06/2.65 | | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 13.06/2.65 | | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_36_4) = 0) |
% 13.06/2.65 | | | | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_36_3) = 0) | ~
% 13.06/2.65 | | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) =
% 13.06/2.65 | | | | | v2 & in(v2, all_36_4) = 0 & $i(v2) & $i(v1)))
% 13.06/2.65 | | | | |
% 13.06/2.65 | | | | | ALPHA: (50) implies:
% 13.06/2.65 | | | | | (51) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_36_3) =
% 13.06/2.65 | | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 13.06/2.65 | | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_36_4) = 0) |
% 13.06/2.65 | | | | | ~ $i(v2)))
% 13.06/2.65 | | | | |
% 13.06/2.65 | | | | | BETA: splitting (31) gives:
% 13.06/2.65 | | | | |
% 13.06/2.65 | | | | | Case 1:
% 13.06/2.65 | | | | | |
% 13.06/2.65 | | | | | | (52) ~ $i(all_36_2)
% 13.06/2.65 | | | | | |
% 13.06/2.66 | | | | | | PRED_UNIFY: (9), (52) imply:
% 13.06/2.66 | | | | | | (53) $false
% 13.06/2.66 | | | | | |
% 13.06/2.66 | | | | | | CLOSE: (53) is inconsistent.
% 13.06/2.66 | | | | | |
% 13.06/2.66 | | | | | Case 2:
% 13.06/2.66 | | | | | |
% 13.06/2.66 | | | | | | (54) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_36_2)
% 13.06/2.66 | | | | | | = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 13.06/2.66 | | | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_36_4) = 0)
% 13.06/2.66 | | | | | | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_36_2) = 0)
% 13.06/2.66 | | | | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 13.06/2.66 | | | | | | (ordered_pair(v1, v0) = v2 & in(v2, all_36_4) = 0 & $i(v2)
% 13.06/2.66 | | | | | | & $i(v1)))
% 13.06/2.66 | | | | | |
% 13.06/2.66 | | | | | | ALPHA: (54) implies:
% 13.06/2.66 | | | | | | (55) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_36_2)
% 13.06/2.66 | | | | | | = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 13.06/2.66 | | | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_36_4) = 0)
% 13.06/2.66 | | | | | | | ~ $i(v2)))
% 13.06/2.66 | | | | | |
% 13.06/2.66 | | | | | | GROUND_INST: instantiating (16) with all_56_1, simplifying with
% 13.06/2.66 | | | | | | (45), (46) gives:
% 13.06/2.66 | | | | | | (56) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_56_1
% 13.06/2.66 | | | | | | & $i(v1) & $i(v0))
% 13.06/2.66 | | | | | |
% 13.06/2.66 | | | | | | DELTA: instantiating (56) with fresh symbols all_76_0, all_76_1
% 13.06/2.66 | | | | | | gives:
% 13.06/2.66 | | | | | | (57) ordered_pair(all_76_1, all_76_0) = all_56_1 & $i(all_76_0) &
% 13.06/2.66 | | | | | | $i(all_76_1)
% 13.06/2.66 | | | | | |
% 13.06/2.66 | | | | | | ALPHA: (57) implies:
% 13.06/2.66 | | | | | | (58) $i(all_76_1)
% 13.06/2.66 | | | | | | (59) $i(all_76_0)
% 13.06/2.66 | | | | | | (60) ordered_pair(all_76_1, all_76_0) = all_56_1
% 13.06/2.66 | | | | | |
% 13.06/2.66 | | | | | | GROUND_INST: instantiating (3) with all_76_1, all_76_0, all_36_3,
% 13.06/2.66 | | | | | | all_36_2, all_56_1, all_36_1, all_56_0, simplifying
% 13.06/2.66 | | | | | | with (8), (9), (15), (47), (58), (59), (60) gives:
% 13.06/2.66 | | | | | | (61) all_56_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_76_0,
% 13.06/2.66 | | | | | | all_36_2) = v1 & in(all_76_1, all_36_3) = v0 & ( ~ (v1 =
% 13.06/2.66 | | | | | | 0) | ~ (v0 = 0)))
% 13.06/2.66 | | | | | |
% 13.06/2.66 | | | | | | BETA: splitting (61) gives:
% 13.06/2.66 | | | | | |
% 13.06/2.66 | | | | | | Case 1:
% 13.06/2.66 | | | | | | |
% 13.06/2.66 | | | | | | | (62) all_56_0 = 0
% 13.06/2.66 | | | | | | |
% 13.06/2.66 | | | | | | | REDUCE: (44), (62) imply:
% 13.06/2.66 | | | | | | | (63) $false
% 13.06/2.66 | | | | | | |
% 13.06/2.66 | | | | | | | CLOSE: (63) is inconsistent.
% 13.06/2.66 | | | | | | |
% 13.06/2.66 | | | | | | Case 2:
% 13.06/2.66 | | | | | | |
% 13.06/2.66 | | | | | | | (64) ? [v0: any] : ? [v1: any] : (in(all_76_0, all_36_2) = v1
% 13.06/2.66 | | | | | | | & in(all_76_1, all_36_3) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 13.06/2.66 | | | | | | | 0)))
% 13.06/2.66 | | | | | | |
% 13.06/2.66 | | | | | | | DELTA: instantiating (64) with fresh symbols all_89_0, all_89_1
% 13.06/2.66 | | | | | | | gives:
% 13.06/2.66 | | | | | | | (65) in(all_76_0, all_36_2) = all_89_0 & in(all_76_1, all_36_3)
% 13.06/2.66 | | | | | | | = all_89_1 & ( ~ (all_89_0 = 0) | ~ (all_89_1 = 0))
% 13.06/2.66 | | | | | | |
% 13.06/2.66 | | | | | | | ALPHA: (65) implies:
% 13.06/2.66 | | | | | | | (66) in(all_76_1, all_36_3) = all_89_1
% 13.06/2.66 | | | | | | | (67) in(all_76_0, all_36_2) = all_89_0
% 13.06/2.66 | | | | | | | (68) ~ (all_89_0 = 0) | ~ (all_89_1 = 0)
% 13.06/2.66 | | | | | | |
% 13.06/2.66 | | | | | | | GROUND_INST: instantiating (51) with all_76_1, all_89_1,
% 13.06/2.66 | | | | | | | simplifying with (58), (66) gives:
% 13.06/2.66 | | | | | | | (69) all_89_1 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~
% 13.06/2.66 | | | | | | | (ordered_pair(all_76_1, v0) = v1) | ~ (in(v1, all_36_4)
% 13.06/2.66 | | | | | | | = 0) | ~ $i(v0))
% 13.06/2.66 | | | | | | |
% 13.06/2.66 | | | | | | | GROUND_INST: instantiating (55) with all_76_0, all_89_0,
% 13.06/2.66 | | | | | | | simplifying with (59), (67) gives:
% 13.06/2.66 | | | | | | | (70) all_89_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~
% 13.06/2.66 | | | | | | | (ordered_pair(v0, all_76_0) = v1) | ~ (in(v1, all_36_4)
% 13.06/2.66 | | | | | | | = 0) | ~ $i(v0))
% 13.06/2.66 | | | | | | |
% 13.06/2.67 | | | | | | | BETA: splitting (68) gives:
% 13.06/2.67 | | | | | | |
% 13.06/2.67 | | | | | | | Case 1:
% 13.06/2.67 | | | | | | | |
% 13.06/2.67 | | | | | | | | (71) ~ (all_89_0 = 0)
% 13.06/2.67 | | | | | | | |
% 13.06/2.67 | | | | | | | | BETA: splitting (70) gives:
% 13.06/2.67 | | | | | | | |
% 13.06/2.67 | | | | | | | | Case 1:
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | (72) all_89_0 = 0
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | REDUCE: (71), (72) imply:
% 13.06/2.67 | | | | | | | | | (73) $false
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | CLOSE: (73) is inconsistent.
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | Case 2:
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | (74) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0,
% 13.06/2.67 | | | | | | | | | all_76_0) = v1) | ~ (in(v1, all_36_4) = 0) | ~
% 13.06/2.67 | | | | | | | | | $i(v0))
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | GROUND_INST: instantiating (74) with all_76_1, all_56_1,
% 13.06/2.67 | | | | | | | | | simplifying with (46), (58), (60) gives:
% 13.06/2.67 | | | | | | | | | (75) $false
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | CLOSE: (75) is inconsistent.
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | End of split
% 13.06/2.67 | | | | | | | |
% 13.06/2.67 | | | | | | | Case 2:
% 13.06/2.67 | | | | | | | |
% 13.06/2.67 | | | | | | | | (76) ~ (all_89_1 = 0)
% 13.06/2.67 | | | | | | | |
% 13.06/2.67 | | | | | | | | BETA: splitting (69) gives:
% 13.06/2.67 | | | | | | | |
% 13.06/2.67 | | | | | | | | Case 1:
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | (77) all_89_1 = 0
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | REDUCE: (76), (77) imply:
% 13.06/2.67 | | | | | | | | | (78) $false
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | CLOSE: (78) is inconsistent.
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | Case 2:
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | (79) ! [v0: $i] : ! [v1: $i] : ( ~
% 13.06/2.67 | | | | | | | | | (ordered_pair(all_76_1, v0) = v1) | ~ (in(v1,
% 13.06/2.67 | | | | | | | | | all_36_4) = 0) | ~ $i(v0))
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | GROUND_INST: instantiating (79) with all_76_0, all_56_1,
% 13.06/2.67 | | | | | | | | | simplifying with (46), (59), (60) gives:
% 13.06/2.67 | | | | | | | | | (80) $false
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | | CLOSE: (80) is inconsistent.
% 13.06/2.67 | | | | | | | | |
% 13.06/2.67 | | | | | | | | End of split
% 13.06/2.67 | | | | | | | |
% 13.06/2.67 | | | | | | | End of split
% 13.06/2.67 | | | | | | |
% 13.06/2.67 | | | | | | End of split
% 13.06/2.67 | | | | | |
% 13.06/2.67 | | | | | End of split
% 13.06/2.67 | | | | |
% 13.06/2.67 | | | | End of split
% 13.06/2.67 | | | |
% 13.06/2.67 | | | End of split
% 13.06/2.67 | | |
% 13.06/2.67 | | End of split
% 13.06/2.67 | |
% 13.06/2.67 | End of split
% 13.06/2.67 |
% 13.06/2.67 End of proof
% 13.06/2.67 % SZS output end Proof for theBenchmark
% 13.06/2.67
% 13.06/2.67 2059ms
%------------------------------------------------------------------------------