TSTP Solution File: SEU251+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU251+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 : n019.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 17:43:39 EDT 2023
% Result : Theorem 9.99s 2.24s
% Output : Proof 14.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU251+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 20:53:13 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.61 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.81/1.12 Prover 4: Preprocessing ...
% 2.81/1.13 Prover 1: Preprocessing ...
% 3.19/1.16 Prover 0: Preprocessing ...
% 3.19/1.16 Prover 5: Preprocessing ...
% 3.19/1.16 Prover 6: Preprocessing ...
% 3.19/1.16 Prover 3: Preprocessing ...
% 3.19/1.16 Prover 2: Preprocessing ...
% 6.13/1.63 Prover 1: Warning: ignoring some quantifiers
% 6.64/1.67 Prover 5: Proving ...
% 6.64/1.68 Prover 6: Proving ...
% 6.64/1.68 Prover 4: Warning: ignoring some quantifiers
% 6.64/1.69 Prover 3: Warning: ignoring some quantifiers
% 6.64/1.70 Prover 1: Constructing countermodel ...
% 6.64/1.70 Prover 3: Constructing countermodel ...
% 6.95/1.71 Prover 2: Proving ...
% 6.95/1.73 Prover 4: Constructing countermodel ...
% 7.23/1.76 Prover 0: Proving ...
% 9.99/2.24 Prover 0: proved (1618ms)
% 9.99/2.24
% 9.99/2.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.99/2.24
% 10.91/2.25 Prover 2: stopped
% 10.91/2.26 Prover 6: stopped
% 10.91/2.26 Prover 3: stopped
% 10.91/2.27 Prover 5: stopped
% 10.91/2.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.91/2.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.91/2.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.91/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.91/2.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.30/2.32 Prover 13: Preprocessing ...
% 11.30/2.32 Prover 8: Preprocessing ...
% 11.30/2.32 Prover 11: Preprocessing ...
% 11.30/2.32 Prover 10: Preprocessing ...
% 11.30/2.34 Prover 7: Preprocessing ...
% 11.70/2.41 Prover 13: Warning: ignoring some quantifiers
% 11.70/2.43 Prover 13: Constructing countermodel ...
% 11.70/2.44 Prover 10: Warning: ignoring some quantifiers
% 11.70/2.44 Prover 8: Warning: ignoring some quantifiers
% 11.70/2.44 Prover 7: Warning: ignoring some quantifiers
% 12.42/2.45 Prover 10: Constructing countermodel ...
% 12.42/2.45 Prover 8: Constructing countermodel ...
% 12.42/2.47 Prover 7: Constructing countermodel ...
% 13.15/2.55 Prover 11: Warning: ignoring some quantifiers
% 13.15/2.58 Prover 11: Constructing countermodel ...
% 14.00/2.66 Prover 10: gave up
% 14.00/2.66 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 14.00/2.69 Prover 16: Preprocessing ...
% 14.00/2.72 Prover 4: Found proof (size 90)
% 14.00/2.72 Prover 4: proved (2100ms)
% 14.00/2.72 Prover 7: stopped
% 14.00/2.72 Prover 13: stopped
% 14.00/2.72 Prover 11: stopped
% 14.00/2.72 Prover 8: stopped
% 14.00/2.73 Prover 1: stopped
% 14.00/2.73 Prover 16: stopped
% 14.00/2.74
% 14.00/2.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.00/2.74
% 14.00/2.75 % SZS output start Proof for theBenchmark
% 14.60/2.75 Assumptions after simplification:
% 14.60/2.75 ---------------------------------
% 14.60/2.75
% 14.60/2.75 (cc2_funct_1)
% 14.60/2.78 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.60/2.78 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 14.60/2.78 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 14.60/2.78 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 14.60/2.78 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 14.60/2.78 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 14.60/2.78 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 14.60/2.78 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 14.60/2.78 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 14.60/2.78 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 14.60/2.78 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 14.60/2.78 0)))
% 14.60/2.78
% 14.60/2.78 (commutativity_k3_xboole_0)
% 14.60/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2)
% 14.60/2.78 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & !
% 14.60/2.78 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) |
% 14.60/2.78 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 14.60/2.78
% 14.60/2.78 (d1_wellord1)
% 14.60/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 14.60/2.80 | v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2)
% 14.60/2.80 = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ?
% 14.60/2.80 [v6: int] : ( ~ (v6 = 0) & ordered_pair(v3, v1) = v5 & in(v5, v0) = v6 &
% 14.60/2.80 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 14.60/2.80 $i] : (v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) |
% 14.60/2.80 ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 14.60/2.80 [v5: any] : ? [v6: any] : (in(v4, v0) = v5 & in(v3, v2) = v6 & ( ~ (v5 = 0)
% 14.60/2.80 | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 14.60/2.80 [v4: $i] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~
% 14.60/2.80 (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 14.60/2.80 any] : ? [v6: any] : (in(v4, v0) = v6 & in(v3, v2) = v5 & ( ~ (v5 = 0) |
% 14.60/2.80 (v6 = 0 & ~ (v3 = v1))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.60/2.80 ! [v3: $i] : ( ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2)
% 14.60/2.80 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 14.60/2.80 (ordered_pair(v3, v1) = v4 & in(v4, v0) = 0 & $i(v4))) & ? [v0: $i] : !
% 14.60/2.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (fiber(v1, v2) = v3) | ~
% 14.60/2.80 (relation(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ?
% 14.60/2.80 [v5: any] : ? [v6: $i] : ? [v7: any] : (ordered_pair(v4, v2) = v6 & in(v6,
% 14.60/2.80 v1) = v7 & in(v4, v0) = v5 & $i(v6) & $i(v4) & ( ~ (v7 = 0) | ~ (v5 =
% 14.60/2.80 0) | v4 = v2) & (v5 = 0 | (v7 = 0 & ~ (v4 = v2))))) & ! [v0: $i] :
% 14.60/2.80 ! [v1: $i] : ! [v2: $i] : ( ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) |
% 14.60/2.80 ~ (in(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 14.60/2.80
% 14.60/2.80 (d3_tarski)
% 14.60/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.60/2.80 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 14.60/2.80 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 14.60/2.80 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 14.60/2.80 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 14.60/2.80 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.60/2.80 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 14.60/2.80 $i(v0) | in(v2, v1) = 0)
% 14.60/2.80
% 14.60/2.80 (d6_wellord1)
% 14.60/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) =
% 14.60/2.80 v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 14.60/2.80 (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2 & $i(v3) &
% 14.60/2.80 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.60/2.80 (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~
% 14.60/2.80 $i(v0) | ? [v3: $i] : (relation_restriction(v0, v1) = v3 &
% 14.60/2.80 set_intersection2(v0, v2) = v3 & $i(v3)))
% 14.60/2.80
% 14.60/2.80 (dt_k2_wellord1)
% 14.60/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) =
% 14.60/2.80 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (relation(v2)
% 14.60/2.80 = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 14.60/2.80
% 14.60/2.80 (t16_wellord1)
% 14.60/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 14.60/2.81 (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ $i(v2) | ~
% 14.60/2.81 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8:
% 14.60/2.81 any] : (cartesian_product2(v1, v1) = v7 & relation(v2) = v5 & in(v0, v7) =
% 14.60/2.81 v8 & in(v0, v2) = v6 & $i(v7) & ( ~ (v5 = 0) | (( ~ (v8 = 0) | ~ (v6 = 0)
% 14.60/2.81 | v4 = 0) & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0))))))
% 14.60/2.81
% 14.60/2.81 (t21_wellord1)
% 14.60/2.81 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 14.60/2.81 $i] : ? [v6: int] : ( ~ (v6 = 0) & relation_restriction(v2, v0) = v3 &
% 14.60/2.81 subset(v4, v5) = v6 & fiber(v3, v1) = v4 & fiber(v2, v1) = v5 & relation(v2)
% 14.60/2.81 = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 14.60/2.81
% 14.60/2.81 (t2_subset)
% 14.60/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 14.60/2.81 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 &
% 14.60/2.81 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : (
% 14.60/2.81 ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 14.60/2.81 any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 14.60/2.81
% 14.60/2.81 (function-axioms)
% 14.60/2.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.60/2.81 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 14.60/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.60/2.81 (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) =
% 14.60/2.81 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 14.60/2.81 ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 14.60/2.81 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.60/2.81 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 14.60/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.60/2.81 (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 14.60/2.81 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 14.60/2.81 (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.60/2.81 [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 14.60/2.81 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 14.60/2.81 : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~
% 14.60/2.81 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.60/2.81 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) =
% 14.60/2.81 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.60/2.81 (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : !
% 14.60/2.81 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 14.60/2.81 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.60/2.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~
% 14.60/2.81 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.60/2.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 14.60/2.81 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.60/2.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 14.60/2.81 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.60/2.81 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 14.60/2.81 (empty(v2) = v0))
% 14.60/2.81
% 14.60/2.81 Further assumptions not needed in the proof:
% 14.60/2.81 --------------------------------------------
% 14.60/2.82 antisymmetry_r2_hidden, cc1_funct_1, commutativity_k2_tarski, d5_tarski,
% 14.60/2.82 dt_k1_tarski, dt_k1_wellord1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski,
% 14.60/2.82 dt_k2_zfmisc_1, dt_k3_xboole_0, dt_k4_tarski, dt_m1_subset_1,
% 14.60/2.82 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, idempotence_k3_xboole_0,
% 14.60/2.82 rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0, rc3_funct_1,
% 14.60/2.82 reflexivity_r1_tarski, t1_subset, t2_boole, t3_subset, t4_subset, t5_subset,
% 14.60/2.82 t6_boole, t7_boole, t8_boole
% 14.60/2.82
% 14.60/2.82 Those formulas are unsatisfiable:
% 14.60/2.82 ---------------------------------
% 14.60/2.82
% 14.60/2.82 Begin of proof
% 14.60/2.82 |
% 14.60/2.82 | ALPHA: (cc2_funct_1) implies:
% 14.60/2.82 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 14.60/2.82 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 14.60/2.82 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 14.60/2.82 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ?
% 14.60/2.82 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 &
% 14.60/2.82 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 14.60/2.82 | ~ (v2 = 0) | v1 = 0)))
% 14.60/2.82 |
% 14.60/2.82 | ALPHA: (commutativity_k3_xboole_0) implies:
% 14.60/2.82 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1,
% 14.60/2.82 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) =
% 14.60/2.82 | v2 & $i(v2)))
% 14.60/2.82 |
% 14.60/2.82 | ALPHA: (d1_wellord1) implies:
% 14.60/2.82 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (fiber(v0,
% 14.60/2.82 | v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ~
% 14.60/2.82 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 14.60/2.82 | (ordered_pair(v3, v1) = v4 & in(v4, v0) = 0 & $i(v4)))
% 14.60/2.82 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 14.60/2.82 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~
% 14.60/2.82 | (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 14.60/2.82 | ? [v5: any] : ? [v6: any] : (in(v4, v0) = v6 & in(v3, v2) = v5 & ( ~
% 14.60/2.82 | (v5 = 0) | (v6 = 0 & ~ (v3 = v1)))))
% 14.60/2.82 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 14.60/2.82 | (v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) |
% 14.60/2.82 | ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 14.60/2.82 | | ? [v5: any] : ? [v6: any] : (in(v4, v0) = v5 & in(v3, v2) = v6 &
% 14.60/2.82 | ( ~ (v5 = 0) | v6 = 0)))
% 14.60/2.82 |
% 14.60/2.82 | ALPHA: (d3_tarski) implies:
% 14.60/2.83 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 14.60/2.83 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 14.60/2.83 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 14.60/2.83 |
% 14.60/2.83 | ALPHA: (d6_wellord1) implies:
% 14.60/2.83 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0,
% 14.60/2.83 | v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 14.60/2.83 | [v3: $i] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0,
% 14.60/2.83 | v3) = v2 & $i(v3) & $i(v2)))
% 14.60/2.83 |
% 14.60/2.83 | ALPHA: (t2_subset) implies:
% 14.60/2.83 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 14.60/2.83 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 14.60/2.83 | (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 14.60/2.83 |
% 14.60/2.83 | ALPHA: (function-axioms) implies:
% 14.60/2.83 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 14.60/2.83 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 14.60/2.83 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 14.60/2.83 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 14.60/2.83 | v0))
% 14.60/2.83 |
% 14.60/2.83 | DELTA: instantiating (t21_wellord1) with fresh symbols all_38_0, all_38_1,
% 14.60/2.83 | all_38_2, all_38_3, all_38_4, all_38_5, all_38_6 gives:
% 14.60/2.83 | (12) ~ (all_38_0 = 0) & relation_restriction(all_38_4, all_38_6) =
% 14.60/2.83 | all_38_3 & subset(all_38_2, all_38_1) = all_38_0 & fiber(all_38_3,
% 14.60/2.83 | all_38_5) = all_38_2 & fiber(all_38_4, all_38_5) = all_38_1 &
% 14.60/2.83 | relation(all_38_4) = 0 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) &
% 14.60/2.83 | $i(all_38_4) & $i(all_38_5) & $i(all_38_6)
% 14.60/2.83 |
% 14.60/2.83 | ALPHA: (12) implies:
% 14.60/2.83 | (13) ~ (all_38_0 = 0)
% 14.60/2.83 | (14) $i(all_38_6)
% 14.60/2.83 | (15) $i(all_38_5)
% 14.60/2.83 | (16) $i(all_38_4)
% 14.60/2.83 | (17) $i(all_38_2)
% 14.60/2.83 | (18) $i(all_38_1)
% 14.60/2.83 | (19) relation(all_38_4) = 0
% 14.60/2.83 | (20) fiber(all_38_4, all_38_5) = all_38_1
% 14.60/2.83 | (21) fiber(all_38_3, all_38_5) = all_38_2
% 14.60/2.83 | (22) subset(all_38_2, all_38_1) = all_38_0
% 14.60/2.83 | (23) relation_restriction(all_38_4, all_38_6) = all_38_3
% 14.60/2.83 |
% 14.60/2.83 | GROUND_INST: instantiating (1) with all_38_4, simplifying with (16), (19)
% 14.60/2.83 | gives:
% 14.60/2.83 | (24) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_38_4) =
% 14.60/2.83 | v2 & function(all_38_4) = v1 & empty(all_38_4) = v0 & ( ~ (v1 = 0) |
% 14.60/2.84 | ~ (v0 = 0) | v2 = 0))
% 14.60/2.84 |
% 14.60/2.84 | GROUND_INST: instantiating (7) with all_38_2, all_38_1, all_38_0, simplifying
% 14.60/2.84 | with (17), (18), (22) gives:
% 14.60/2.84 | (25) all_38_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 14.60/2.84 | all_38_1) = v1 & in(v0, all_38_2) = 0 & $i(v0))
% 14.60/2.84 |
% 14.60/2.84 | GROUND_INST: instantiating (8) with all_38_4, all_38_6, all_38_3, simplifying
% 14.60/2.84 | with (14), (16), (19), (23) gives:
% 14.60/2.84 | (26) ? [v0: $i] : (cartesian_product2(all_38_6, all_38_6) = v0 &
% 14.60/2.84 | set_intersection2(all_38_4, v0) = all_38_3 & $i(v0) & $i(all_38_3))
% 14.60/2.84 |
% 14.60/2.84 | GROUND_INST: instantiating (dt_k2_wellord1) with all_38_4, all_38_6, all_38_3,
% 14.60/2.84 | simplifying with (14), (16), (23) gives:
% 14.60/2.84 | (27) ? [v0: any] : ? [v1: any] : (relation(all_38_3) = v1 &
% 14.60/2.84 | relation(all_38_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 14.60/2.84 |
% 14.60/2.84 | DELTA: instantiating (27) with fresh symbols all_50_0, all_50_1 gives:
% 14.60/2.84 | (28) relation(all_38_3) = all_50_0 & relation(all_38_4) = all_50_1 & ( ~
% 14.60/2.84 | (all_50_1 = 0) | all_50_0 = 0)
% 14.60/2.84 |
% 14.60/2.84 | ALPHA: (28) implies:
% 14.60/2.84 | (29) relation(all_38_4) = all_50_1
% 14.60/2.84 | (30) relation(all_38_3) = all_50_0
% 14.60/2.84 | (31) ~ (all_50_1 = 0) | all_50_0 = 0
% 14.60/2.84 |
% 14.60/2.84 | DELTA: instantiating (26) with fresh symbol all_52_0 gives:
% 14.60/2.84 | (32) cartesian_product2(all_38_6, all_38_6) = all_52_0 &
% 14.60/2.84 | set_intersection2(all_38_4, all_52_0) = all_38_3 & $i(all_52_0) &
% 14.60/2.84 | $i(all_38_3)
% 14.60/2.84 |
% 14.60/2.84 | ALPHA: (32) implies:
% 14.60/2.84 | (33) $i(all_38_3)
% 14.60/2.84 | (34) $i(all_52_0)
% 14.60/2.84 | (35) set_intersection2(all_38_4, all_52_0) = all_38_3
% 14.60/2.84 |
% 14.60/2.84 | DELTA: instantiating (24) with fresh symbols all_54_0, all_54_1, all_54_2
% 14.60/2.84 | gives:
% 14.60/2.84 | (36) one_to_one(all_38_4) = all_54_0 & function(all_38_4) = all_54_1 &
% 14.60/2.84 | empty(all_38_4) = all_54_2 & ( ~ (all_54_1 = 0) | ~ (all_54_2 = 0) |
% 14.60/2.84 | all_54_0 = 0)
% 14.60/2.84 |
% 14.60/2.84 | ALPHA: (36) implies:
% 14.60/2.84 | (37) one_to_one(all_38_4) = all_54_0
% 14.60/2.84 |
% 14.60/2.84 | BETA: splitting (25) gives:
% 14.60/2.84 |
% 14.60/2.84 | Case 1:
% 14.60/2.84 | |
% 14.60/2.84 | | (38) all_38_0 = 0
% 14.60/2.84 | |
% 14.60/2.84 | | REDUCE: (13), (38) imply:
% 14.60/2.84 | | (39) $false
% 14.60/2.84 | |
% 14.60/2.84 | | CLOSE: (39) is inconsistent.
% 14.60/2.84 | |
% 14.60/2.84 | Case 2:
% 14.60/2.84 | |
% 14.60/2.84 | | (40) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_38_1) = v1 &
% 14.60/2.84 | | in(v0, all_38_2) = 0 & $i(v0))
% 14.60/2.84 | |
% 14.60/2.84 | | DELTA: instantiating (40) with fresh symbols all_78_0, all_78_1 gives:
% 14.60/2.85 | | (41) ~ (all_78_0 = 0) & in(all_78_1, all_38_1) = all_78_0 & in(all_78_1,
% 14.60/2.85 | | all_38_2) = 0 & $i(all_78_1)
% 14.60/2.85 | |
% 14.60/2.85 | | ALPHA: (41) implies:
% 14.60/2.85 | | (42) ~ (all_78_0 = 0)
% 14.60/2.85 | | (43) $i(all_78_1)
% 14.60/2.85 | | (44) in(all_78_1, all_38_2) = 0
% 14.60/2.85 | | (45) in(all_78_1, all_38_1) = all_78_0
% 14.60/2.85 | |
% 14.60/2.85 | | GROUND_INST: instantiating (10) with 0, all_50_1, all_38_4, simplifying with
% 14.60/2.85 | | (19), (29) gives:
% 14.60/2.85 | | (46) all_50_1 = 0
% 14.60/2.85 | |
% 14.60/2.85 | | BETA: splitting (31) gives:
% 14.60/2.85 | |
% 14.60/2.85 | | Case 1:
% 14.60/2.85 | | |
% 14.60/2.85 | | | (47) ~ (all_50_1 = 0)
% 14.60/2.85 | | |
% 14.60/2.85 | | | REDUCE: (46), (47) imply:
% 14.60/2.85 | | | (48) $false
% 14.60/2.85 | | |
% 14.60/2.85 | | | CLOSE: (48) is inconsistent.
% 14.60/2.85 | | |
% 14.60/2.85 | | Case 2:
% 14.60/2.85 | | |
% 14.60/2.85 | | | (49) all_50_0 = 0
% 14.60/2.85 | | |
% 14.60/2.85 | | | REDUCE: (30), (49) imply:
% 14.60/2.85 | | | (50) relation(all_38_3) = 0
% 14.60/2.85 | | |
% 14.60/2.85 | | | GROUND_INST: instantiating (9) with all_78_1, all_38_1, all_78_0,
% 14.60/2.85 | | | simplifying with (18), (43), (45) gives:
% 14.60/2.85 | | | (51) all_78_0 = 0 | ? [v0: any] : ? [v1: any] : (element(all_78_1,
% 14.60/2.85 | | | all_38_1) = v0 & empty(all_38_1) = v1 & ( ~ (v0 = 0) | v1 =
% 14.60/2.85 | | | 0))
% 14.60/2.85 | | |
% 14.60/2.85 | | | GROUND_INST: instantiating (4) with all_38_3, all_38_5, all_38_2,
% 14.60/2.85 | | | all_78_1, simplifying with (15), (17), (21), (33), (43),
% 14.60/2.85 | | | (44), (50) gives:
% 14.60/2.85 | | | (52) ? [v0: $i] : (ordered_pair(all_78_1, all_38_5) = v0 & in(v0,
% 14.60/2.85 | | | all_38_3) = 0 & $i(v0))
% 14.60/2.85 | | |
% 14.60/2.85 | | | GROUND_INST: instantiating (2) with all_38_4, all_54_0, simplifying with
% 14.60/2.85 | | | (16), (37) gives:
% 14.60/2.85 | | | (53) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_38_4) =
% 14.60/2.85 | | | v0 & function(all_38_4) = v2 & empty(all_38_4) = v1 & ( ~ (v2 =
% 14.60/2.85 | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | all_54_0 = 0))
% 14.60/2.85 | | |
% 14.60/2.85 | | | GROUND_INST: instantiating (3) with all_52_0, all_38_4, all_38_3,
% 14.60/2.85 | | | simplifying with (16), (34), (35) gives:
% 14.60/2.85 | | | (54) set_intersection2(all_52_0, all_38_4) = all_38_3 & $i(all_38_3)
% 14.60/2.85 | | |
% 14.60/2.85 | | | DELTA: instantiating (52) with fresh symbol all_113_0 gives:
% 14.60/2.85 | | | (55) ordered_pair(all_78_1, all_38_5) = all_113_0 & in(all_113_0,
% 14.60/2.85 | | | all_38_3) = 0 & $i(all_113_0)
% 14.60/2.85 | | |
% 14.60/2.85 | | | ALPHA: (55) implies:
% 14.60/2.85 | | | (56) $i(all_113_0)
% 14.60/2.85 | | | (57) in(all_113_0, all_38_3) = 0
% 14.60/2.85 | | | (58) ordered_pair(all_78_1, all_38_5) = all_113_0
% 14.60/2.85 | | |
% 14.60/2.85 | | | DELTA: instantiating (53) with fresh symbols all_125_0, all_125_1,
% 14.60/2.85 | | | all_125_2 gives:
% 14.60/2.85 | | | (59) relation(all_38_4) = all_125_2 & function(all_38_4) = all_125_0 &
% 14.60/2.85 | | | empty(all_38_4) = all_125_1 & ( ~ (all_125_0 = 0) | ~ (all_125_1
% 14.60/2.85 | | | = 0) | ~ (all_125_2 = 0) | all_54_0 = 0)
% 14.60/2.85 | | |
% 14.60/2.85 | | | ALPHA: (59) implies:
% 14.60/2.85 | | | (60) relation(all_38_4) = all_125_2
% 14.60/2.85 | | |
% 14.60/2.85 | | | BETA: splitting (51) gives:
% 14.60/2.85 | | |
% 14.60/2.85 | | | Case 1:
% 14.60/2.85 | | | |
% 14.60/2.85 | | | | (61) all_78_0 = 0
% 14.60/2.85 | | | |
% 14.60/2.85 | | | | REDUCE: (42), (61) imply:
% 14.60/2.85 | | | | (62) $false
% 14.60/2.85 | | | |
% 14.60/2.85 | | | | CLOSE: (62) is inconsistent.
% 14.60/2.85 | | | |
% 14.60/2.85 | | | Case 2:
% 14.60/2.85 | | | |
% 14.60/2.85 | | | |
% 14.60/2.85 | | | | GROUND_INST: instantiating (10) with 0, all_125_2, all_38_4, simplifying
% 14.60/2.85 | | | | with (19), (60) gives:
% 14.60/2.85 | | | | (63) all_125_2 = 0
% 14.60/2.85 | | | |
% 14.60/2.86 | | | | GROUND_INST: instantiating (t16_wellord1) with all_113_0, all_38_6,
% 14.60/2.86 | | | | all_38_4, all_38_3, 0, simplifying with (14), (16), (23),
% 14.60/2.86 | | | | (56), (57) gives:
% 14.60/2.86 | | | | (64) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 14.60/2.86 | | | | (cartesian_product2(all_38_6, all_38_6) = v2 &
% 14.60/2.86 | | | | relation(all_38_4) = v0 & in(all_113_0, v2) = v3 &
% 14.60/2.86 | | | | in(all_113_0, all_38_4) = v1 & $i(v2) & ( ~ (v0 = 0) | (v3 = 0
% 14.60/2.86 | | | | & v1 = 0)))
% 14.60/2.86 | | | |
% 14.60/2.86 | | | | GROUND_INST: instantiating (5) with all_38_3, all_38_5, all_38_2,
% 14.60/2.86 | | | | all_78_1, all_113_0, simplifying with (15), (17), (21),
% 14.60/2.86 | | | | (33), (43), (50), (58) gives:
% 14.60/2.86 | | | | (65) ? [v0: any] : ? [v1: any] : (in(all_113_0, all_38_3) = v1 &
% 14.60/2.86 | | | | in(all_78_1, all_38_2) = v0 & ( ~ (v0 = 0) | (v1 = 0 & ~
% 14.60/2.86 | | | | (all_78_1 = all_38_5))))
% 14.60/2.86 | | | |
% 14.60/2.86 | | | | GROUND_INST: instantiating (6) with all_38_4, all_38_5, all_38_1,
% 14.60/2.86 | | | | all_78_1, all_113_0, simplifying with (15), (16), (18),
% 14.60/2.86 | | | | (19), (20), (43), (58) gives:
% 14.60/2.86 | | | | (66) all_78_1 = all_38_5 | ? [v0: any] : ? [v1: any] :
% 14.60/2.86 | | | | (in(all_113_0, all_38_4) = v0 & in(all_78_1, all_38_1) = v1 & (
% 14.60/2.86 | | | | ~ (v0 = 0) | v1 = 0))
% 14.60/2.86 | | | |
% 14.60/2.86 | | | | GROUND_INST: instantiating (5) with all_38_4, all_38_5, all_38_1,
% 14.60/2.86 | | | | all_78_1, all_113_0, simplifying with (15), (16), (18),
% 14.60/2.86 | | | | (19), (20), (43), (58) gives:
% 14.60/2.86 | | | | (67) ? [v0: any] : ? [v1: any] : (in(all_113_0, all_38_4) = v1 &
% 14.60/2.86 | | | | in(all_78_1, all_38_1) = v0 & ( ~ (v0 = 0) | (v1 = 0 & ~
% 14.60/2.86 | | | | (all_78_1 = all_38_5))))
% 14.60/2.86 | | | |
% 14.60/2.86 | | | | DELTA: instantiating (65) with fresh symbols all_166_0, all_166_1 gives:
% 14.60/2.86 | | | | (68) in(all_113_0, all_38_3) = all_166_0 & in(all_78_1, all_38_2) =
% 14.60/2.86 | | | | all_166_1 & ( ~ (all_166_1 = 0) | (all_166_0 = 0 & ~ (all_78_1
% 14.60/2.86 | | | | = all_38_5)))
% 14.60/2.86 | | | |
% 14.60/2.86 | | | | ALPHA: (68) implies:
% 14.60/2.86 | | | | (69) in(all_78_1, all_38_2) = all_166_1
% 14.60/2.86 | | | | (70) ~ (all_166_1 = 0) | (all_166_0 = 0 & ~ (all_78_1 = all_38_5))
% 14.60/2.86 | | | |
% 14.60/2.86 | | | | DELTA: instantiating (67) with fresh symbols all_168_0, all_168_1 gives:
% 14.60/2.86 | | | | (71) in(all_113_0, all_38_4) = all_168_0 & in(all_78_1, all_38_1) =
% 14.60/2.86 | | | | all_168_1 & ( ~ (all_168_1 = 0) | (all_168_0 = 0 & ~ (all_78_1
% 14.60/2.86 | | | | = all_38_5)))
% 14.60/2.86 | | | |
% 14.60/2.86 | | | | ALPHA: (71) implies:
% 14.60/2.86 | | | | (72) in(all_78_1, all_38_1) = all_168_1
% 14.60/2.86 | | | | (73) in(all_113_0, all_38_4) = all_168_0
% 14.60/2.86 | | | |
% 14.60/2.86 | | | | DELTA: instantiating (64) with fresh symbols all_174_0, all_174_1,
% 14.60/2.86 | | | | all_174_2, all_174_3 gives:
% 14.60/2.86 | | | | (74) cartesian_product2(all_38_6, all_38_6) = all_174_1 &
% 14.60/2.86 | | | | relation(all_38_4) = all_174_3 & in(all_113_0, all_174_1) =
% 14.60/2.86 | | | | all_174_0 & in(all_113_0, all_38_4) = all_174_2 & $i(all_174_1)
% 14.60/2.86 | | | | & ( ~ (all_174_3 = 0) | (all_174_0 = 0 & all_174_2 = 0))
% 14.60/2.86 | | | |
% 14.60/2.86 | | | | ALPHA: (74) implies:
% 14.60/2.86 | | | | (75) in(all_113_0, all_38_4) = all_174_2
% 14.60/2.86 | | | | (76) relation(all_38_4) = all_174_3
% 14.60/2.87 | | | | (77) ~ (all_174_3 = 0) | (all_174_0 = 0 & all_174_2 = 0)
% 14.60/2.87 | | | |
% 14.60/2.87 | | | | GROUND_INST: instantiating (11) with 0, all_166_1, all_38_2, all_78_1,
% 14.60/2.87 | | | | simplifying with (44), (69) gives:
% 14.60/2.87 | | | | (78) all_166_1 = 0
% 14.60/2.87 | | | |
% 14.60/2.87 | | | | GROUND_INST: instantiating (11) with all_78_0, all_168_1, all_38_1,
% 14.60/2.87 | | | | all_78_1, simplifying with (45), (72) gives:
% 14.60/2.87 | | | | (79) all_168_1 = all_78_0
% 14.60/2.87 | | | |
% 14.60/2.87 | | | | GROUND_INST: instantiating (11) with all_168_0, all_174_2, all_38_4,
% 14.60/2.87 | | | | all_113_0, simplifying with (73), (75) gives:
% 14.60/2.87 | | | | (80) all_174_2 = all_168_0
% 14.60/2.87 | | | |
% 14.60/2.87 | | | | GROUND_INST: instantiating (10) with 0, all_174_3, all_38_4, simplifying
% 14.60/2.87 | | | | with (19), (76) gives:
% 14.60/2.87 | | | | (81) all_174_3 = 0
% 14.60/2.87 | | | |
% 14.60/2.87 | | | | BETA: splitting (70) gives:
% 14.60/2.87 | | | |
% 14.60/2.87 | | | | Case 1:
% 14.60/2.87 | | | | |
% 14.60/2.87 | | | | | (82) ~ (all_166_1 = 0)
% 14.60/2.87 | | | | |
% 14.60/2.87 | | | | | REDUCE: (78), (82) imply:
% 14.60/2.87 | | | | | (83) $false
% 14.60/2.87 | | | | |
% 14.60/2.87 | | | | | CLOSE: (83) is inconsistent.
% 14.60/2.87 | | | | |
% 14.60/2.87 | | | | Case 2:
% 14.60/2.87 | | | | |
% 14.60/2.87 | | | | | (84) all_166_0 = 0 & ~ (all_78_1 = all_38_5)
% 14.60/2.87 | | | | |
% 14.60/2.87 | | | | | ALPHA: (84) implies:
% 14.60/2.87 | | | | | (85) ~ (all_78_1 = all_38_5)
% 14.60/2.87 | | | | |
% 14.60/2.87 | | | | | BETA: splitting (66) gives:
% 14.60/2.87 | | | | |
% 14.60/2.87 | | | | | Case 1:
% 14.60/2.87 | | | | | |
% 14.60/2.87 | | | | | | (86) all_78_1 = all_38_5
% 14.60/2.87 | | | | | |
% 14.60/2.87 | | | | | | REDUCE: (85), (86) imply:
% 14.60/2.87 | | | | | | (87) $false
% 14.60/2.87 | | | | | |
% 14.60/2.87 | | | | | | CLOSE: (87) is inconsistent.
% 14.60/2.87 | | | | | |
% 14.60/2.87 | | | | | Case 2:
% 14.60/2.87 | | | | | |
% 14.60/2.87 | | | | | | (88) ? [v0: any] : ? [v1: any] : (in(all_113_0, all_38_4) = v0
% 14.60/2.87 | | | | | | & in(all_78_1, all_38_1) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 14.60/2.87 | | | | | |
% 14.60/2.87 | | | | | | DELTA: instantiating (88) with fresh symbols all_223_0, all_223_1
% 14.60/2.87 | | | | | | gives:
% 14.60/2.87 | | | | | | (89) in(all_113_0, all_38_4) = all_223_1 & in(all_78_1, all_38_1)
% 14.60/2.87 | | | | | | = all_223_0 & ( ~ (all_223_1 = 0) | all_223_0 = 0)
% 14.60/2.87 | | | | | |
% 14.60/2.87 | | | | | | ALPHA: (89) implies:
% 14.60/2.87 | | | | | | (90) in(all_78_1, all_38_1) = all_223_0
% 14.60/2.87 | | | | | | (91) in(all_113_0, all_38_4) = all_223_1
% 14.60/2.87 | | | | | | (92) ~ (all_223_1 = 0) | all_223_0 = 0
% 14.60/2.87 | | | | | |
% 14.60/2.87 | | | | | | BETA: splitting (77) gives:
% 14.60/2.87 | | | | | |
% 14.60/2.87 | | | | | | Case 1:
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | (93) ~ (all_174_3 = 0)
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | REDUCE: (81), (93) imply:
% 14.60/2.87 | | | | | | | (94) $false
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | CLOSE: (94) is inconsistent.
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | Case 2:
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | (95) all_174_0 = 0 & all_174_2 = 0
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | ALPHA: (95) implies:
% 14.60/2.87 | | | | | | | (96) all_174_2 = 0
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | COMBINE_EQS: (80), (96) imply:
% 14.60/2.87 | | | | | | | (97) all_168_0 = 0
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | SIMP: (97) implies:
% 14.60/2.87 | | | | | | | (98) all_168_0 = 0
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | REDUCE: (73), (98) imply:
% 14.60/2.87 | | | | | | | (99) in(all_113_0, all_38_4) = 0
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | GROUND_INST: instantiating (11) with all_78_0, all_223_0,
% 14.60/2.87 | | | | | | | all_38_1, all_78_1, simplifying with (45), (90)
% 14.60/2.87 | | | | | | | gives:
% 14.60/2.87 | | | | | | | (100) all_223_0 = all_78_0
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | GROUND_INST: instantiating (11) with 0, all_223_1, all_38_4,
% 14.60/2.87 | | | | | | | all_113_0, simplifying with (91), (99) gives:
% 14.60/2.87 | | | | | | | (101) all_223_1 = 0
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | BETA: splitting (92) gives:
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | | Case 1:
% 14.60/2.87 | | | | | | | |
% 14.60/2.87 | | | | | | | | (102) ~ (all_223_1 = 0)
% 14.60/2.87 | | | | | | | |
% 14.60/2.87 | | | | | | | | REDUCE: (101), (102) imply:
% 14.60/2.87 | | | | | | | | (103) $false
% 14.60/2.87 | | | | | | | |
% 14.60/2.87 | | | | | | | | CLOSE: (103) is inconsistent.
% 14.60/2.87 | | | | | | | |
% 14.60/2.87 | | | | | | | Case 2:
% 14.60/2.87 | | | | | | | |
% 14.60/2.87 | | | | | | | | (104) all_223_0 = 0
% 14.60/2.87 | | | | | | | |
% 14.60/2.87 | | | | | | | | COMBINE_EQS: (100), (104) imply:
% 14.60/2.87 | | | | | | | | (105) all_78_0 = 0
% 14.60/2.87 | | | | | | | |
% 14.60/2.87 | | | | | | | | REDUCE: (42), (105) imply:
% 14.60/2.87 | | | | | | | | (106) $false
% 14.60/2.87 | | | | | | | |
% 14.60/2.87 | | | | | | | | CLOSE: (106) is inconsistent.
% 14.60/2.87 | | | | | | | |
% 14.60/2.87 | | | | | | | End of split
% 14.60/2.87 | | | | | | |
% 14.60/2.87 | | | | | | End of split
% 14.60/2.87 | | | | | |
% 14.60/2.87 | | | | | End of split
% 14.60/2.87 | | | | |
% 14.60/2.87 | | | | End of split
% 14.60/2.87 | | | |
% 14.60/2.87 | | | End of split
% 14.60/2.87 | | |
% 14.60/2.87 | | End of split
% 14.60/2.87 | |
% 14.60/2.87 | End of split
% 14.60/2.87 |
% 14.60/2.87 End of proof
% 14.60/2.87 % SZS output end Proof for theBenchmark
% 14.60/2.87
% 14.60/2.87 2272ms
%------------------------------------------------------------------------------